Pricing perpetual put options by the Black-Scholes equation with a nonlinear volatility function
We investigate qualitative and quantitative behavior of a solution to the problem of pricing American style of perpetual put options. We assume the option price is a solution to a stationary generalized Black-Scholes equation in which the volatility may depend on the second derivative of the option...
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| Other Authors: | , |
| Format: | workingPaper |
| Language: | eng |
| Published: |
2018
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| Subjects: | |
| Online Access: | http://hdl.handle.net/10400.5/16343 |
| Country: | Portugal |
| Oai: | oai:www.repository.utl.pt:10400.5/16343 |
| Summary: | We investigate qualitative and quantitative behavior of a solution to the problem of pricing American style of perpetual put options. We assume the option price is a solution to a stationary generalized Black-Scholes equation in which the volatility may depend on the second derivative of the option price itself. We prove existence and uniqueness of a solution to the free boundary problem. We derive a single implicit equation for the free boundary position and the closed form formula for the option price. It is a generalization of the well-known explicit closed form solution derived by Merton for the case of a constant volatility. We also present results of numerical computations of the free boundary position, option price and their dependence on model parameters. |
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