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Quantitative Finance


Prices a portfolio of LIBOR swaptions on a LIBOR Market Model using a Monte-Carlo simulation and computes Greeks.

Prices a portfolio of American call options using a Binomial lattice (Cox, Ross and Rubenstein method).

Benchmark Description

This application prices a portfolio of LIBOR swaptions on a LIBOR Market Model using a Monte-Carlo simulation. It simultaneously calculates first order sensitivities to the initial forward rates (the delta Greeks) using path-wise Adjoint Algorithmic Differentiation (AD).

In each Monte-Carlo path, the LIBOR forward rates are generated randomly at all required maturities following the LIBOR Market Model, starting from the initial LIBOR rates. The swaption portfolio payoff is then computed and discounted to the pricing date. Averaging the per-path prices gives the final net present value of the portfolio.

The full algorithm is illustrated in the processing graph below:

LiborGreeksGraph

More details can be found in Prof. Mike Giles’ notes [1].

This benchmark uses a portfolio of 15 swaptions with maturities between 4 and 40 years and 80 forward rates (and hence 80 delta Greeks). The performance is measured with varying numbers of Monte-Carlo paths (from 256K to 2,048K).

[1] M. Giles, “Monte Carlo evaluation of sensitivities in computational finance,” HERCMA Conference, Athens, Sep. 2007.

  • Application Class: Pricer
  • Model: Libor Market Model
  • Instrument Type: Swaption Portfolio
  • Numerical Method: Monte-Carlo
  • Portfolio Size: 15 swaptions
  • Maturities: 4 to 40 years
  • Number of Forward Rates: 80
  • Sensitivities: first order (delta)
  • Number of Sensitivities: 80
  • Monte-Carlo Paths: 256K-2,048K

This benchmark application prices a portfolio of American call options using a Binomial lattice (Cox, Ross and Rubenstein method).

For a given size N of the binomial tree, the option payoff at the N leaf nodes is computed first (the value at maturity for different stock prices, using the Black-Scholes model). Then, the pricer works towards the root node backwards in time, multiplying the 2 child nodes by the pre-computed pseudo-probabilities that the price goes up or down, including discounting at the risk-free rate, and adding the results. After repeating this process for all time steps, the root node holds the present value.

The algorithm is illustrated in the graph below:

Binomial tree illustration

This binomial pricing method is applied for every option in the portfolio.

For this benchmark, we use 1,024 steps (the depth of the tree). We vary the number of options in the portfolio to study the performance.

  • Application Class: Batch Pricer
  • Model: Black-Scholes
  • Instrument Type: American Option
  • Numerical Method: Binomial Lattice
  • Portfolio Size: 128K-2,048K
  • Maturities: 1-5 years
  • Depth of Lattice: 1,024

SystemOperating SystemImplementationMemory (RAM)CompilerECCPrecision ModeOther
Intel HaswellRedHat EL 6.6 (64bit)C++ / Xcelerit SDK 3.1128GBIntel Compiler 17.0ondouble2x Hyperthreading
Intel Xeon PhiRedHat EL 7.1 (64bit)C++ / Xcelerit SDK 3.164GB (host)Intel Compiler 15.0ondoubleMPSS 3.4.5, 4x Hyperthreading
SystemOperating SystemImplementationMemory (RAM)CompilerECCPrecision ModeOther
Intel HaswellRedHat EL 6.6 (64bit)C++ / Xcelerit SDK 3.1128GBIntel Compiler 17.0ondoubleno Hyperthreading
Intel Xeon PhiRedHat EL 7.1 (64bit)C++ / Xcelerit SDK 3.164GB (host)Intel Compiler 15.0ondoubleMPSS 3.4.5, 4x Hyperthreading

The application is executed 100 times and the average wall-clock time is reported. The first cold run is dropped. The full algorithm execution time from inputs to outputs is measured. This includes setup of accelerators and data transfers if applicable. The speedup vs. a sequential implementation on a single core is reported.

Hardware Specification

ProcessorCoresLogical CoresFrequencyGFLOPs (double)Max. MemoryMax. Memory B/W
Dual Intel Xeon E5-2698 v3 CPU (Haswell)2 x 162 x 322.30 GHz2 x 663768 GB2 x 68 GB/s
Intel Xeon Phi 7120P (Knight's Corner)612441.238 GHz1,20816 GB352 GB/s
ProcessorCoresLogical CoresFrequencyGFLOPs (double)Max. MemoryMax. Memory B/W
Dual Intel Xeon E5-2698 v3 CPU (Haswell)2 x 162 x 322.30 GHz2 x 663768 GB2 x 68 GB/s
Intel Xeon Phi 7120P (Knight's Corner)612441.238 GHz1,20816 GB352 GB/s

Speedup vs. Sequential*

*the sequential version runs on a single core of an Intel Xeon E5-2698 v3 CPU
*the sequential version runs on a single core of an Intel Xeon E5-2698 v3 CPU

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