Generic pricing of FX,inflation and stock options under stochastic interest rates and stochastic volatility |
| |
Authors: | Alexander van Haastrecht Antoon Pelsser |
| |
Affiliation: | 1. Department of Finance , VU University Amsterdam , De Boelelaan 1105, 1081 HV Amsterdam, The Netherlands;2. Delta Lloyd Leven, Expertisecentrum , Spaklerweg 4, PO Box 1000, 1000 BA Amsterdam, The Netherlands ahaastrecht@feweb.vu.nl;4. Department of Finance, Department of Quantitative Economics , Maastricht University , PO Box 616, 6200 MD Maastricht, The Netherlands |
| |
Abstract: | 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 that 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 Schöbel and Zhu [Eur. Finance Rev., 1999, 4, 23–46] stochastic volatility, whereas we devise an (Monte Carlo) approximation in the form of a very effective control variate for the general Heston [Rev. Financial Stud., 1993, 6, 327–343] model. Finally, we investigate the quality of this approximation numerically and consider a calibration example to FX and inflation market data. |
| |
Keywords: | Foreign Exchange Inflation Equity Stochastic volatility Stochastic interest rates Hybrids |
|
|