Pricing Engine Kernel APIs

CPICapFloorEngine

Defined in <xf_fintech/cpi_capfloor_engine.hpp>

class CPICapFloorEngine

DiscountingBondEngine

Defined in <xf_fintech/discounting_bond_engine.hpp>

class DiscountingBondEngine

InflationCapFloorEngine

Defined in <xf_fintech/inflation_capfloor_engine.hpp>

class InflationCapFloorEngine

FdHullWhiteEngine

Defined in <xf_fintech/fd_hullwhite_engine.hpp>

class FdHullWhiteEngine

FdG2SwaptionEngine

Defined in <xf_fintech/fd_g2_swaption_engine.hpp>

class FdG2SwaptionEngine

binomialTreeEngine

#include "xf_fintech/bt_engine.hpp"

template <typename DT>
DT binomialTreeEngine (
    BinomialTreeInputDataType <DT>* inputData,
    int optionType
    )

BinomialTree Engine using CRR (Cox, Ross & Rubinstein)

Parameters:

inputData	A structure containing the input model parameters
optionType	Calculate for NPV European or American Call or Put

Returns:

The calculated NPV

cfBSMEngine

#include "xf_fintech/cf_bsm.hpp"

template <typename DT>
void cfBSMEngine (
    DT s,
    DT v,
    DT r,
    DT t,
    DT k,
    DT q,
    unsigned int call,
    DT* price,
    DT* delta,
    DT* gamma,
    DT* vega,
    DT* theta,
    DT* rho
    )

Single option price plus associated Greeks.

Produces a single price and associated Greeks for the given input parameters. This function is optimized to be synthesized by the HLS compiler and as such uses the hls namespace for the maths functions. In addition, the code is structured to calculate common elements (in parallel where possible) and reuse as appropriate.

Parameters:

DT	Data Type used for this function
s	underlying
v	volatility (decimal form)
r	risk-free rate (decimal form)
t	time to maturity
k	strike price
q	continuous dividend yield rate
call	control whether call or put is calculated
price	call/put premium
delta	model sensitivity
gamma	model sensitivity
vega	model sensitivity
theta	model sensitivity
rho	model sensitivity

FdDouglas

#include "xf_fintech/fd_solver.hpp"

template <
    typename DT,
    unsigned int MEM_WIDTH,
    unsigned int INDEX_WIDTH,
    unsigned int A_SIZE,
    unsigned int M_SIZE,
    unsigned int LOG2_M_SIZE,
    unsigned int DIM2_SIZE1,
    unsigned int DIM2_SIZE2
    >
void FdDouglas (
    DT A [A_SIZE],
    unsigned int Ar [A_SIZE],
    unsigned int Ac [A_SIZE],
    unsigned int Annz,
    DT A1 [M_SIZE][DIM2_SIZE1],
    DT A2 [M_SIZE][DIM2_SIZE2],
    DT X1 [M_SIZE][DIM2_SIZE1],
    DT X2 [M_SIZE][DIM2_SIZE2],
    DT b [M_SIZE],
    DT u0 [M_SIZE],
    unsigned int M1,
    unsigned int M2,
    unsigned int N,
    DT u [M_SIZE]
    )

Top level callable function to perform the Douglas ADI method.

This function creates the solver/stream wrapper objects and connects them up It also provides the extra connectivity for the non-streaming blocks

Parameters:

A	Sparse matrix value
Ar	Sparse matrix row
Ac	Sparse matrix column
Annz	Number of non-zeros in sparse matrix (how many elements of A/Ar/Ac are valid)
A1	Tridiagonal matrix stored as three vectors lower/main/upper
A2	Pentadiagonal matrix stored as five vectors lower/lower/main/upper/upper
X1	Tridiagonal matrix stored as three vectors lower/main/upper
X2	Pentadiagonal matrix stored as five vectors lower/lower/main/upper/upper
b	Boundary condition vector
u0	Initial condition (payoff condition for a call option)
M1	Size of array [0..M1] in S direction
M2	Size of array [0..M2] in V direction
N	Iteration count
u	Calculated price grid

hcfEngine

#include "xf_fintech/hcf_engine.hpp"

template <typename DT>
DT hcfEngine (struct hcfEngineInputDataType <DT>* input_data)

Engine for Heston Closed Form Solution.

Parameters:

input_data

A structure containing the kerenl model parameters

Returns:

the calculated call value

M76Engine

#include "xf_fintech/m76_engine.hpp"

template <typename DT>
void M76Engine (
    struct jump_diffusion_params <DT>* p,
    DT* call_price
    )

Engine for the Merton Jump Diffusion Model.

Parameters:

p	A structure containing the jump diffusion parameters
call_price	An array of BS solutions multiplied by the jump weighting Note that these must be subsequently summed to get the Jump Diffusion solution

MCEuropeanEngine

#include "xf_fintech/mc_engine.hpp"

template <
    typename DT = double,
    int UN = 10,
    bool Antithetic = false
    >
void MCEuropeanEngine (
    DT underlying,
    DT volatility,
    DT dividendYield,
    DT riskFreeRate,
    DT timeLength,
    DT strike,
    bool optionType,
    ap_uint <32>* seed,
    DT* output,
    DT requiredTolerance = 0.02,
    unsigned int requiredSamples = 1024,
    unsigned int timeSteps = 100,
    unsigned int maxSamples = 134217727
    )

European Option Pricing Engine using Monte Carlo Method. This implementation uses Black-Scholes valuation model.

Parameters:

DT	supported data type including double and float data type, which decides the precision of result, default double-precision data type.
UN	number of Monte Carlo Module in parallel, which affects the latency and resources utilization, default 10.
Antithetic	antithetic is used for variance reduction, default this feature is disabled.
underlying	intial value of underlying asset at time 0.
volatility	fixed volatility of underlying asset.
dividendYield	the constant dividend rate for continuous dividends.
riskFreeRate	risk-free interest rate.
timeLength	the time length of contract from start to end.
strike	the strike price also known as exericse price, which is settled in the contract.
optionType	option type. 1: put option, 0: call option.
seed	array to store the inital seed for each RNG.
output	output array.
requiredTolerance	the tolerance required. If requiredSamples is not set, when reaching the required tolerance, simulation will stop, default 0.02.
requiredSamples	the samples number required. When reaching the required number, simulation will stop, default 1024.
timeSteps	the number of discrete steps from 0 to T, T is the expiry time, default 100.
maxSamples	the maximum sample number. When reaching it, the simulation will stop, default 2,147,483,648.

