Probability Seminar: Pavel Gapeev - Perpetual American Options in Two-Dimensional Diffusion Models
| Dates: | 2 April 2025 |
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| Times: | 14:00 - 15:00 |
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| What is it: | Seminar |
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| Organiser: | Department of Mathematics |
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Pavel Gapeev (London School of Economics) will speak at the Probability seminar.
Title: Perpetual American Options in Two-Dimensional Diffusion Models
Abstract:
We study optimal stopping problems for two-dimensional geometric Brownian motions driven by constantly correlated standard Brownian motions on an infinite time interval. These problems are related to the pricing of perpetual American options such as basket options (with an additive payoff structure) and traffic-light options (with a multiplicative payoff structure) in a two-dimensional Black-Merton-Scholes model. We find closed formulas for the value functions expressed in terms of the optimal stopping boundaries which in turn are shown to be unique solutions to the appropriate nonlinear Fredholm integral equations. A key argument in the existence proof is played by a pointwise maximisation of the expressions obtained by the change-of-measure arguments. This provides tight bounds on the optimal exercise boundaries describing its asymptotic behaviour for marginal coordinate values.
The presentation is based on the ongoing work with Goran Peskir (Manchester).
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Alan Turing Building
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