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Weak convergence of equity derivatives pricing with default risk

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  • Qiao, Gaoxiu
  • Yao, Qiang

Abstract

This paper presents a discrete-time equity derivatives pricing model with default risk in a no-arbitrage framework. Using the equity-credit reduced form approach where default intensity mainly depends on the firm’s equity value, we deduce the Arrow–Debreu state prices and the explicit pricing result in discrete time after embedding default risk in the pricing model. We prove that the discrete-time defaultable equity derivatives pricing has convergence stability, and it converges weakly to the continuous-time pricing results.

Suggested Citation

  • Qiao, Gaoxiu & Yao, Qiang, 2015. "Weak convergence of equity derivatives pricing with default risk," Statistics & Probability Letters, Elsevier, vol. 103(C), pages 46-56.
    • Handle: RePEc:eee:stapro:v:103:y:2015:i:c:p:46-56
    DOI: 10.1016/j.spl.2015.04.015
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    References listed on IDEAS

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    1. Robert A. Jarrow & Stuart M. Turnbull, 2008. "Pricing Derivatives on Financial Securities Subject to Credit Risk," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 17, pages 377-409, World Scientific Publishing Co. Pte. Ltd..
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    3. J.W. Nieuwenhuis & M.H. Vellekoop, 2004. "Weak convergence of tree methods, to price options on defaultable assets," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 27(2), pages 87-107, December.
    4. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
    5. Duffie, Darrell & Singleton, Kenneth J, 1999. "Modeling Term Structures of Defaultable Bonds," The Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 687-720.
    6. Christophette Blanchet-Scalliet & Monique Jeanblanc, 2004. "Hazard rate for credit risk and hedging defaultable contingent claims," Finance and Stochastics, Springer, vol. 8(1), pages 145-159, January.
    7. Darrell Duffie & Philip Protter, 1992. "From Discrete‐ to Continuous‐Time Finance: Weak Convergence of the Financial Gain Process1," Mathematical Finance, Wiley Blackwell, vol. 2(1), pages 1-15, January.
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