Doctoral thesis

Hedging and risk measurement for option portfolios


117 p

Thèse de doctorat: Università della Svizzera italiana, 2004 (jury note: Summa cum laude)

English In the first part of this work we address the problem of parameter misspecification in a generic class of stochastic volatility models. We extend the approach proposed by Avellaneda, Levy and Paràs (1995) (hereafter ALP) by moving from a framework with uncertain volatility to the uncertainty on volatility process parameters. We assume that parameter values of the stochastic volatility model are unknown but limited between two bounds and we find a PDE whose solutions represent seller and buyer’s prices of a European contingent claim. Compared to the super-hedging bounds of the ALP approach, the super-hedging bounds under stochastic volatility get closer to each other and they could be conveniently used to define a bid-ask spread. Moreover, a Monte Carlo experiment shows that the super-hedging under stochastic volatility solves both the parameter misspecification problem and some cases of model misspecification. Also in this case, the proposed super-hedging performs better than the ALP approach. We show that seller and buyer’s prices of a plain vanilla option can be approximated by Heston formula with a slight change of parameters. Moreover, we propose a self-financing strategy in order to super-replicates the claim in a stochastic volatility framework. In the second part of this work, we aim to show the impact of large option positions on different Value-at-Risk (hereafter VaR) estimation methods. The first method considered is completely parametric and it is based on a quadratic approximation while the second is the nonparametric method based on historical simulations. Two generalizations of the standard historical simulation method are presented. The first is proposed by Boudoukh, Richardson and Whitelaw (1998) while the second is proposed by Barone-Adesi, Bourgoin and Giannopoulos (1998). The latter approach is known as filtered historical simulation method. A generalization of the filtered historical simulation method is also presented. The different VaR estimation methods are tested by using an unconditional and a conditional test. The test results show that the methods based on the filtered historical simulation approach performs better than the other VaR estimation methods.
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