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Exact Pricing with Stochastic Volatility and Jumps

25 Pages Posted: 4 Oct 2014 Last revised: 11 Oct 2014

Fernanda D'Ippoliti

Independent

Enrico Moretto

University of Insubria - Department of Economics; CNR - IMATI

Sara Pasquali

CNR-IMATI

Barbara Trivellato

Polytechnic University of Turin - Dipartimento di Matematica

Date Written: 2010

Abstract

A stochastic volatility jump-diffusion model for pricing derivatives with jumps in both spot returns and volatility dynamics is presented. This model admits, in the spirit of Heston, a closed-form solution for European-style options. The structure of the model is also suitable to obtain the fair delivery price of variance swaps. To evaluate derivatives whose value does not admit a closed-form expression, a methodology based on an "exact algorithm'', in the sense that no discretization of equations is required, is developed and applied to barrier options. Goodness of pricing algorithm is tested using DJ Euro Stoxx 50 market data for European options. Finally, the algorithm is applied to compute prices and Greeks of barrier options.

Keywords: Monte Carlo simulation, derivative valuation, stochastic volatility jump-diffusion model

Suggested Citation

D'Ippoliti, Fernanda and Moretto, Enrico and Pasquali, Sara and Trivellato, Barbara, Exact Pricing with Stochastic Volatility and Jumps (2010). International Journal of Theoretical and Applied Finance, Vol. 13, No. 6, 2010. Available at SSRN: https://ssrn.com/abstract=2504645

Fernanda D'Ippoliti

Independent ( email )

No Address Available

Enrico Moretto (Contact Author)

University of Insubria - Department of Economics ( email )

Via Ravasi 2
Varese, 21100
Italy

CNR - IMATI ( email )

via Bassini 15
Milano, 20133
Italy

Sara Pasquali

CNR-IMATI ( email )

via Bassini 15
Milano, 20133
Italy

Barbara Trivellato

Polytechnic University of Turin - Dipartimento di Matematica ( email )

Corso Duca degli Abruzzi, 24
Torino, Torino 10129
Italy

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