Option pricing under linear autoregressive dynamics,heteroskedasticity, and conditional leptokurtosis |
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| Affiliation: | 1. Electrabel, R&D Energy Markets, Traverse d''Esope 6, B-1348 Louvain-la-Neuve, Belgium;2. Institut für Statistik und Ökonometrie, Humboldt-Universität zu Berlin, Spandauer Str. 1, D-10178 Berlin, Germany;1. Department of Trauma and Orthopaedic Surgery, Whittington Hospital, London, UK;2. Department of Anaesthesia and Critical Care, Queen''s Medical Centre, Nottingham, UK;3. First Department of Orthopedics, Athens University Medical School, Athens, Greece;4. Department of Anatomy, Medical School, National and Kapodistrian University of Athens, Greece;1. Department of Mathematics and Statistics, Hang Seng Management College, Hang Shin Link, Siu Lek Yuen, Shatin, N.T., Hong Kong;2. Department of Information Systems, Business Statistics and Operations Management, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong;1. University of Portsmouth, Portsmouth Business School, Economics and Finance Subject Group, Richmond Building, Portland Street, PO1 3DE, UK;2. Al Yamamah University, 7010 King Fahd Road, Al Qirawan, Riyadh 13541, Saudi Arabia;1. Departamento de Matemática, ICMC-USP - São Carlos, Caixa Postal 668, 13560-970 São Carlos SP, Brazil;2. School of Mathematics, Statistics and Physics, Newcastle University, NE1 7RU, United Kingdom;3. Departamento de Matemática, Universidad técnica Federico Santa María, 2360102 Valparaíso, Chile |
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| Abstract: | Daily returns of financial assets are frequently found to exhibit positive autocorrelation at lag 1. When specifying a linear AR(1) conditional mean, one may ask how this predictability affects option prices. We investigate the dependence of option prices on autoregressive dynamics under stylized facts of stock returns, i.e. conditional heteroskedasticity, leverage effect, and conditional leptokurtosis. Our analysis covers both a continuous and discrete time framework. The results suggest that a non-zero autoregression coefficient tends to increase the deviation of option prices from Black and Scholes prices caused by stochastic volatility. |
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