Explain how a Monte Carlo simulation of forward rates works and where it is applied
The idea
Monte Carlo forward-rate simulation generates many random paths of future rates, often monthly, using an assumed volatility and a model of rate behaviour. Cash flows are projected along each path, which suits path-dependent securities such as mortgage-backed securities whose prepayments depend on past rates, and discounted at that path's rates. The value is the average of the path values. The model must first be made arbitrage-free: if it misprices benchmark bonds, a constant drift adjustment is added to the simulated rates until those bonds are priced correctly. More paths reduce sampling error but do not fix a biased model. Mean reversion or bounds can keep rates in a plausible range.
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