Tools for Computational Finance pp 175-202 | Cite as

# Pricing of Exotic Options

Chapter

## 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),
which was obtained from the Black-Scholes equation (4.1) for
with constants

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

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

*c*_{ i },*j*= 0, 1, 2.## Keywords

Peclet Number Upwind Scheme Total Variation Diminish Barrier Option Asian Option
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## References

- 1.The name has no geographical relevance.Google Scholar
- 2.after interpolation; MATLAB graphics; courtesy of S. Göbel; simlar [ZFV99]Google Scholar
- 3.In fact, the situation is more subtle. We postpone an outline of how
*dispersion*is responsible for the oscillations to the Section 6.4.2.Google Scholar - 1.This notation with
*σ*is not related with volatility.Google Scholar - 2.repeated independent trials, where only two possible outcomes are possible for each trial, such as tossing a coinGoogle Scholar
- 3.These digits are listed in [Moro95].Google Scholar

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© Springer-Verlag Berlin Heidelberg 2004