Early exercise boundary and option prices in Levy driven models

S. Z. Levendorski

Quantitative Finance, 2004, vol. 4, issue 5, 525-547

Abstract: Pricing and hedging of European. American, barrier options and interest rate derivatives for wide classes of Levy driven models is consideref in situatins where qualitative and quantitative differences between gaussian and Levy modelling are most prominent, and the dependence on the choice of a family of Levy processes is analysed. Asymptotics of option prices near the barrier and expiry are calculated; for American options, two fast numerical methods are constructed. It is shown that for many classes of Levy processes, the early exercise boundary of the American put is separated from the strike by a non-vanishing margin, and as the riskless rate vanishes, the early exercise boundary tends to 0 uniformly over the interval [0, T). Implications for fitting of parameters are discussed.

Date: 2004
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DOI: 10.1080/14697680400000036

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