Abstract:
Options are very important nancial instruments and, like any other its kind, require
very accurate quantitative models in order to serve its usefulness. The Black-Scholes
model provides a good option pricing formula in a given market setting. In this work,
we quantify the e ects of the assumptions of the Black-Schole's nancial market on
their pricing formula. We expand their model by relaxing these assumptions and
derive an option pricing formula in a more realistic nancial environment. This
requires the introduction of a new hedging strategy and the remodeling of stock
prices and therefore the market volatility in the Black-Scholes pricing formula to
re
ect some activities and consequences of modern exchanges or trading markets.
This work is organized such that the numerical treatment of the Black-Scholes'
classical linear option pricing model is considered, followed by the derivation of an
option pricing equation based on the relaxation of Black-Scholes market assumptions
and then, the presentation of a numerical solution of the resulting nonlinear and
generalized Black-Scholes model.
