Hedging and option pricing:
Black-Scholes model and beyond
Author: Karol Zyczkowski
The celebrated Black-Scholes model allows one to compute the price of an option (or
some other financial derivatives) and to find the optimal strategy for hedging the
investors portfolio. However, the solution obtained is correct only within the theoretical
model based on the assumptions of the ideal market.
In existing financial markets several assumptions, crucial for derivation of the
Black-Scholes formula, are not fulfilled. We review the list of these assumptions and
discuss, to what extend it is possible to extend the classical B-S theory to make it
applicable for the real markets. In particular we study the model with non Gaussian
distributions of the relative price changes and analyze the influence of the market
friction (transaction costs).
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