A Note on Calibration of Markov Processes
34 Pages Posted: 3 Apr 2009
Date Written: April 3, 2009
Using Malliavin calculus, we derive under the forward probability measure Ito's formula for anticipating processes in the multi-dimensional case. We use it when the instantaneous volatility, the spot rate and the dividend yield of the stock price are Markov processes to approximate solutions of the Black type to the prices of call options as well as binary options. The stochastic dividend yield makes it possible to consider the pricing of contingent claims not only in the equity market but also in the commodities, fixed income and forex markets. We then derive the Greeks of the model, which will be used for the risk management of the exotic products, and approximate the implied volatility surface induced by the model.
Keywords: Malliavin calculus, stochastic dividend yield, stochastic volatility, calibation
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