Using the Laplace transform approach, we compute expected value and variance of the error of a hedging strategy for a contingent claim when trading in discrete time. The method applies to a fairly general class of models, including Black-Scholes, Merton's jump-diffusion and Normal Inverse Gaussian, and to several interesting strategies, as the Black-Scholes delta, the Wilmott's improved-delta and the locally risk-minimizing strategy. The formulas obtained are valid for any fixed number of trading dates, whereas all previous results are asymptotic approximations. They can also be employed under model mispecification, to measure the influence of model risk on a hedging strategy.
Measuring the error of dynamic hedging:a Laplace transform approach
ANGELINI, Flavio;
2009
Abstract
Using the Laplace transform approach, we compute expected value and variance of the error of a hedging strategy for a contingent claim when trading in discrete time. The method applies to a fairly general class of models, including Black-Scholes, Merton's jump-diffusion and Normal Inverse Gaussian, and to several interesting strategies, as the Black-Scholes delta, the Wilmott's improved-delta and the locally risk-minimizing strategy. The formulas obtained are valid for any fixed number of trading dates, whereas all previous results are asymptotic approximations. They can also be employed under model mispecification, to measure the influence of model risk on a hedging strategy.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