MCEuropeanPriBypassEngine

#include "xf_fintech/mc_engine.hpp"

template <
    typename DT = double,
    int UN = 10
    >
void MCEuropeanPriBypassEngine (
    DT underlying,
    DT volatility,
    DT dividendYield,
    DT riskFreeRate,
    DT timeLength,
    DT strike,
    bool optionType,
    ap_uint <32>* seed,
    DT* output,
    DT requiredTolerance = 0.02,
    unsigned int requiredSamples = 1024,
    unsigned int timeSteps = 100,
    unsigned int maxSamples = 134217727
    )

path pricer bypass variant (interface compatible with standard MCEuropeanEngine)

Parameters:

DT	supported data type including double and float data type, which decides the precision of result, default double-precision data type.
UN	number of Monte Carlo Module in parallel, which affects the latency and resources utilization, default 10.
underlying	intial value of underlying asset at time 0.
volatility	fixed volatility of underlying asset.
dividendYield	the constant dividend rate for continuous dividends.
riskFreeRate	risk-free interest rate.
timeLength	the time length of contract from start to end.
strike	the strike price also known as exericse price, which is settled in the contract.
optionType	option type. 1: put option, 0: call option.
seed	array to store the inital seed for each RNG.
output	output array.
requiredTolerance	the tolerance required. If requiredSamples is not set, when reaching the required tolerance, simulation will stop, default 0.02.
requiredSamples	the samples number required. When reaching the required number, simulation will stop, default 1024.
timeSteps	the number of discrete steps from 0 to T, T is the expiry time, default 100.
maxSamples	the maximum sample number. When reaching it, the simulation will stop, default 2,147,483,648.

MCEuropeanHestonEngine

#include "xf_fintech/mc_engine.hpp"

template <
    typename DT = double,
    int UN = 8,
    DiscreType discretization = kDTQuadraticExponential,
    bool Antithetic = false
    >
void MCEuropeanHestonEngine (
    DT underlying,
    DT riskFreeRate,
    DT sigma,
    DT v0,
    DT theta,
    DT kappa,
    DT rho,
    DT dividendYield,
    bool optionType,
    DT strike,
    DT timeLength,
    ap_uint <32> seed [UN][2],
    DT* outputs,
    DT requiredTolerance = 0.02,
    unsigned int requiredSamples = 1024,
    unsigned int timeSteps = 100,
    unsigned int maxSamples = 134217727
    )

European Option Pricing Engine using Monte Carlo Method based on Heston valuation model.

Parameters:

DT	supported data type including double and float, which decides the precision of output, default double-precision data type.
UN	number of Monte Carlo Module in parallel, which affects the latency and resources utilization, default 10.
DiscreType	methods which is used to discrete the stochastic process. Currently, five discrete types, including kDTPartialTruncation, kDTFullTruncation, kDTReflection, kDTQuadraticExponential and kDTQuadraticExponentialMartingale, are supported, default kDTQuadraticExponential.
Antithetic	antithetic is used for variance reduction, default this feature is disabled.
underlying	the initial price of underlying asset at time 0.
riskFreeRate	risk-free interest rate.
sigma	the volatility of volatility
v0	initial volatility of stock
theta	the long variance, as t tends to infinity, the expected value of vt tends to theta.
kappa	the rate at which vt tends to theta.
rho	the correlation coefficient between price and variance.
dividendYield	the constant dividend rate for continuous dividends.
optionType	option type. 1: put option, 0: call option.
strike	the strike price also known as exericse price, which is settled in the contract.
timeLength	time length from now to expiry date.
seed	the seeds used to initialize RNG.
outputs	pricing result array of this engine.
requiredTolerance	the tolerance required. If requiredSamples is not set, when reaching the required tolerance, simulation will stop.
requiredSamples	the samples number required. When reaching the required number, simulation will stop, default 1024.
timeSteps	the number of discrete steps from 0 to T, T is the expiry time, default 100.
maxSamples	the maximum sample number. When reaching it, the simulation will stop, default 2,147,483,648.

MCMultiAssetEuropeanHestonEngine

#include "xf_fintech/mc_engine.hpp"

template <
    typename DT = double,
    int ASSETS = 5,
    int UN = 1,
    DiscreType discretization = kDTQuadraticExponential
    >
void MCMultiAssetEuropeanHestonEngine (
    DT underlying [ASSETS],
    DT riskFreeRate,
    DT sigma [ASSETS],
    DT v0 [ASSETS],
    DT theta [ASSETS],
    DT kappa [ASSETS],
    DT corrMatrix [ASSETS *2+1][ASSETS],
    DT rho [ASSETS],
    DT dividendYield [ASSETS],
    bool optionType,
    DT strike,
    DT timeLength,
    ap_uint <32> seed [UN][2],
    DT* outputs,
    DT requiredTolerance = 0.02,
    ap_uint <32> requiredSamples = 0,
    ap_uint <32> timeSteps = 100,
    ap_uint <32> maxSamples = 134217727
    )

Multiple Asset European Option Pricing Engine using Monte Carlo Method based on Heston valuation model.

Parameters:

DT	supported data type including double and float, which decides the precision of output, default double-precision data type.
ASSETS	number of underlying assets supported.
UN	number of Monte Carlo Module in parallel, which affects the latency and resources utilization, default 10.
DiscreType	methods which is used to discrete the stochastic process. Currently, five discrete types, including kDTPartialTruncation, kDTFullTruncation, kDTReflection, kDTQuadraticExponential and kDTQuadraticExponentialMartingale, are supported, default kDTQuadraticExponential.
underlying	the initial price of underlying asset at time 0.
riskFreeRate	risk-free interest rate.
sigma	the volatility of volatility
v0	initial volatility of stock
theta	the long variance, as t tends to infinity, the expected value of vt tends to theta.
kappa	the rate at which vt tends to theta.
corrMatrix	the LU decomposition result of correlation matrix of all stochastic variables, only none-zero elements are stored.
rho	the correlation coefficient between price and variance.
dividendYield	the constant dividend rate for continuous dividends.
optionType	option type. 1: call option, 0: put option.
strike	the strike price also known as exericse price, which is settled in the contract.
timeLength	time length from now to expiry date.
seed	the seeds used to initialize RNG.
outputs	pricing result array of this engine.
requiredTolerance	the tolerance required. If requiredSamples is not set, when reaching the required tolerance, simulation will stop.
requiredSamples	the samples number required. When reaching the required number, simulation will stop, default 1024.
timeSteps	the number of discrete steps from 0 to T, T is the expiry time, default 100.
maxSamples	the maximum sample number. When reaching it, the simulation will stop, default 2,147,483,648.

