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The European options hedge perfectly in a Poisson-Gaussian stock market model

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Author Info
C. Mancini
Abstract

It is shown that n + 1 European call options written on a stock S with different strike prices (or the stock and n calls) are non-redundant assets in a model for the stock driven by a Brownian motion and n independent Poisson processes. That extends the result obtained for n = 1 by Pham and implies that the proposed model can price and perfectly hedge any integrable derivative on S .

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Article provided by Taylor and Francis Journals in its journal Applied Mathematical Finance.

Volume (Year): 9 (2002)
Issue (Month): 2 (June)
Pages: 87-102
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Handle: RePEc:taf:apmtfi:v:9:y:2002:i:2:p:87-102

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Related research
Keywords: Jump-DIFFUSION Stock Model; M-VARIATE Poisson Process; Call Options; Volatility Coefficients; T-BASIS; Total Convergence; Completeness;

References listed on IDEAS
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  1. Rubinstein, Mark, 1994. " Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July. [Downloadable!] (restricted)
  2. Naik, Vasanttilak & Lee, Moon, 1990. "General Equilibrium Pricing of Options on the Market Portfolio with Discontinuous Returns," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 3(4), pages 493-521. [Downloadable!] (restricted)
  3. Amin, Kaushik I, 1993. " Jump Diffusion Option Valuation in Discrete Time," Journal of Finance, American Finance Association, vol. 48(5), pages 1833-63, December. [Downloadable!] (restricted)
  4. Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, vol. 4(1), pages 141-183, Spring. [Downloadable!] (restricted)
  5. Bajeux, I. & Rochet, J.C., 1994. "Dynamic Spanning: Are Options an Appropriate Instrument?," Papers 94.329, Toulouse - GREMAQ.
  6. Cox, John C. & Ross, Stephen A., 1976. "The valuation of options for alternative stochastic processes," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 145-166. [Downloadable!] (restricted)
  7. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144. [Downloadable!] (restricted)
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  8. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June. [Downloadable!] (restricted)
  9. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley. [Downloadable!]
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