Ekonomická a finančná matematika

Seminar z financnej matematiky
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Autor:  sevcovic [ Pon Nov 19, 2007 10:17 pm ]
Predmet príspevku:  Seminar z financnej matematiky

Seminár z numerických metód riešenia parciálnych diferenciálnych rovníc

On the numerical solution of nonlinear Black-Scholes equations
Julia Ankudinova
Technical University Berlin
dňa 21. novembra 2007 o 15.00 v miestnosti F1/326,
pavilón fyziky, FMFI UK

Abstrakt: Nonlinear Black-Scholes equations have been increasingly attracting interest over the last two decades, since they provide a more accurate evaluation of financial derivatives by taking into account more realistic assumptions, such as transaction costs, risks from an unprotected portfolio, large investor's preferences or illiquid markets, which may have an impact on the stock price, the volatility, the drift and the option price itself. In this talk we will be concerned with several transaction cost models from the most relevant class of nonlinear Black-Scholes equations for European options, where the volatility depends on different factors, such as the stock price, the time, the option price and its derivatives. We will analytically approach the option price by transforming the problem for a European Call option into a convection-diffusion equation with a nonlinear term. Finally, we will present the results of different numerical discretization schemes for various volatility models including the Leland model, the Barles and Soner model and the Risk adjusted pricing methodology model.

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