Efficient Analytic Approximation of the Optimal Hedging Strategy for a European Call Option with Transaction Costs

This article investigates the optimal hedging problem of the European contingent claims written on non-tradable assets. We assume that the risky assets satisfy jump diffusion models with a common jump process which reflects the correlated jump risk. The non-tradable asset and jump risk lead to an incomplete financial market. Hence, the cross-hedging method will be used to reduce the potential risk of the contingent claims seller. First, we obtain an explicit closed-form solution for the locally risk-minimizing hedging strategies of the European contingent claims by using the Föllmer–Schweizer decomposition. Then, we consider the hedging for a European call option as a special case. The value of the European call option under the minimal martingale measure is derived by the Fourier transform method. Next, some semi-closed solution formulae of the locally risk-minimizing hedging strategies for the European call option are obtained. Finally, some numerical examples are provided to illustrate the sensitivities of the optimal hedging strategies. By comparing the optimal hedging strategies when the underlying asset is a non-tradable asset or a tradable asset, we find that the liquidity risk has a significant impact on the optimal hedging strategies.

Download Full-text

Nonconvergence in the Variation of the Hedging Strategy of a European Call Option

Mathematical Finance ◽

10.1111/1467-9965.t01-1-00024 ◽

2003 ◽

Vol 13 (4) ◽

pp. 467-480

Author(s):

R. Th. Peters

Keyword(s):

Call Option ◽

Hedging Strategy ◽

European Call Option

Download Full-text

THE BEST HEDGING STRATEGY IN THE PRESENCE OF TRANSACTION COSTS

International Journal of Theoretical and Applied Finance ◽

10.1142/s0219024909005488 ◽

2009 ◽

Vol 12 (06) ◽

pp. 833-860 ◽

Cited By ~ 2

Author(s):

VALERI ZAKAMOULINE

Keyword(s):

Transaction Costs ◽

Theoretical Work ◽

Optimization Method ◽

Call Option ◽

Empirical Comparison ◽

Hedging Strategy ◽

Option Hedging ◽

Hedging Strategies ◽

Short Call ◽

The Subject

Considerable theoretical work has been devoted to the problem of option pricing and hedging with transaction costs. A variety of methods have been suggested and are currently being used for dynamic hedging of options in the presence of transaction costs. However, very little was done on the subject of an empirical comparison of different methods for option hedging with transaction costs. In a few existing studies the different methods are compared by studying their empirical performances in hedging only a plain-vanilla short call option. The reader is tempted to assume that the ranking of the different methods for hedging any kind of option remains the same as that for a vanilla call. The main goal of this paper is to show that the ranking of the alternative hedging strategies depends crucially on the type of the option position being hedged and the risk preferences of the hedger. In addition, we present and implement a simple optimization method that, in some cases, improves considerably the performance of some hedging strategies.

Download Full-text