Generic pricing of FX, inflation and stock options under stochastic interest rates and stochastic volatility
AbstractWe 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 InfoArticle provided by Taylor and Francis Journals in its journal Quantitative Finance.
Volume (Year): 11 (2011)
Issue (Month): 5 ()
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- Mordecai Avriel & Jens Hilscher & Alon Raviv, 2012.
"Inflation Derivatives Under Inflation Target Regimes,"
43, Brandeis University, Department of Economics and International Businesss School.
- 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.
- Griselda Deelstra & Grégory Rayée, 2013.
"Local Volatility Pricing Models for Long-Dated FX Derivatives,"
Applied Mathematical Finance,
Taylor and Francis Journals, vol. 20(4), pages 380-402, September.
- Griselda Deelstra & Gr\'egory Ray\'ee, 2012. "Local Volatility Pricing Models for Long-dated FX Derivatives," Papers 1204.0633, arXiv.org.
- Alessandro Gnoatto & Martino Grasselli, 2013. "An analytic multi-currency model with stochastic volatility and stochastic interest rates," Papers 1302.7246, arXiv.org, revised Mar 2013.
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