Example PDE and MC derivative pricing models

These real-world examples and their timings demonstrate the accelerations that can be achieved with SciFinance GPU-enabled PDE and Monte Carlo derivative pricing models.

PDE example derivatives pricing model

Power Reverse Dual Currency Swap

Cancellable, knockout, power-reverse dual-currency swap with stochastic interest rates in both foreign and domestic currencies as well as a term structure of FX volatility. The FX rate is modeled using a simple lognormal process while the domestic and foreign interest rates are modeled using a one-factor Gaussian G1 model. The drift term corresponding to the foreign rate includes a quanto correction arising from changing from the foreign risk-neutral measure to the domestic.

Timing

The SciGPU-enabled model runs 13x-31x faster on one GPU than the serial code on one CPU. Timings in chart are given for the entire pricer code (initialization, memory transfers and kernels).

Performance of SciGPU-enabled model (double precision) vs. CPU serial code

Monte Carlo example derivatives pricing models

Digital Cliquet Heston Stochastic Volatility Model

Cliquet option priced under a Heston stochastic volatility model via Monte Carlo. The cliquet option is locally and globally capped and floored.

Timing

The SciGPU-enabled model runs 29x faster on one GPU than the serial code on one CPU.

Basket Equity-linked Structured Note Model

Equity-linked structured note in which the note is linked to a basket of indices. If on observation dates the performance of all indices is above the knockout barrier for that date, the note redeems early at par plus a bonus coupon. If early redemption does not occur, then at maturity either:

• the note redeems at par plus maturity coupon; or
• if the performance of the least KINum of the indices have been below the knock-in barrier during the tenor, on a continuously observed basis, then the note redeems at the performance percentage of the worst index.

The indices follow correlated Heston stochastic volatility processes and we allow for a term structure of rates.

Timing

The SciGPU-enabled model runs 33x faster on one GPU than the serial code on one CPU.

Snowblade Under a Two-Factor LIBOR Market Model

Snowblade priced under a two-factor LIBOR market model (LMM). A snowblade is a snowball note with an automatic redemption exercise feature, also called a TARNes snowball. In general, the TARN feature is defined by two parameters, a lifetime cap and lifetime floor. On each coupon payment date, if the cumulative coupon rate is greater than the lifetime cap or less than the lifetime floor, the note is automatically exercised on that date. In this case, the issuer buys back the note paying the remaining principal. The coupon paid at redemption is scaled up or down to meet exactly the redemption target.

Timing

The SciGPU-enabled model runs 45x faster on one GPU than the serial code on one CPU.

Performance of SciGPU-enabled models (double precision) vs. CPU serial code

All timings were performed on an Intel Xeon E5405 2.0GHz CPU running Windows XP with a NVIDIA Tesla 20-Series C2050.