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Advisor(s)
Abstract(s)
We analyze and calculate the early exercise boundary for a class of stationary generalized Black- Scholes equations in which the volatility function depends on the second derivative of the option price itself. A motivation for studying the nonlinear Black Scholes equation with a nonlinear volatility arises from option pricing models including, e.g., non-zero transaction costs, investors preferences, feedback and illiquid markets effects and risk from unprotected portfolio. We present a method how to transform the problem of American style of perpetual put options into a solution of an ordinary differential equation and implicit equation for the free boundary position. We finally present results of numerical approximation of the early exercise boundary, option price and their dependence on model parameters.
Description
Keywords
Option Pricing Nonlinear Black-Scholes Equation Transaction Costs Early Exercise Boundary
Pedagogical Context
Citation
Grossinho, Maria do Rosário, Yaser Faghan and Daniel Ševčovič. (2017). "Analytical and numerical results for American style of perpetual put options through transformation into nonlinear stationary Black-Scholes equations." In Novel Methods in Computational Finance. Matthias Ehrhardt, Michael Gunther and E. Jan W. ter Maten, (Eds.) Chapter 8 : pp. 129-142. (Search PDF in 2023).
Publisher
Springer