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Generic pricing of FX, inflation and stock options under stochastic interest rates and stochastic volatility

  • Alexander van Haastrecht
  • Antoon Pelsser

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 Schobel 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.

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Article provided by Taylor & Francis Journals in its journal Quantitative Finance.

Volume (Year): 11 (2011)
Issue (Month): 5 ()
Pages: 665-691

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Handle: RePEc:taf:quantf:v:11:y:2011:i:5:p:665-691
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