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A Note on a Moving Boundary Problem Arising in the American Put Option
Author(s) -
Knessl Charles
Publication year - 2001
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/1467-9590.00183
Subject(s) - singular perturbation , mathematics , free boundary problem , put option , boundary (topology) , valuation of options , boundary problem , black–scholes model , asian option , asymptotic expansion , nonlinear system , mathematical analysis , expiration date , volatility (finance) , economics , econometrics , actuarial science , physics , quantum mechanics , chemistry , food science
We consider an American put option, under the Black–Scholes model. This corresponds to a moving boundary problem for a PDE. We convert the problem to a nonlinear integral equation for the moving boundary, which corresponds to the optimal exercise of the option. We use singular perturbation methods to compute the moving boundary, as well as the full solution to the PDE, in various asymptotic limits. We consider times close to the expiration date, as well as systems where the interest rate is large or small, relative to the volatility of the asset for which the option is sold.