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A No-Arbitrage Martingale Analysis for Jump-Diffusion Valuation

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  • Chang, Carolyn W

Abstract

This 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.

Suggested Citation

  • Chang, Carolyn W, 1995. "A No-Arbitrage Martingale Analysis for Jump-Diffusion Valuation," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 18(3), pages 351-381, Fall.
  • Handle: RePEc:bla:jfnres:v:18:y:1995:i:3:p:351-81
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    Cited by:

    1. David Cummins & Christopher Lewis & Richard Phillips, 1999. "Pricing Excess-of-Loss Reinsurance Contracts against Cat as trophic Loss," NBER Chapters,in: The Financing of Catastrophe Risk, pages 93-148 National Bureau of Economic Research, Inc.
    2. Chang, Carolyn W. & S.K. Chang, Jack & Lim, Kian-Guan, 1998. "Information-time option pricing: theory and empirical evidence," Journal of Financial Economics, Elsevier, vol. 48(2), pages 211-242, May.

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