MCAmericanEnginePreSamples

#include "xf_fintech/mc_engine.hpp"

template <
    typename DT = double,
    int UN = 2
    >
void MCAmericanEnginePreSamples (
    DT underlying,
    DT volatility,
    DT riskFreeRate,
    DT dividendYield,
    DT timeLength,
    DT strike,
    bool optionType,
    ap_uint <32>* seed,
    ap_uint <8*sizeof (DT)*UN>* priceOut,
    ap_uint <8*sizeof (DT)>* matOut,
    unsigned int calibSamples = 4096,
    unsigned int timeSteps = 100
    )

American Option Pricing Engine using Monte Carlo Method. PreSample kernel: this kernel samples some amount of path and store them to external memory.

Parameters:

DT	supported data type including double and float data type, which decides the precision of result, default double-precision data type.
UN	number of Monte Carlo Module in parallel (in path dimension), which affects the latency and resources utilization, default 2.
underlying	intial value of underlying asset at time 0.
volatility	fixed volatility of underlying asset.
dividendYield	the constant dividend rate for continuous dividends.
riskFreeRate	risk-free interest rate.
timeLength	the time length of contract from start to end.
strike	the strike price also known as exericse price, which is settled in the contract.
optionType	option type. 1: put option, 0: call option.
seed	array to store the inital seed for each RNG.
priceOut	price data output, the data can be stored to HBM or DDR
matOut	matrix output, the data can be stored to HBM or DDR
calibSamples	sample numbers that used in calibration, default 4096.
timeSteps	the number of discrete steps from 0 to T, T is the expiry time, default 100.

MCAmericanEngineCalibrate

#include "xf_fintech/mc_engine.hpp"

template <
    typename DT = double,
    int UN = 2,
    int UN_STEP = 2
    >
void MCAmericanEngineCalibrate (
    DT timeLength,
    DT riskFreeRate,
    DT strike,
    bool optionType,
    ap_uint <8*sizeof (DT)*UN>* priceIn,
    ap_uint <8*sizeof (DT)>* matIn,
    ap_uint <8*sizeof (DT)*4>* coefOut,
    unsigned int calibSamples = 4096,
    unsigned int timeSteps = 100
    )

American Option Pricing Engine using Monte Carlo Method. Calibrate kernel: this kernel reads the sample price data from external memory and use them to calculate the coefficient.

Parameters:

DT	supported data type including double and float data type, which decides the precision of result, default double-precision data type.
UN	number of Monte Carlo Module in parallel (in path dimension), which affects the latency and resources utilization, default 2. [this unroll number should be equal to UN in MCAmericanEnginePresample]
UN_STEP	number of Monte Carlo Module in parallel (in time steps dimension), which affects the latency and resources utilization, default 2. [this Unroll is completely resource bounded, unrelated to other params]
timeLength	the time length of contract from start to end.
riskFreeRate	risk-free interest rate.
strike	the strike price also known as exericse price, which is settled in the contract.
optionType	option type. 1: put option, 0: call option.
priceIn	the price data, read in from DDR or HBM
matIn	the matrix data, read in from DDR or HBM
coefOut	the coef data that calculated by this kernel, the data can be stored to DDR or HBM
calibSamples	sample numbers that used in calibration, default 4096.
timeSteps	the number of discrete steps from 0 to T, T is the expiry time, default 100.

MCAmericanEnginePricing

#include "xf_fintech/mc_engine.hpp"

template <
    typename DT = double,
    int UN = 2
    >
void MCAmericanEnginePricing (
    DT underlying,
    DT volatility,
    DT dividendYield,
    DT riskFreeRate,
    DT timeLength,
    DT strike,
    bool optionType,
    ap_uint <32>* seed,
    ap_uint <8*sizeof (DT)*4>* coefIn,
    DT* output,
    DT requiredTolerance = 0.02,
    unsigned int requiredSamples = 4096,
    unsigned int timeSteps = 100,
    unsigned int maxSamples = 134217727
    )

American Option Pricing Engine using Monte Carlo Method. Pricing kernel.

Parameters:

DT	supported data type including double and float data type, which decides the precision of result, default double-precision data type.
UN	number of Monte Carlo Module in parallel (in path dimension), which affects the latency and resources utilization, default 2. [this unroll number should be equal to UN in MCAmericanEnginePresample]
underlying	intial value of underlying asset at time 0.
volatility	fixed volatility of underlying asset.
dividendYield	the constant dividend rate for continuous dividends.
riskFreeRate	risk-free interest rate.
timeLength	the time length of contract from start to end.
strike	the strike price also known as exericse price, which is settled in the contract.
optionType	option type. 1: put option, 0: call option.
seed	array of seed to initialize RNG.
coefIn	the coef data that calculated by this kernel, the data is loaded from DDR or HBM
output	the output price data (size=1), can be stroed in DDR or HBM
requiredTolerance	the tolerance required. If requiredSamples is not set, when reaching the required tolerance, simulation will stop, default 0.02.
requiredSamples	the samples number required. When reaching the required number, simulation will stop, default 1024.
timeSteps	the number of discrete steps from 0 to T, T is the expiry time.
maxSamples	the maximum sample number. When reaching it, the simulation will stop, default 2,147,483,648.

MCAmericanEngine

#include "xf_fintech/mc_engine.hpp"

template <
    typename DT = double,
    int UN_PATH = 1,
    int UN_STEP = 1,
    int UN_PRICING = 2
    >
void MCAmericanEngine (
    DT underlying,
    DT volatility,
    DT riskFreeRate,
    DT dividendYield,
    DT timeLength,
    DT strike,
    bool optionType,
    ap_uint <32>* seed,
    ap_uint <8*sizeof (DT)*UN_PATH>* priceData,
    ap_uint <8*sizeof (DT)>* matData,
    DT* output,
    DT requiredTolerance = 0.02,
    unsigned int calibSamples = 4096,
    unsigned int requiredSamples = 4096,
    unsigned int timeSteps = 100,
    unsigned int maxSamples = 134217727
    )

American Option Pricing Engine using Monte Carlo Method. calibration process and pricing process all in one kernel.

