Exercise Boundary of the American Put Near Maturity in an Exponential Lévy Model

2011/05/02 by Damien Lamberton, Lamberton, Damien, Mohammed Mikou +1 · 2 citations
Economics, Econometrics and Finance · Social Sciences · #60G40 #60G51 #91G20 #FOS: Economics and business #Financial Markets and Investment Strategies #Insurance, Mortality, Demography, Risk Management #Pricing of Securities (q-fin.PR) #Stochastic processes and financial applications #msc:60G40 #msc:60G51 #msc:91G20 #q-fin.PR

paper · pdf · doi:10.48550/arxiv.1105.0284

arxiv created 2011/05/02 · openalex publication_date 2011/05/02 · arxiv updated 2011/05/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the behavior of the critical price of an American put option near maturity in the exponential Lévy model when the underlying stock pays dividends at a continuous rate. In particular, we prove that, in situations where the limit of the critical price is equal to the stock price, the rate of convergence to the limit is linear if and only if the underlying Lévy process has finite variation. In the case of infinite variation, a variety of rates of convergence can be observed: we prove that, when the negative part of the Lévy measure exhibits an α-stable density near the origin, with 1

Citations

• The Pricing of Options and Corporate Liabilities

Cited by

• Near-Maturity Asymptotics of Critical Prices of American Put Options under Exponential Lévy Models
• American options valuation in time-dependent jump-diffusion models via integral equations and characteristic functions

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