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We consider option hedging in a model where the underlying follows an exponential Levy process. We derive approximations to the variance-optimal and to some suboptimal strategies as well as to their mean squared hedging errors. The results are obtained by considering the Levy model as a perturbation of the Black-Scholes model. The approximations depend on the first four moments of logarithmic stock returns in the Levy model and option price sensitivities (greeks) in the limiting Black-Scholes model. We illustrate numerically that our formulas work well for a variety of Levy models suggested in the literature. From a theoretical point of view, it turns out that jumps have a similar effect on hedging errors as discrete-time hedging in the Black-Scholes model.
We discuss the difference between locally risk-minimizing and delta hedging strategies for exponential Levy models, where delta hedging strategies in this paper are defined under the minimal martingale measure. We give firstly model-independent upper
We consider a stochastic volatility model with Levy jumps for a log-return process $Z=(Z_{t})_{tgeq 0}$ of the form $Z=U+X$, where $U=(U_{t})_{tgeq 0}$ is a classical stochastic volatility process and $X=(X_{t})_{tgeq 0}$ is an independent Levy proce
We continue a series of papers where prices of the barrier options written on the underlying, which dynamics follows some one factor stochastic model with time-dependent coefficients and the barrier, are obtained in semi-closed form, see (Carr and It
This article presents differential equations and solution methods for the functions of the form $Q(x) = F^{-1}(G(x))$, where $F$ and $G$ are cumulative distribution functions. Such functions allow the direct recycling of Monte Carlo samples from one
Management of systemic risk in financial markets is traditionally associated with setting (higher) capital requirements for market participants. There are indications that while equity ratios have been increased massively since the financial crisis,