Parameters:

DT	supported data type including double and float data type, which decides the precision of result, default double-precision data type.
UN_PATH	number of Monte Carlo Module of calibration process in parallel (in path dimension), which affects the latency and resources utilization, default 1.
UN_STEP	number of Monte Carlo Module of calibration process in parallel (in time steps dimension), which affects the latency and resources utilization, default 1.
UN_PRICING	number of Monte Carlo Module of pricing process in parallel (in path dimension), which affects the latency and resources utilization, default 2. Three unroll numbers UN_PATH, UN_STEP and UN_PRICING are independent. Each unroll number affects the execution speed of part of AmericanEngine. On-board test reveals that the pricing phase takes longest time of execution. Therefore, setting larger UN_PRICING benifits most with limited resources.
underlying	intial value of underlying asset at time 0.
volatility	fixed volatility of underlying asset.
dividendYield	the constant dividend rate for continuous dividends.
riskFreeRate	risk-free interest rate.
timeLength	the time length of contract from start to end.
strike	the strike price also known as exericse price, which is settled in the contract.
optionType	option type. 1: put option, 0: call option.
seed	array of seed to initialize RNG.
priceData	the price data, used as the intermediate result storage location. It should be mapped to an external memory: DDR or HBM.
matData	the matrix data, used as the intermediate result storage location. It should be mapped to an external memory: DDR or HBM.
output	the output price data (size=1), can be stroed in DDR or HBM
requiredTolerance	the tolerance required. If requiredSamples is not set, when reaching the required tolerance, simulation will stop, default 0.02.
requiredSamples	the samples number required. When reaching the required number, simulation will stop, default 1024.
calibSamples	sample numbers that used in calibration, default 4096.
timeSteps	the number of discrete steps from 0 to T, T is the expiry time.
maxSamples	the maximum sample number. When reaching it, the simulation will stop, default 2,147,483,648.

MCAsianGeometricAPEngine

#include "xf_fintech/mc_engine.hpp"

template <
    typename DT = double,
    int UN = 16
    >
void MCAsianGeometricAPEngine (
    DT underlying,
    DT volatility,
    DT dividendYield,
    DT riskFreeRate,
    DT timeLength,
    DT strike,
    bool optionType,
    ap_uint <32>* seed,
    DT* output,
    DT requiredTolerance = 0.02,
    unsigned int requiredSamples = 1024,
    unsigned int timeSteps = 100,
    unsigned int maxSamples = 134217727
    )

Asian Arithmetic Average Price Engine using Monte Carlo Method Based on Black-Scholes Model. The settlement price of the underlying asset at expiry time is the geomertic average of asset price during the option lifetime.

Parameters:

DT	Supported data type including double and float, which decides the precision of output.
UN	The number of Monte Carlo Module in parallel, which affects the latency and resources utilization.
underlying	The initial price of underlying asset.
volatility	The market’s price volatility.
dividendYield	The dividend yield is the company’s total annual dividend payments divided by its market capitalization, or the dividend per share, divided by the price per share.
riskFreeRate	The risk-free interest rate is the rate of return of a hypothetical investment with no risk of financial loss, over a given period of time.
timeLength	The given period of time.
strike	The strike price also known as exericse price, which is settled in the contract.
optionType	Option type. 1: put option, 0: call option.
seed	array of seed to initialize RNG.
output	Output array.
requiredTolerance	The tolerance required. If requiredSamples is not set, simulation will not stop, unless the requiredTolerance is reached, default 0.02.
requiredSamples	The samples number required. When reaching the required number, simulation will stop, default 1024.
timeSteps	Number of interval, default 100.
maxSamples	The maximum sample number. When reaching it, the simulation will stop, default 2147483648.

MCAsianArithmeticAPEngine

#include "xf_fintech/mc_engine.hpp"

template <
    typename DT = double,
    int UN = 16
    >
void MCAsianArithmeticAPEngine (
    DT underlying,
    DT volatility,
    DT dividendYield,
    DT riskFreeRate,
    DT timeLength,
    DT strike,
    bool optionType,
    ap_uint <32>* seed,
    DT* output,
    DT requiredTolerance = 0.02,
    unsigned int requiredSamples = 1024,
    unsigned int timeSteps = 100,
    unsigned int maxSamples = 134217727
    )

Asian Arithmetic Average Price Engine using Monte Carlo Method Based on Black-Scholes Model. The settlement price of the underlying asset at expiry time is the arithmetic average of asset price during the option lifetime.

Parameters:

DT	Supported data type including double and float, which decides the precision of output.
UN	The number of Monte Carlo Module in parallel, which affects the latency and resources utilization.
underlying	The initial price of underlying asset.
volatility	The market’s price volatility.
dividendYield	The dividend yield is the company’s total annual dividend payments divided by its market capitalization, or the dividend per share, divided by the price per share.
riskFreeRate	The risk-free interest rate is the rate of return of a hypothetical investment with no risk of financial loss, over a given period of time.
timeLength	The given period of time.
strike	The strike price also known as exericse price, which is settled in the contract.
optionType	Option type. 1: put option, 0: call option.
seed	array of seed to initialize RNG.
output	Output array.
requiredTolerance	The tolerance required. If requiredSamples is not set, simulation will not stop, unless the requiredTolerance is reached, default 0.02.
requiredSamples	The samples number required. When reaching the required number, simulation will stop, default 1024.
timeSteps	Number of interval, default 100.
maxSamples	The maximum sample number. When reaching it, the simulation will stop, default 2147483648.

MCAsianArithmeticASEngine

#include "xf_fintech/mc_engine.hpp"

template <
    typename DT = double,
    int UN = 16
    >
void MCAsianArithmeticASEngine (
    DT underlying,
    DT volatility,
    DT dividendYield,
    DT riskFreeRate,
    DT timeLength,
    DT strike,
    bool optionType,
    ap_uint <32>* seed,
    DT* output,
    DT requiredTolerance = 0.02,
    unsigned int requiredSamples = 1024,
    unsigned int timeSteps = 100,
    unsigned int maxSamples = 134217727
    )

Asian Arithmetic Average Strike Engine using Monte Carlo Method Based on Black-Scholes Model. The settlement price of the underlying asset at expiry time is the asset price at expiry time, but the stock price is the arithmetic average of asset price during the option lifetime.

Parameters:

DT	Supported data type including double and float, which decides the precision of output.
UN	The number of Monte Carlo Module in parallel, which affects the latency and resources utilization.
underlying	The initial price of underlying asset.
volatility	The market’s price volatility.
dividendYield	The dividend yield is the company’s total annual dividend payments divided by its market capitalization, or the dividend per share, divided by the price per share.
riskFreeRate	The risk-free interest rate is the rate of return of a hypothetical investment with no risk of financial loss, over a given period of time.
timeLength	The given period of time.
strike	The strike price also known as exericse price, which is settled in the contract.
optionType	Option type. 1: put option, 0: call option.
seed	array of seed to initialize RNG.
output	Output array.
requiredTolerance	the tolerance required. If requiredSamples is not set, when reaching the required tolerance, simulation will stop, default 0.02.
requiredSamples	the samples number required. When reaching the required number, simulation will stop, default 1024.
timeSteps	the number of discrete steps from 0 to T, T is the expiry time, default 100.
maxSamples	the maximum sample number. When reaching it, the simulation will stop, default 2,147,483,648.

