Abstract
This chapter is devoted to exotic options, which include multifactor options and Asian options. Non-constant coefficients require numerical methods for more general PDEs than those discussed in Chap. 6 Upwind schemes, stability issues and total variation diminishing are discussed. The final part of the chapter is devoted to penalty methods, here applied to a two-asset option.
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Notes
- 1.
Again, the name has no geographical relevance.
- 2.
The ordinary integral A t is random but has zero quadratic variation [340].
- 3.
After interpolation; MATLAB graphics; similar [385].
- 4.
In case of a continuous dividend flow δ, replace r by r −δ.
- 5.
L stands for the wave length or the length of the interval. In case of a partition into n steps of size Δx, ηΔx = 2π∕n. Without loss of generality, we may set L = 2π, so η = 1 for the following analysis. It will be sufficient to study the propagation of eikx.
- 6.
In fact, the situation is more subtle. We postpone an outline of how dispersion is responsible for the oscillations to Sect. 6.5.2.
- 7.
Actually, the LCP (6.44) is nonlinear as well, which is not correctly reflected by the name “LCP”.
- 8.
For δ 1 > r or δ 2 > r the “other” quotient is upwind.
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Seydel, R.U. (2017). Pricing of Exotic Options. In: Tools for Computational Finance. Universitext. Springer, London. https://doi.org/10.1007/978-1-4471-7338-0_6
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