![]() That is, in every Monte-Carlo path, the stock value at a fixed grid of time steps is computed using a geometric Brownian motion with constant volatility and the risk-free rate. The Black-Scholes model is used to generate the paths. This benchmark application prices a portfolio of up-and-in barrier options with European exercise, using a Monte-Carlo simulation. We vary the number of options in the portfolio to study the performance. This binomial pricing method is applied for every option in the portfolio.įor this benchmark, we use 1,024 steps (the depth of the tree). The algorithm is illustrated in the graph below: After repeating this process for all time steps, the root node holds the present value. ![]() 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. This benchmark application prices a portfolio of American call options using a Binomial lattice (Cox, Ross and Rubenstein method).įor 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). Giles, “Monte Carlo evaluation of sensitivities in computational finance,” HERCMA Conference, Athens, Sep. To study the performance, the number of Monte-Carlo paths is varied between 128K-2,048K. 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 full algorithm is illustrated in the processing graph below: ![]() Averaging the per-path prices gives the final net present value of the portfolio. The swaption portfolio payoff is then computed and discounted to the pricing date. 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. This application prices a portfolio of LIBOR swaptions on a LIBOR Market Model using a Monte-Carlo simulation. ![]()
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