MCBarrierNoBiasEngine

#include "xf_fintech/mc_engine.hpp"

template <
    typename DT = double,
    int UN = 10
    >
void MCBarrierNoBiasEngine (
    DT underlying,
    DT volatility,
    DT dividendYield,
    DT riskFreeRate,
    DT timeLength,
    DT barrier,
    DT strike,
    ap_uint <2> barrierType,
    bool optionType,
    ap_uint <32>* seed,
    DT* output,
    DT rebate = 0,
    DT requiredTolerance = 0.02,
    unsigned int requiredSamples = 1024,
    unsigned int timeSteps = 100,
    unsigned int maxSamples = 134217727
    )

Barrier Option Pricing Engine using Monte Carlo Simulation. Using brownian bridge to generate the non-biased result.

Parameters:

DT	supported data type including double and float data type, which decides the precision of result, default double-precision data type.
UN	number of Monte Carlo Module in parallel, which affects the latency and resources utilization, default 10.
underlying	intial value of underlying asset at time 0.
volatility	fixed volatility of underlying asset.
dividendYield	the constant dividend rate for continuous dividends.
riskFreeRate	risk-free interest rate.
timeLength	the time length of contract from start to end.
barrier	single barrier value.
strike	the strike price also known as exericse price, which is settled in the contract.
barrierType	barrier type including: DownIn(0), DownOut(1), UpIn(2), UpOut(3).
optionType	option type. 1: put option, 0: call option.
seed	array to store the inital seeds of RNG.
output	output array.
rebate	rebate value which is paid when the option is not triggered, default 0.
requiredTolerance	the tolerance required. If requiredSamples is not set, when reaching the required tolerance, simulation will stop, default 0.02.
requiredSamples	the samples number required. When reaching the required number, simulation will stop, default 1024.
timeSteps	the number of discrete steps from 0 to T, T is the expiry time, default 100.
maxSamples	the maximum sample number. When reaching it, the simulation will stop, default 2,147,483,648.

MCBarrierEngine

#include "xf_fintech/mc_engine.hpp"

template <
    typename DT = double,
    int UN = 10
    >
void MCBarrierEngine (
    DT underlying,
    DT volatility,
    DT dividendYield,
    DT riskFreeRate,
    DT timeLength,
    DT barrier,
    DT strike,
    ap_uint <2> barrierType,
    bool optionType,
    ap_uint <32>* seed,
    DT* output,
    DT rebate = 0,
    DT requiredTolerance = 0.02,
    unsigned int requiredSamples = 1024,
    unsigned int timeSteps = 100,
    unsigned int maxSamples = 134217727
    )

Barrier Option Pricing Engine using Monte Carlo Simulation.

Parameters:

DT	supported data type including double and float data type, which decides the precision of result, default double-precision data type.
UN	number of Monte Carlo Module in parallel, which affects the latency and resources utilization, default 10.
underlying	intial value of underlying asset at time 0.
volatility	fixed volatility of underlying asset.
dividendYield	the constant dividend rate for continuous dividends.
riskFreeRate	risk-free interest rate.
timeLength	the time length of contract from start to end.
barrier	single barrier value.
strike	the strike price also known as exericse price, which is settled in the contract.
barrierType	barrier type including: DownIn(0), DownOut(1), UpIn(2), UpOut(3).
optionType	option type. 1: put option, 0: call option.
seed	array to store the inital seeds for each RNG.
output	output array.
rebate	rebate value which is paid when the option is not triggered, default 0.
requiredTolerance	the tolerance required. If requiredSamples is not set, when reaching the required tolerance, simulation will stop, default 0.02.
requiredSamples	the samples number required. When reaching the required number, simulation will stop, default 1024.
timeSteps	the number of discrete steps from 0 to T, T is the expiry time, default 100.
maxSamples	the maximum sample number. When reaching it, the simulation will stop, default 2,147,483,648.

MCCliquetEngine

#include "xf_fintech/mc_engine.hpp"

template <
    typename DT = double,
    int UN = 10
    >
void MCCliquetEngine (
    DT underlying,
    DT volatility,
    DT dividendYield,
    DT riskFreeRate,
    DT timeLength,
    DT strike,
    bool optionType,
    DT* resetDates,
    ap_uint <32>* seed,
    DT* output,
    DT requiredTolerance = 0.02,
    unsigned int timeSteps = 100,
    unsigned int requiredSamples = 1024,
    unsigned int maxSamples = 134217727
    )

Cliquet Option Pricing Engine using Monte Carlo Simulation. The B-S model used to describe the dynamics of undelying asset.

Parameters:

DT	supported data type including double and float data type, which decides the precision of result, default double-precision data type.
UN	number of Monte Carlo Module in parallel, which affects the latency and resources utilization, default 10.
underlying	intial value of underlying asset.
volatility	fixed volatility of underlying asset.
dividendYield	the constant dividend rate for continuous dividends.
riskFreeRate	risk-free interest rate.
timeLength	the time length of contract from start to end.
strike	the strike price also known as exericse price, which is settled in the contract.
optionType	option type. 1: put option, 0: call option.
resetDates	array for reset dates, such as Semiannual, Quarterly.
seed	array to store the inital seeds of RNG.
output	output array.
requiredTolerance	the tolerance required. If requiredSamples is not set, when reaching the required tolerance, simulation will stop. default 0.02.
requiredSamples	the samples number required. When reaching the required number, simulation will stop, default 1024.
timeSteps	the number of discrete steps from 0 to T, T is the expiry time, default 100.
maxSamples	the maximum sample number. When reaching it, the simulation will stop, default 2,147,483,648.

MCDigitalEngine

#include "xf_fintech/mc_engine.hpp"

template <
    typename DT = double,
    int UN = 10
    >
void MCDigitalEngine (
    DT underlying,
    DT volatility,
    DT dividendYield,
    DT riskFreeRate,
    DT timeLength,
    DT strike,
    DT cashPayoff,
    bool optionType,
    bool exEarly,
    ap_uint <32>* seed,
    DT* output,
    DT requiredTolerance = 0.02,
    unsigned int timeSteps = 100,
    unsigned int requiredSamples = 1024,
    unsigned int maxSamples = 134217727
    )

Digital Option Pricing Engine using Monte Carlo Simulation. The B-S model is used to describe dynamics of undelying asset price.

