returns the asset value after a time interval $\Delta$ according to the given discretization. By default, it returns $$ E(\mathrm{x}_0,t_0,\Delta t) + S(\mathrm{x}_0,t_0,\Delta t) \cdot \Delta \mathrm{w} $$ where $E$ is the expectation and $S$ the standard deviation.
returns the expectation $$ E(\mathrm{x}{t_0 + \Delta t} | \mathrm{x}{t_0} = \mathrm{x}_0) $$ of the process after a time interval $ \Delta t $ according to the given discretization. This method can be overridden in derived classes which want to hard-code a particular discretization.
returns the standard deviation $$ S(\mathrm{x}{t_0 + \Delta t} | \mathrm{x}{t_0} = \mathrm{x}_0) $$ of the process after a time interval $ \Delta t $ according to the given discretization. This method can be overridden in derived classes which want to hard-code a particular discretization.
returns the time value corresponding to the given date in the reference system of the stochastic process.
note As a number of processes might not need this functionality, a default implementation is given which raises an exception.
libor-forward-model process
stochastic process of a libor forward model using the rolling forward measure incl. predictor-corrector step
References:
Glasserman, Paul, 2004, Monte Carlo Methods in Financial Engineering, Springer, Section 3.7
Antoon Pelsser, 2000, Efficient Methods for Valuing Interest Rate Derivatives, Springer, 8
Hull, John, White, Alan, 1999, Forward Rate Volatilities, Swap Rate Volatilities and the Implementation of the Libor Market Model (http://www.rotman.utoronto.ca/~amackay/fin/libormktmodel2.pdf)
test the correctness is tested by Monte-Carlo reproduction of caplet & ratchet NPVs and comparison with Black pricing.
warning this class does not work correctly with Visual C++ 6.