Variance Optimal Hedging in the Black-Scholes Model for a given Number of TransactionsReport as inadecuate




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1 MATHFI - Financial mathematics Inria Paris-Rocquencourt, ENPC - École des Ponts ParisTech, UPEC UP12 - Université Paris-Est Créteil Val-de-Marne - Paris 12

Abstract : In the Black-Scholes option pricing paradigm it is assumed that the market-mak- er designs a continuous-time hedge. This is not realistic from a practical point of view. We introduce trading restrictions in the Black-Scholes model in the sense that hedging is only allowed a given number of times-only the number is fixed, the market-maker is free to choose the stopping times and hedge ratios. We identify the strategy which minimizes the variance of the tracking error for a given initial value of the portfolio. The minimal variance is shown to be the solution to a sequence of optimal stopping problems. Existence and uniqueness is proved. We design a lattice algorithm with complexity N3 N being the number of lattice points to solve the corresponding discrete problem in the Cox-Ross-Rubinstein setting. The convergence of the scheme relies on a viscosity solution argument. Numerical results and dynamic simulations are provided.

Keywords : STOCHASTIC INTEGRAL DYNAMIC PROGRAMMING OPTION PRICING VISCOSITY SOLUTIONS OPTIMAL STOPPING DISCRETE HEDGING BLACK-SCHOLES MODEL





Author: Claude Martini - Christophe Patry

Source: https://hal.archives-ouvertes.fr/



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