Keep on smiling? The pricing of Quanto options when all covariances are stochastic
AbstractThe paper introduces a model for the joint dynamics of asset prices which can capture both a stochastic correlation between stock returns as well as between stock returns and volatilities (stochastic leverage). By relying on two factors for stochastic volatility, the model allows for stochastic leverage and is thus able to explain time-varying slopes of the smiles. The use of Wishart processes for the covariance matrix of returns enables the model to also capture stochastic correlations between the assets. Our model offers an integrated pricing approach for both Quanto and plain-vanilla options on the stock as well as the foreign exchange rate. We derive semi-closed form solutions for option prices and analyze the impact of state variables. Quanto options offer a significant exposure to the stochastic covariance between stock prices and exchange rates. In contrast to standard models, the smile of stock options, the smile of currency options, and the price differences between Quanto options and plain-vanilla options can change independently of each other.
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Bibliographic InfoArticle provided by Elsevier in its journal Journal of Banking & Finance.
Volume (Year): 36 (2012)
Issue (Month): 6 ()
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Web page: http://www.elsevier.com/locate/jbf
Stochastic volatility; Stochastic correlation; Quantos; Wishart processes;
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- G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
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- 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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