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Abstract: In equity and foreign exchange markets the risk-neutral dynamics of theunderlying asset are commonly represented by stochastic volatility models withjumps. In this paper we consider a dense subclass of such models and developanalytically tractable formulae for the prices of a range of first-generationexotic derivatives. We provide closed form formulae for the Fourier transformsof vanilla and forward starting option prices as well as a formula for theslope of the implied volatility smile for large strikes. A simple explicitapproximation formula for the variance swap price is given. The prices ofvolatility swaps and other volatility derivatives are given as aone-dimensional integral of an explicit function. Analytically tractableformulae for the Laplace transform in maturity of the double-no-touch optionsand the Fourier-Laplace transform in strike and maturity of the doubleknock-out call and put options are obtained. The proof of the latter formulaeis based on extended matrix Wiener-Hopf factorisation results. We also provideconvergence results.



Autor: Aleksandar Mijatović, Martijn Pistorius

Fuente: https://arxiv.org/



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