Pricing of Exotic Options

  • Rüdiger Seydel
Part of the Universitext book series (UTX)


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.


Peclet Number Upwind Scheme Total Variation Diminish Barrier Option Asian Option 
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  1. 1.
    The name has no geographical relevance.Google Scholar
  2. 2.
    after interpolation; MATLAB graphics; courtesy of S. Göbel; simlar [ZFV99]Google Scholar
  3. 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
  4. 1.
    This notation with σ is not related with volatility.Google Scholar
  5. 2.
    repeated independent trials, where only two possible outcomes are possible for each trial, such as tossing a coinGoogle Scholar
  6. 3.
    These digits are listed in [Moro95].Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Rüdiger Seydel
    • 1
  1. 1.Institute of MathematicsUniversity of KölnKölnGermany

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