Pricing of Exotic Options

Abstract

In Chapter 4 we have discussed the pricing of plain-vanilla options by means of finite differences. The methods were based on the simple partial differential equation (4.2),

$$$${}_{{c_j}}{S^j}\frac{{{\partial ^j}y}}{{\partial {S^j}}}$$$$

which was obtained from the Black-Scholes equation (4.1) for V (S, t) via the transformations (4.3). These transformations could be applied because ∂V/∂t in the Black-Scholes equation is a linear combination of terms of the type

$$$$d{X_t} = a({X_t},t)dt + b({X_t},t)d{W_t}\quad for\quad 0 \leqslant t \leqslant T.$$$$

with constants c _i , j = 0, 1, 2.