A Jump and Smile Ride: Jump and Variance Risk Premia in Option Pricing

46 Pages Posted: 17 Jul 2015 Last revised: 10 Mar 2019

See all articles by Dario Alitab

Dario Alitab

Scuola Normale Superiore

Giacomo Bormetti

University of Bologna - Department of Mathematics

Fulvio Corsi

University of Pisa - Department of Economics; City University London

Adam Majewski

Capital Fund Management

Date Written: March 8, 2019

Abstract

We introduce a discrete-time model for log-return dynamics with observable volatility and jumps. Our proposal extends the class of Realized Volatility heterogeneous auto-regressive gamma (HARG) processes adding a jump component with time-varying intensity. The model is able to reproduce the temporary increase in the probability of occurrence of a jump immediately after an abrupt large movement of the asset price. Belonging to the class of exponentially affine models, the moment generating function under the physical measure is available in closed-form. Thanks to a flexible specification of the pricing kernel compensating for equity, volatility, and jump risks, the generating function under the risk-neutral measure inherits analytical tractability too. An application of the leveraged HARG model with dynamic jump intensity to the pricing of a large sample of S&P500 index options assesses its superior performances with respect to state-of-the-art benchmark models.

Keywords: High-frequency, Realized volatility, HARG, Option pricing, Variance risk premium, Jumps

JEL Classification: G12, G13

Suggested Citation

Alitab, Dario and Bormetti, Giacomo and Corsi, Fulvio and Majewski, Adam, A Jump and Smile Ride: Jump and Variance Risk Premia in Option Pricing (March 8, 2019). Available at SSRN: https://ssrn.com/abstract=2631155 or http://dx.doi.org/10.2139/ssrn.2631155

Dario Alitab (Contact Author)

Scuola Normale Superiore ( email )

Piazza dei Cavalieri, 7
Pisa, 56126
Italy

Giacomo Bormetti

University of Bologna - Department of Mathematics ( email )

Piazza di Porta S. Donato , 5
Bologna, Bologna 40126
Italy

Fulvio Corsi

University of Pisa - Department of Economics ( email )

via Ridolfi 10
I-56100 Pisa, PI 56100
Italy

HOME PAGE: http://people.unipi.it/fulvio_corsi/

City University London ( email )

Northampton Square
London, EC1V OHB
United Kingdom

Adam Majewski

Capital Fund Management ( email )

23 rue de l'Université
Paris, 75007
France

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