Generic Pricing of FX, Inflation and Stock Options Under Stochastic Interest Rates and Stochastic Volatility
Alexander Van Haastrecht
Delta Lloyd; VU University Amsterdam - Faculty of Economics and Business Administration
Maastricht University; Netspar
February 7, 2009
We consider the pricing of FX, inflation and stock options under stochastic interest rates and stochastic volatility, for which we use a generic multi-currency framework. We allow for a general correlation structure between the drivers of the volatility, the inflation index, the domestic (nominal) and the foreign (real) rates. Having the flexibility to correlate the underlying FX/Inflation/Stock index with both stochastic volatility and stochastic interest rates yields a realistic model, which is of practical importance for the pricing and hedging of options with a long-term exposure. We derive explicit valuation formulas for various securities, such as vanilla call/put options, forward starting options, inflation-indexed swaps and inflation caps/floors. These vanilla derivatives can be valued in closed-form under Schobel and Zhu (1999) stochastic volatility, whereas we devise an (Monte Carlo) approximation in the form of a very effective control variate for the general Heston (1993) model. Finally, we numerical investigate the quality of this approximation and consider a calibration example to FX market data.
Number of Pages in PDF File: 45
Keywords: Stochastic volatility, Stochastic interest rates, Foreign Exchange, Inflation, Equity, Hybrids
JEL Classification: C10working papers series
Date posted: August 6, 2008 ; Last revised: February 22, 2009
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