The Pricing and Hedging of Options in Finitely Elastic Markets
Standard derivative pricing theory is based on the assumption of the market for the underlying asset being infinitely elastic. We relax this hypothesis and study if and how a large agent whose trades move prices can replicate the payoff of a derivative contract. Our analysis extends a prior work of Jarrow who has analyzed this question in a binomial setting to economies with continuous security trading. We characterize the solution to the hedge problem in terms of a nonlinear partial differential equation and provide results on existence and uniqueness of this equation. Simulations are used to compare the hedge ratio in our model to standard Black-Scholes strategies. Moreover, we discuss how standard option pricing theory can be extended to finitely elastic markets.
|Date of creation:||Jun 1996|
|Date of revision:|
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- Yaacov Z. Bergman & Bruce D. Grundy & Zvi Wiener, . "Theory of Rational Option Pricing: II (Revised: 1-96)," Rodney L. White Center for Financial Research Working Papers 11-95, Wharton School Rodney L. White Center for Financial Research.
- Basak, Suleyman, 1995. "A General Equilibrium Model of Portfolio Insurance," Review of Financial Studies, Society for Financial Studies, vol. 8(4), pages 1059-90.
- Jarrow, Robert A., 1992. "Market Manipulation, Bubbles, Corners, and Short Squeezes," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 27(03), pages 311-336, September.
- Platen, Eckhard & Martin Schweizer, 1994. "On Smile and Skewness," Discussion Paper Serie B 302, University of Bonn, Germany.
- Gennotte, Gerard & Leland, Hayne, 1990.
"Market Liquidity, Hedging, and Crashes,"
American Economic Review,
American Economic Association, vol. 80(5), pages 999-1021, December.
- Gerard Gennotte and Hayne Leland., 1989. "Market Liquidity, Hedging and Crashes," Research Program in Finance Working Papers RPF-192, University of California at Berkeley.
- Gerard Gennotte and Hayne Leland., 1989. "Market Liquidity, Hedging and Crashes," Research Program in Finance Working Papers RPF-184, University of California at Berkeley.
- Jarrow, Robert A., 1994. "Derivative Security Markets, Market Manipulation, and Option Pricing Theory," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 29(02), pages 241-261, June.
- Sanford J. Grossman, 1987.
"An Analysis of the Implications for Stock and Futures Price Volatility of Program Trading and Dynamic Hedging Strategies,"
NBER Working Papers
2357, National Bureau of Economic Research, Inc.
- Grossman, Sanford J, 1988. "An Analysis of the Implications for Stock and Futures Price Volatility of Program Trading and Dynamic Hedging Strategies," The Journal of Business, University of Chicago Press, vol. 61(3), pages 275-98, July.
- Oliver D. Hart, 1977. "On The Profitability of Speculation," The Quarterly Journal of Economics, Oxford University Press, vol. 91(4), pages 579-597.
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