Conditional Monte Carlo Allowing for Stochastic Drift in Long-term Implied Volatility Calibration
Document ID: 2008-927 (previously 2008/006)
Published on: 31st July 2008
The presence of stochastic “drift” in models describing equity, FX and inflation indices makes the evaluation of vanilla option prices in such models non-trivial and Monte Carlo is often required in the absence of analytic pricing formulae. Unfortunately, “brute force” Monte Carlo is often too inefficient for fast calibration purposes. This note describes a variance reduction technique, Conditional Monte Carlo, in which Monte Carlo estimates are supplemented with analytic results where available. We illustrate how the technique can be applied to valuation of vanilla equity and FX options in the presence of stochastic interest-rates and demonstrate its effectiveness in calibrating these models.
