Scandinavian Working Papers in Economics

SSE/EFI Working Paper Series in Economics and Finance,
Stockholm School of Economics

No 165: Discrete Time Hedging of OTC Options in a GARCH Environment: A Simulation Experiment

Gustaf E. Hagerud
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Gustaf E. Hagerud: Department of Finance, Postal: Stockholm School of Economics, Box 6501, 113 83 Stockholm, Sweden

Abstract: This paper examines the effect of using Black and Scholes formula for pricing and hedging options in a discrete time heteroskedastic environment. This is done by a simulation procedure where asset returns are generated from a GARCH (1,1)-t model. In the simulation a hypothetical trader writes an option and then delta- hedges his position until the option expires. It is shown that the variance of the returns on the hedged position is considerably higher in a GARCH (1,1) environment than in a homoskedastic environment. The variance of returns depends greatly on the level of kurtosis in the returns process and on the first-order autocorrelation in centered and squared returns.

Keywords: GARCH; option pricing; Black and Scholes formula; Monte Carlo experiment

JEL-codes: C15; C22

22 pages, March 1997

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