Parameters:

DT	supported data type including double and float data type, which decides the precision of result, default double-precision data type.
UN	number of Monte Carlo Module in parallel, which affects the latency and resources utilization, default 10.
underlying	intial value of underlying asset at time 0.
volatility	fixed volatility of underlying asset.
dividendYield	the constant dividend rate for continuous dividends.
riskFreeRate	risk-free interest rate.
timeLength	the time length of contract from start to end.
strike	the strike price also known as exericse price, which is settled in the contract.
cashPayoff	fixed payoff when option is exercised.
exEarly	exercise early or not, true: option exercise at anytime. false: option only exericse at expiry time.
optionType	option type. 1: put option, 0: call option.
seed	array to store the inital seeds for each RNG.
output	output array.
requiredTolerance	the tolerance required. If requiredSamples is not set, when reaching the required tolerance, simulation will stop, default 0.02.
requiredSamples	the samples number required. When reaching the required number, simulation will stop, default 1024.
timeSteps	the number of discrete steps from 0 to T, T is the expiry time, default 100.
maxSamples	the maximum sample number. When reaching it, the simulation will stop, default 2,147,483,648.

MCEuropeanHestonGreeksEngine

#include "xf_fintech/mc_engine.hpp"

template <
    typename DT = double,
    int UN = 1,
    DiscreType discretization = kDTQuadraticExponential
    >
void MCEuropeanHestonGreeksEngine (
    DT underlying,
    DT riskFreeRate,
    DT sigma,
    DT v0,
    DT theta,
    DT kappa,
    DT rho,
    DT dividendYield,
    bool optionType,
    DT strike,
    DT timeLength,
    ap_uint <32> seed [UN][2],
    DT* greeks,
    DT requiredTolerance = 0.02,
    unsigned int requiredSamples = 1024,
    unsigned int timeSteps = 100,
    unsigned int maxSamples = 134217727
    )

European Option Greeks Calculating Engine using Monte Carlo Method based on Heston valuation model.

Parameters:

DT	supported data type including double and float, which decides the precision of output, default double-precision data type.
UN	number of Monte Carlo Module in parallel, which affects the latency and resources utilization, default 10.
DiscreType	methods which is used to discrete the stochastic process. Currently, five discrete types, including kDTPartialTruncation, kDTFullTruncation, kDTReflection, kDTQuadraticExponential and kDTQuadraticExponentialMartingale, are supported, default kDTQuadraticExponential.
underlying	the initial price of underlying asset at time 0.
riskFreeRate	risk-free interest rate.
sigma	the volatility of volatility
v0	initial volatility of stock
theta	the long variance, as t tends to infinity, the expected value of vt tends to theta.
kappa	the rate at which vt tends to theta.
rho	the correlation coefficient between price and variance.
dividendYield	the constant dividend rate for continuous dividends.
optionType	option type. 1: put option, 0: call option.
strike	the strike price also known as exericse price, which is settled in the contract.
timeLength	time length from now to expiry date.
seed	the seeds used to initialize RNG.
greeks	output calculated greeks.
requiredTolerance	the tolerance required. If requiredSamples is not set, when reaching the required tolerance, simulation will stop.
requiredSamples	the samples number required. When reaching the required number, simulation will stop, default 1024.
timeSteps	the number of discrete steps from 0 to T, T is the expiry time, default 100.
maxSamples	the maximum sample number. When reaching it, the simulation will stop, default 2,147,483,648.

MCHullWhiteCapFloorEngine

#include "xf_fintech/mc_engine.hpp"

template <
    typename DT = double,
    int UN = 1
    >
void MCHullWhiteCapFloorEngine (
    DT nomial,
    DT initRate,
    DT strike,
    bool isCap,
    DT singlePeriod,
    DT alpha,
    DT sigma,
    ap_uint <32>* seed,
    DT* output,
    DT requiredTolerance = 0.02,
    unsigned int requiredSamples = 0,
    unsigned int timeSteps = 2,
    unsigned int maxSamples = 134217727
    )

Cap/Floor Pricing Engine using Monte Carlo Simulation. The Hull-White model is used to describe dynamics of short-term interest. This engine assume a flat term structure.

Parameters:

DT	supported data type including double and float data type, which decides the precision of result, default double-precision data type.
UN	number of Monte Carlo Module in parallel, which affects the latency and resources utilization, default 10.
nomial	Nomial of capfloor contract.
initRate	Current spot rate and forward rate (flat term structure).
strike	Strike rate of capfloor contract
isCap	True for cap, false for floor
singlePeriod	period between each settlement date.
alpha	Hull White model parameter
sigma	Hull White model parameter
seed	Array to store the inital seed for each RNG.
output	Array to store result
requiredTolerance	the tolerance required. If requiredSamples is not set, when reaching the required tolerance, simulation will stop, default 0.02.
requiredSamples	the samples number required. When reaching the required number, simulation will stop, default 1024.
timeSteps	the number of cap/floor settlement date.
maxSamples	the maximum sample number. When reaching it, the simulation will stop, default 2,147,483,648.

McmcCore

#include "xf_fintech/pop_mcmc.hpp"

template <
    typename DT,
    unsigned int NCHAINS,
    unsigned int NSAMPLES_MAX
    >
void McmcCore (
    DT temp_inv [NCHAINS],
    DT sigma [NCHAINS],
    DT x [NSAMPLES_MAX],
    unsigned int nSamples
    )

Top level Kernel function. Consists of INIT_LOOP and main sample loop: SAMPLES_LOOP

Generates sample from target distribution function.

Uses multiple Markov Chains to allow drawing samples from multi mode target distribution functions.

Proposal is generated ussing Normal Distribution

.

Parameters:

DT	Data type used in whole function (double by default)
NCHAINS	Number of chains
NSAMPLES_MAX	Maximum Number of chains for synthesis purpose
temp_inv	Array of Inverted temperatures of the chain that density is generate for (1/Temp)
sigma	Array of sigmas for Proposal generation for each chain
nSamples	Number of samples to generate
x	Sample output

treeSwaptionEngine

#include "xf_fintech/tree_engine.hpp"

template <
    typename DT,
    typename Model,
    typename Process,
    int DIM,
    int LEN,
    int LEN2
    >
void treeSwaptionEngine (
    Model& model,
    DT* process,
    int type,
    DT fixedRate,
    int timestep,
    DT initTime [LEN],
    int initSize,
    int* exerciseCnt,
    int* floatingCnt,
    int* fixedCnt,
    DT flatRate,
    DT nominal,
    DT x0,
    DT spread,
    DT* NPV
    )

Tree Swaption Pricing Engine using Trinomial Tree based 1D Lattice method.

