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


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  • 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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Bibliographic Info

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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Keywords: Foreign Exchange; Inflation; Equity; Stochastic volatility; Stochastic interest rates; Hybrids;


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Cited by:
  1. Singor, Stefan N. & Grzelak, Lech A. & van Bragt, David D.B. & Oosterlee, Cornelis W., 2013. "Pricing inflation products with stochastic volatility and stochastic interest rates," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 286-299.
  2. Mordecai Avriel & Jens Hilscher & Alon Raviv, 2013. "Inflation Derivatives Under Inflation Target Regimes," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 33(10), pages 911-938, October.
  3. Alessandro Gnoatto & Martino Grasselli, 2013. "An analytic multi-currency model with stochastic volatility and stochastic interest rates," Papers 1302.7246,, revised Mar 2013.
  4. Griselda Deelstra & Gr\'egory Ray\'ee, 2012. "Local Volatility Pricing Models for Long-dated FX Derivatives," Papers 1204.0633,
  5. Grzelak, Lech & Oosterlee, Kees, 2010. "On cross-currency models with stochastic volatility and correlated interest rates," MPRA Paper 23020, University Library of Munich, Germany.


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