A No-Arbitrage Martingale Analysis for Jump-Diffusion Valuation
AbstractThis study presents a jump-diffusion valuation framework using the no-arbitrage martingale approach. Equilibrium conditions needed to support a jump-diffusion pricing standard process are derived. The results are a generalized jump-diffusion security market line and its corresponding equilibrium valuation relation that prices both jump and diffusion risk. To value options, a fundamental formula is derived that includes existing jump-diffusion option valuation formulas as special cases. I find Merton's (1976) assumption of diversifiable jump risk to be consistent with no-arbitrage only when the aggregate consumption flow does not jump. Simulation shows that Merton's formula undervalues/overvalues options on hedging/cyclical assets. When the jump arrival frequency is larger, the mispricing is larger/smaller for in-the-money/out-of-the-money options.
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Bibliographic InfoArticle provided by Southern Finance Association & Southwestern Finance Association in its journal Journal of Financial Research.
Volume (Year): 18 (1995)
Issue (Month): 3 (Fall)
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- David Cummins & Christopher Lewis & Richard Phillips, 1999.
"Pricing Excess-of-Loss Reinsurance Contracts against Cat as trophic Loss,"
in: The Financing of Catastrophe Risk, pages 93-148
National Bureau of Economic Research, Inc.
- J. David Cummins & Christopher M. Lewis & Richard D. Phillips, 1998. "Pricing Excess-of-loss Reinsurance Contracts Against Catastrophic Loss," Center for Financial Institutions Working Papers 98-09, Wharton School Center for Financial Institutions, University of Pennsylvania.
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