Internal Design of Tree Bermudan Swaption Engine

Overview

Swap engine, swaption engine, capfloor engine and callable engine are all pricing engines to price the interested products. The swap is mainly an interest rate swap. For both parties to the swap, the buyer needs execute a specified swap agreement with the issuer on a specified future date.

The swaption mainly refers to an option to do swap. The buyer acquires the right but not the obligation to enter into a specified swap agreement with the issuer on a specified future date.

The capfloor includes 2 interest rate derivatives: cap, and floor. For the interest rate cap, the buyer receives payments from the issuer at the end of each period in which the interest rate exceeds the agreed strike price. For interest rate floor, the buyer receives payments from the issuer at the end of each period in which the interest rate is below the agreed strike price.

The callable bond is a type of bond that provides the issuer of the bond with the right, but not the obligation, to redeem the bond on a specified future date before its maturity date.

Implemention

As shown in the figure below, this engine uses the framework of Tree Lattice in L1. It has a Rate Model and 1 or 2 Stochastic Process as input.

1. From the input parameters, the time grid and the corresponding counter of exercise times and payment times of fixed or floating interest rate are obtained (All time points are relative values based on the reference date in year, and the engine only supports the case where the time point is not less than 0).
2. By calling the function setup of the framework, the floating interest rates and tree related parameters are calculated from 0 to N timepoint-by-timepoint to prepare the interest rates and the tree related parameters for the following calculations.
3. Take treeSwaptionEngine, for example, by calling the function rollback of the framework using the same structure of the tree, the net present value (NPV) is calculated from N to 0 timepoint-by-timepoint. The implementation is shown in the figure below, where the data flow along with the arrows.

Profiling

The hardware resources are listed in the following table (from Vivado 18.3 report).

Table 11 Table 1 Hardware resources

Engine	Models	BRAM	URAM	DSP	FF	LUT	clock period(ns)
treeSwaptionEngine	HWModel	112	0	452	87469	67212	3.053
treeSwaptionEngine	BKModel	116	0	495	99209	82034	3.190
treeSwaptionEngine	CIRModel	104	0	417	82910	51160	3.110
treeSwaptionEngine	ECIRModel	116	0	442	102802	81395	3.205
treeSwaptionEngine	VModel	104	0	377	74551	48322	3.054
treeSwaptionEngine	G2Model	18	136	625	139467	90205	3.896
treeSwapEngine	HWModel	104	0	408	84628	65744	3.896
treeCapFloorEngine	HWModel	104	0	364	79489	64863	3.180
treeCallableEngine	HWModel	104	0	320	76577	62445	3.043

The following table shows the comparison of the performance between U250 result and CPU based Quantlib result. (treeSwaptionEngine+G2Model FPGA System Clock: 250MHz, others FPGA System Clock: 300MHz)

Table 12 Table 2 Comparison between CPU and FPGA

Engine	Models	Timesteps	50	100	500	1000
treeSwaptionEngine	HWModel	CPU Execution time(ms)	1.0	4.8	353.9	2493.5
		FPGA Execution time-HLS(ms)	0.28	0.61	5.72	18.17
treeSwaptionEngine	BKModel	CPU Execution time(ms)	1.9	8.6	438.2	2813.1
		FPGA Execution time-HLS(ms)	0.72	1.53	11.93	34.21
treeSwaptionEngine	CIRModel	CPU Execution time(ms)	0.5	1.4	26.6	100.7
		FPGA Execution time-HLS(ms)	0.16	0.31	2.22	6.18
treeSwaptionEngine	ECIRModel	CPU Execution time(ms)	1.1	5.5	439.5	3322.5
		FPGA Execution time-HLS(ms)	0.72	1.36	10.17	28.47
treeSwaptionEngine	VModel	CPU Execution time(ms)	0.5	1.8	40.1	161.7
		FPGA Execution time-HLS(ms)	0.14	0.29	2.42	7.42
treeSwaptionEngine	G2Model	CPU Execution time(ms)	258.0	2133.5
		FPGA Execution time-HLS(ms)	1.93	14.56
treeSwapEngine	HWModel	CPU Execution time(ms)	1.0	4.3	291.2	2056.5
		FPGA Execution time-HLS(ms)	0.28	0.61	5.61	18.16
treeCapFloorEngine	HWModel	CPU Execution time(ms)	0.7	3.4	217.6	1581.3
		FPGA Execution time-HLS(ms)	0.30	0.64	5.89	18.51
treeCallableEngine	HWModel	CPU Execution time(ms)	1.4	3.5	155.2	1142.0
		FPGA Execution time-HLS(ms)	0.28	0.60	5.67	17.89