Parameters:

DT	supported data type including double and float data type, which decides the precision of result.
Model	short-rate model class
Process	stochastic process class
DIM	1D or 2D short-rate model
LEN	maximum length of timestep, which affects the latency and resources utilization.
LEN2	maximum length of node of tree, which affects the latency and resources utilization.
model	short-rate model that has been initialized
process	parameters of stochastic process
type	0: Payer, 1: Receiver
fixedRate	fixed annual interest rate.
timestep	estimate the number of discrete steps from 0 to T, T is the maturity time.
initTime	the time including begin timepoint, end timepoint, exercise timepoints, floating coupon timepoints, and fixed coupon timepoints is arranged from small to large. The timepoints are relative values based on the reference date the unit is year.
initSize	the length of array initTime.
exerciseCnt	exercise timepoints count in initTime.
floatingCnt	floating coupon timepoints count in initTime.
fixedCnt	fixed coupon timepoints count in initTime.
flatRate	floating benchmark annual interest rate
nominal	nominal principal
x0	initial underlying
spread	spreads on interest rates
NPV	is pricing result array of this engine

#include "xf_fintech/tree_engine.hpp"

template <
    typename DT,
    typename Model,
    typename Process,
    int DIM,
    int LEN,
    int LEN2
    >
void treeSwaptionEngine (
    Model& model,
    DT* process1,
    DT* process2,
    int type,
    DT fixedRate,
    int timestep,
    DT initTime [LEN],
    int initSize,
    int* exerciseCnt,
    int* floatingCnt,
    int* fixedCnt,
    DT flatRate,
    DT nominal,
    DT x0,
    DT spread,
    DT rho,
    DT* NPV
    )

Tree Swaption Pricing Engine using Trinomial Tree based 2D Lattice method.

Parameters:

DT	supported data type including double and float data type, which decides the precision of result.
Model	short-rate model class
Process	stochastic process class
DIM	1D or 2D short-rate model
LEN	maximum length of timestep, which affects the latency and resources utilization.
LEN2	maximum length of node of tree, which affects the latency and resources utilization.
model	short-rate model that has been initialized
process1	1st dimensional parameters of stochastic process
process2	2nd dimensional parameters of stochastic process
type	0: Payer, 1: Receiver
fixedRate	fixed annual interest rate.
timestep	estimate the number of discrete steps from 0 to T, T is the expiry time.
initTime	the time including begin timepoint, end timepoint, exercise timepoints, floating coupon timepoints, and fixed coupon timepoints is arranged from small to large. The timepoints are relative values based on the reference date the unit is year.
initSize	the length of array initTime.
exerciseCnt	exercise timepoints count in initTime.
floatingCnt	floating coupon timepoints count in initTime.
fixedCnt	fixed coupon timepoints count in initTime.
flatRate	floating benchmark annual interest rate
nominal	nominal principal
x0	initial underlying
spread	spreads on interest rates
rho	the correlation coefficient between price and variance.
NPV	is pricing result array of this engine

treeSwapEngine

#include "xf_fintech/tree_engine.hpp"

template <
    typename DT,
    typename Model,
    typename Process,
    int DIM,
    int LEN,
    int LEN2
    >
void treeSwapEngine (
    Model& model,
    DT* process,
    int type,
    DT fixedRate,
    int timestep,
    DT initTime [LEN],
    int initSize,
    int* floatingCnt,
    int* fixedCnt,
    DT flatRate,
    DT nominal,
    DT x0,
    DT spread,
    DT* NPV
    )

Tree Swap Pricing Engine using Trinomial Tree based 1D Lattice method.

Parameters:

DT	supported data type including double and float data type, which decides the precision of result.
Model	short-rate model
Process	stochastic process
DIM	1D or 2D short-rate model
LEN	maximum length of timestep, which affects the latency and resources utilization.
LEN2	maximum length of node of tree, which affects the latency and resources utilization.
model	short-rate model that has been initialized
process	parameters of stochastic process
type	0: Payer, 1: Receiver
fixedRate	fixed annual interest rate.
timestep	estimate the number of discrete steps from 0 to T, T is the expiry time.
initTime	the time including begin timepoint, end timepoint, exercise timepoints, floating coupon timepoints, and fixed coupon timepoints is arranged from small to large. The timepoints are relative values based on the reference date the unit is year.
initSize	the length of array initTime.
floatingCnt	floating coupon timepoints count in initTime.
fixedCnt	fixed coupon timepoints count in initTime.
flatRate	floating benchmark annual interest rate
nominal	nominal principal
x0	initial underlying
spread	spreads on interest rates
NPV	is pricing result array of this engine

#include "xf_fintech/tree_engine.hpp"

template <
    typename DT,
    typename Model,
    typename Process,
    int DIM,
    int LEN,
    int LEN2
    >
void treeSwapEngine (
    Model& model,
    DT* process1,
    DT* process2,
    int type,
    DT fixedRate,
    int timestep,
    DT initTime [LEN],
    int initSize,
    int* floatingCnt,
    int* fixedCnt,
    DT flatRate,
    DT nominal,
    DT x0,
    DT spread,
    DT rho,
    DT* NPV
    )

Tree Swap Pricing Engine using Trinomial Tree based 2D Lattice method.

Parameters:

DT	supported data type including double and float data type, which decides the precision of result.
Model	short-rate model
Process	stochastic process
DIM	1D or 2D short-rate model
LEN	maximum length of timestep, which affects the latency and resources utilization.
LEN2	maximum length of node of tree, which affects the latency and resources utilization.
model	short-rate model that has been initialized
process1	1st dimensional parameters of stochastic process
process2	2nd dimensional parameters of stochastic process
type	0: Payer, 1: Receiver
fixedRate	fixed annual interest rate.
timestep	estimate the number of discrete steps from 0 to T, T is the expiry time.
initTime	the time including begin timepoint, end timepoint, exercise timepoints, floating coupon timepoints, and fixed coupon timepoints is arranged from small to large. The timepoints are relative values based on the reference date the unit is year.
initSize	the length of array initTime.
floatingCnt	floating coupon timepoints count in initTime.
fixedCnt	fixed coupon timepoints count in initTime.
flatRate	floating benchmark annual interest rate
nominal	nominal principal
x0	initial underlying
spread	spreads on interest rates
rho	the correlation coefficient between price and variance.
NPV	is pricing result array of this engine

treeCapFloorEngine

#include "xf_fintech/tree_engine.hpp"

template <
    typename DT,
    typename Model,
    typename Process,
    int DIM,
    int LEN,
    int LEN2
    >
void treeCapFloorEngine (
    Model& model,
    DT* process,
    int type,
    DT fixedRate,
    int timestep,
    DT initTime [LEN],
    int initSize,
    int* floatingCnt,
    DT flatRate,
    DT nominal,
    DT* cfRate,
    DT x0,
    DT spread,
    DT* NPV
    )

Tree CapFloor Pricing Engine using Trinomial Tree based 1D Lattice method.

