Sensitivity analysis in the infinite dimensional Heston model

Fred Espen Benth; Giulia Di Nunno; Iben Cathrine Simonsen

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Sensitivity analysis in the infinite dimensional Heston model

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arxiv 2012.12167 v1 pith:4RERBEZ6 submitted 2020-12-22 math.PR

Fred Espen Benth , Giulia Di Nunno , Iben Cathrine Simonsen This is my paper · ORCID

classification math.PR

keywords dimensionalinfiniteforwardmodelanalysisconsiderdifferentgreeks

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We consider the infinite dimensional Heston stochastic volatility model proposed in \arXiv:1706:03500. The price of a forward contract on a non-storable commodity is modelled by a generalized Ornstein-Uhlenbeck process in the Filipovi\'{c} space with this volatility. We prove different representation formulas for the forward price. Then we consider prices of options written on these forward contracts and we study sensitivity analysis with computation of the Greeks with respect to different parameters in the model. Since these parameters are infinite dimensional, we need to reinterpret the meaning of the Greeks. For this we use infinite dimensional Malliavin calculus and a randomization technique.

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