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

A.A.J. Pelsser, A. van Haastrecht*

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

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 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.

Original languageEnglish
Pages (from-to)665-691
Number of pages27
JournalQuantitative Finance
Volume11
Issue number5
DOIs
Publication statusPublished - 1 Jan 2011

Keywords

  • Foreign Exchange
  • Inflation
  • Equity
  • Stochastic volatility
  • Stochastic interest rates
  • Hybrids

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