Optimal partial hedging of options with small transaction costs
نویسنده
چکیده
We use asymptotic analysis to derive the optimal hedging strategy for an option portfolio hedged using an imperfectly correlated hedging asset with small transaction costs, both fixed per trade and proportional to the value traded. In special cases we opbtain explicit formulae. The hedging strategy involves holding a position in the hedging asset whose value lies between two bounds, which are independent of the value of the hedging asset itself, as is the option value. The bounds depend on the leading order Gamma and Delta of the option position. Decreasing absolute correlation decreases the absolute value of the centre of the no-transaction band, the no-transaction bandwidth and the certainty equivalent value of transaction costs. However generally the increase in unhedgeable risk has a greater effect on option values, which decrease with |ρ|. JEL: G13
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