Discrete time hedging with liquidity risk
AbstractWe study a discrete time hedging and pricing problem in a market with liquidity costs. Using Leland’s discrete time replication scheme [Leland, H.E., 1985. Journal of Finance, 1283–1301], we consider a discrete time version of the Black–Scholes model and a delta hedging strategy. We derive a partial differential equation for the option price in the presence of liquidity costs and develop a modified option hedging strategy which depends on the size of the parameter for liquidity risk. We also discuss an analytic method of solving the pricing equation using a series solution.
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Bibliographic InfoArticle provided by Elsevier in its journal Finance Research Letters.
Volume (Year): 9 (2012)
Issue (Month): 3 ()
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Web page: http://www.elsevier.com/locate/frl
Discrete time; Liquidity cost; Delta hedging;
Find related papers by JEL classification:
- C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General
- C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
- G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
- G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
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- Leland, Hayne E, 1985.
" Option Pricing and Replication with Transactions Costs,"
Journal of Finance,
American Finance Association, vol. 40(5), pages 1283-1301, December.
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- 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.
- U. �etin & R. Jarrow & P. Protter & M. Warachka, 2006. "Pricing Options in an Extended Black Scholes Economy with Illiquidity: Theory and Empirical Evidence," Review of Financial Studies, Society for Financial Studies, vol. 19(2), pages 493-529.
- Back, Kerry, 1993. "Asymmetric Information and Options," Review of Financial Studies, Society for Financial Studies, vol. 6(3), pages 435-72.
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