Abstract
In this chapter we review some exotic optioins and show how they can be priced by Monte Carlo methods. Pricing options that depend on the price history of the underlying is a major theoretical challenge for analytical methods. In many cases Monte Carlo is the only practical solution.
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- 1.
Only one is negative the first time.
- 2.
Expand the function f(a, b) = a ∕ b in a Taylor series through first order terms about the means μ A and μ B and take expectation.
- 3.
This is a discrete example of convolution smoothing. The general form is \(m(t)=\int _{-\infty }^{\infty }f(t-s)k(s)ds\) where f() is the function to be smoothed, m() is the smoothed version and k() is the smoothing kernel. In the discrete analogy here k(s) = 1 for − 5 ≤ s ≤ 5 and 0 otherwise.
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Shonkwiler, R.W. (2013). Pricing Exotic Options. In: Finance with Monte Carlo. Springer Undergraduate Texts in Mathematics and Technology. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8511-7_4
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