95-224 Claudio Albanese and Stathis Tompaidis
Transaction costs and non-Markovian delta hedging (157K, PostScript) May 17, 95
Abstract , Paper (src), View paper (auto. generated ps), Index of related papers

Abstract. We consider the problem of hedging and pricing European and American derivatives in the continuous time formalism. The underlying security is a stock whose trading involves a small relative transaction cost $k$. If $k=0$, the Black and Scholes optimal trading strategy is Markovian, satisfies the self-financing condition and assures a perfect portfolio replication. If $k>0$, transactions occur at random but discrete times. We find an optimal trading strategy that minimizes total transaction costs for a given degree of risk aversion. Since the calculation of rehedging times is part of the problem in the continuous time setting, optimal strategies are non-Markovian. They also break the self-financing constraint because hedge slippages are risky. We compute the leading term in $\sqrt k$ in an asymptotic expansion in the limit of small transaction costs. We express the rehedging thresholds in terms of the Black and Scholes solution and evaluate the total transaction cost by solving a final value problem for a parabolic equation of the Black and Scholes type.

Files: 95-224.ps