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:

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.