Parameters:

DT	supported data type including double and float data type, which decides the precision of result.
Model	short-rate model that has been initialized
Process	parameters of stochastic process
DIM	1D or 2D short-rate model
LEN	maximum length of timestep, which affects the latency and resources utilization.
LEN2	maximum length of node of tree, which affects the latency and resources utilization.
model	short-rate model
process	stochastic process
type	0: Cap, 1: Collar, 2: Floor
fixedRate	fixed annual interest rate.
timestep	estimate the number of discrete steps from 0 to T, T is the expiry time.
initTime	the time including begin timepoint, end timepoint, exercise timepoints, floating coupon timepoints, and fixed coupon timepoints is arranged from small to large. The timepoints are relative values based on the reference date the unit is year.
initSize	the length of array initTime.
floatingCnt	floating coupon timepoints count in initTime.
flatRate	floating benchmark annual interest rate
nominal	nominal principal
cfRate	cap rate and floor rate
x0	initial underlying
spread	spreads on interest rates
NPV	is pricing result array of this engine

#include "xf_fintech/tree_engine.hpp"

template <
    typename DT,
    typename Model,
    typename Process,
    int DIM,
    int LEN,
    int LEN2
    >
void treeCapFloorEngine (
    Model& model,
    DT* process1,
    DT* process2,
    int type,
    DT fixedRate,
    int timestep,
    DT initTime [LEN],
    int initSize,
    int* floatingCnt,
    DT flatRate,
    DT nominal,
    DT* cfRate,
    DT x0,
    DT spread,
    DT rho,
    DT* NPV
    )

Tree CapFloor Pricing Engine using Trinomial Tree based 2D Lattice method.

Parameters:

DT	supported data type including double and float data type, which decides the precision of result.
Model	short-rate model
Process	stochastic process
DIM	1D or 2D short-rate model
LEN	maximum length of timestep, which affects the latency and resources utilization.
LEN2	maximum length of node of tree, which affects the latency and resources utilization.
model	short-rate model that has been initialized
process1	1st dimensional parameters of stochastic process
process2	2nd dimensional parameters of stochastic process
type	0: Cap, 1: Collar, 2: Floor
fixedRate	fixed annual interest rate.
timestep	estimate the number of discrete steps from 0 to T, T is the expiry time.
initTime	the time including begin timepoint, end timepoint, exercise timepoints, floating coupon timepoints, and fixed coupon timepoints is arranged from small to large. The timepoints are relative values based on the reference date the unit is year.
initSize	the length of array initTime.
floatingCnt	floating coupon timepoints count in initTime.
flatRate	floating benchmark annual interest rate
nominal	nominal principal
cfRate	cap rate ans floor rate
x0	initial underlying
spread	spreads on interest rates
rho	the correlation coefficient between price and variance.
NPV	is pricing result array of this engine

treeCallableEngine

#include "xf_fintech/tree_engine.hpp"

template <
    typename DT,
    typename Model,
    typename Process,
    int DIM,
    int LEN,
    int LEN2
    >
void treeCallableEngine (
    Model& model,
    DT* process,
    int type,
    DT fixedRate,
    int timestep,
    DT initTime [LEN],
    int initSize,
    int* callableCnt,
    int* paymentCnt,
    DT flatRate,
    DT nominal,
    DT x0,
    DT spread,
    DT* NPV
    )

Tree Callable Fixed Rate Bond Pricing Engine using Trinomial Tree based 1D Lattice method.

Parameters:

DT	supported data type including double and float data type, which decides the precision of result.
Model	short-rate model
Process	stochastic process
DIM	1D or 2D short-rate model
LEN	maximum length of timestep, which affects the latency and resources utilization.
LEN2	maximum length of node of tree, which affects the latency and resources utilization.
model	short-rate model that has been initialized
process	parameters of stochastic process
type	type of the callability, 0: Call, 1: Put
fixedRate	fixed annual interest rate.
timestep	estimate the number of discrete steps from 0 to T, T is the expiry time.
initTime	the time including begin timepoint, end timepoint, exercise timepoints, floating coupon timepoints, and fixed coupon timepoints is arranged from small to large. The timepoints are relative values based on the reference date the unit is year.
initSize	the length of array initTime.
callableCnt	callable timepoints count in initTime.
paymentCnt	payment timepoints count in initTime.
flatRate	floating benchmark annual interest rate
nominal	nominal principal
x0	initial underlying
spread	spreads on interest rates
NPV	is pricing result array of this engine

#include "xf_fintech/tree_engine.hpp"

template <
    typename DT,
    typename Model,
    typename Process,
    int DIM,
    int LEN,
    int LEN2
    >
void treeCallableEngine (
    Model& model,
    DT* process1,
    DT* process2,
    int type,
    DT fixedRate,
    int timestep,
    DT initTime [LEN],
    int initSize,
    int* callableCnt,
    int* paymentCnt,
    DT flatRate,
    DT nominal,
    DT x0,
    DT spread,
    DT rho,
    DT* NPV
    )

Tree Callable Fixed Rate Bond Pricing Engine using Trinomial Tree based 2D Lattice method.

Parameters:

DT	supported data type including double and float data type, which decides the precision of result.
Model	short-rate model
Process	stochastic process
DIM	1D or 2D short-rate model
LEN	maximum length of timestep, which affects the latency and resources utilization.
LEN2	maximum length of node of tree, which affects the latency and resources utilization.
model	short-rate model that has been initialized
process1	1st dimensional parameters of stochastic process
process2	2nd dimensional parameters of stochastic process
type	type of the callability, 0: Call, 1: Put
fixedRate	fixed annual interest rate.
timestep	estimate the number of discrete steps from 0 to T, T is the expiry time.
initTime	the time including begin timepoint, end timepoint, exercise timepoints, floating coupon timepoints, and fixed coupon timepoints is arranged from small to large. The timepoints are relative values based on the reference date the unit is year.
initSize	the length of array initTime.
callableCnt	callable timepoints count in initTime.
paymentCnt	payment timepoints count in initTime.
flatRate	floating benchmark annual interest rate
nominal	nominal principal
x0	initial underlying
spread	spreads on interest rates
rho	the correlation coefficient between price and variance.
NPV	is pricing result array of this engine