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Monte Carlo Methods

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Interest Rate Derivatives

Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 666))

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Abstract

Monte Carlo simulation is a robust numerical method to price plain-vanilla products as well as exotic interest rate derivatives. Due to the characteristics of the class of Cheyette models, the distribution of the state variables turns out to be normal with time dependent mean and variance. Therefore, we can apply exact simulation methods without any discretization error in time. Consequently, the results are precise and the simulation is fast. The efficiency can even be improved by using Quasi-Monte Carlo simulations. The pricing method is verified numerically for plain-vanilla and exotic interest rate derivatives in the Three Factor Exponential Model.

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Notes

  1. 1.

    Assume that we want to compute the expected value of a function f depending on the underlying S. The underlying S is simulated independently n times and the expected value is approximated as \(V _{n} = \frac{1} {n}\sum \limits _{i=1}^{n}f(S_{i})\). The standard error is defined as

    $$Std.Error = \frac{1} {\sqrt{n}}\sqrt{ \frac{1} {n - 1}\displaystyle\sum \limits _{i=1}^{n}{(f(S_{i}) - V _{n})}^{2}}$$
  2. 2.

    We used a Windows based PC with Intel Core TM 2 Quad CPU @ 2. 66 GHz and 3. 49 GB RAM.

  3. 3.

    Pricing Partners is an independent valuation expert and a world leader in mathematical models and analytics for derivatives and structures products. We like to thank Eric Benhamou and the valuation team of Pricing Partners for their support.

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Authors and Affiliations

  1. Frankfurt School of Finance and Management, Centre for Practical Quantitative Finance, Frankfurt a. M., Germany

    Ingo Beyna

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  1. Ingo Beyna
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Beyna, I. (2013). Monte Carlo Methods. In: Interest Rate Derivatives. Lecture Notes in Economics and Mathematical Systems, vol 666. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34925-6_5

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