THE FORWARD PDE FOR EUROPEAN OPTIONS ON STOCKS WITH FIXED FRACTIONAL JUMPS

Peter Carr and Alireza Javaheri ()
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Alireza Javaheri: Citigroup, 388 Greewich Street, New York, NY 10013, USA;

International Journal of Theoretical and Applied Finance (IJTAF), 2005, vol. 08, issue 02, 239-253

Abstract: We derive a partial integro differential equation (PIDE) which relates the price of a calendar spread to the prices of butterfly spreads and the functions describing the evolution of the process. These evolution functions are the forward local variance rate and a new concept called the forward local default arrival rate. We then specialize to the case where the only jump which can occur reduces the underlying stock price by a fixed fraction of its pre-jump value. This is a standard assumption when valuing an option written on a stock which can default. We discuss novel strategies for calibrating to a term and strike structure of European options prices. In particular using a few calendar dates, we derive closed form expressions for both the local variance and the local default arrival rate.

Keywords: Credit risk; default risk; forward equations; jump diffusion (search for similar items in EconPapers)
Date: 2005
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Citations: View citations in EconPapers (2)

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DOI: 10.1142/S0219024905002974

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