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.
Original language | English (US) |
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Pages (from-to) | 239-253 |
Number of pages | 15 |
Journal | International Journal of Theoretical and Applied Finance |
Volume | 8 |
Issue number | 2 |
DOIs | |
State | Published - Mar 2005 |
Keywords
- Credit risk
- Default risk
- Forward equations
- Jump diffusion
ASJC Scopus subject areas
- Finance
- Economics, Econometrics and Finance(all)