Option pricing with discrete time jump processes |
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| Authors: | Dominique Guégan Florian Ielpo Hanjarivo Lalaharison |
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| Affiliation: | 1. University Paris1 Panthéon – Sorbonne, CES UMR 8174, 106 bd de l''Hôpital, 75013 Paris, France;2. Lombard Odier Asset Management, Avenue des Morgines 6, 1213 Petit-Lancy, Switzerland;3. University Paris 1 Panthéon-Sorbonne, MSE, 106 bd de l''Hôpital, 75013 Paris, France;1. Department of Economics, BI Norwegian Business School, Nydalsveien 37, N-0484 Oslo, Norway;2. Humboldt-Universität zu Berlin, School of Economics and Business, Institute of Economic Policy, Spandauer Straße 1, D-10099 Berlin, Germany;1. Department of International Business, National Chengchi University, Taipei 116, Taiwan;2. Department of Business Administration, Hosei University, Tokyo, Japan;1. Università della Svizzera Italiana, Via Buffi 13, CH-6900 Lugano, Switzerland;2. CREST, CEPREMAP, France;3. University of Toronto, Canada;1. University of Wisconsin-Madison, 1180 Observatory Drive, Madison, WI 53706, United States;2. University of Queensland, Australia;1. Department of Economics, Michigan State University, Marshall-Adams Hall, 486 W Circle Dr. Rm 110, East Lansing, MI 48824-1038, USA;2. Southwestern University of Finance and Economics, Chengdu, China;1. Simon Fraser University, Canada;2. Bank of Canada, 234 Wellington Street, Ottawa, Ontario, Canada K1A 0G9;3. University of International Business and Economics, China |
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| Abstract: | In this paper we propose new option pricing models based on class of models with jumps contained in the Lévy-type based models (NIG-Lévy, Schoutens, 2003, Merton-jump, Merton, 1976 and Duan based model, Duan et al., 2007). By combining these different classes of models with several volatility dynamics of the GARCH type, we aim at taking into account the dynamics of financial returns in a realistic way. The associated risk neutral dynamics of the time series models is obtained through two different specifications for the pricing kernel: we provide a characterization of the change in the probability measure using the Esscher transform and the Minimal Entropy Martingale Measure. We finally assess empirically the performance of this modelling approach, using a dataset of European options based on the S&P 500 and on the CAC 40 indices. Our results show that models involving jumps and a time varying volatility provide realistic pricing and hedging results for options with different kinds of time to maturities and moneyness. These results are supportive of the idea that a realistic time series model can provide realistic option prices making the approach developed here interesting to price options when option markets are illiquid or when such markets simply do not exist. |
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| Keywords: | Option pricing Time Jump processes Exponential affine stochastic discount factor Minimal Entropy Martingale Measure S&P 500 CAC 40 |
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