introjump - presented Along the way the main...

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Financial Mathematics Seminar Introduction to Jump Processes Pierre Garreau January 14, 2010 Abstract It is well known today that L´ evy processes show a better fit to market data than the geometric Brownian motion used in the Black-Scholes Model. Merton’s Jump Diffusion model, introduced in 1976, adds a Jump part to the Brownian component in order to take into account discontinuities in the log-returns. This mini course presents elements of the theory of L´ evy processes in order to fully understand the later model and lead a robust presentation of pricing and hedg- ing vanilla options. After a quick reminder on Poisson processes, a model for the risky asset is
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Unformatted text preview: presented. Along the way, the main characteristics o± L´ evy processes are intro-duced in the Jump DiFusion case: The L´ evy Khintchine ±ormula, Martingale conditions, Independence Lemmas, Admissible strategies. References [1] Benhamou, E., 2000, Option Pricing with L´ evy Processeses . [2] Lamberton, D. and Lapeyre, B, 1996, Introduction to Stochastic Calculus Applied to Finance , Chapman & Hall. [3] Papapantoleous, A, 2005, An Introduction to L´ evy Processes with Applica-tions in Finance , Lecture notes, University o± Piraeus. [4] Tankov, P. and Rama, C., 2008, Financial Modelling with Jump Processes , Chapman & Hall. 1...
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