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A Workout in Computational Finance by Michael Aichinger, Andreas Binder

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11 Valuation of Financial Instruments with Embedded American/Bermudan Options within Monte Carlo Frameworks

In contrast to European options, which can only be exercised at a fixed time, Bermudan options can be exercised at several points in time up to the maturity/expiry of the instrument. As explained before, we call an option which can be exercised at any time up to its expiration an American option. Consequently, finding the option value amounts to finding an optimal exercise rule, which is a matter of solving an optimal stopping problem and then computing the expected discounted payoff.

Pricing Bermudan and American derivatives with Monte Carlo methods is an area of both active academic research and great relevance in practice.1 One technique is to use the least squares approach (Least Squares Monte Carlo (LSMC)), which has become popular through the seminal work of Longstaff and Schwartz (2001).2 Several variations of the methodology have been proposed in the literature, see, for example, Rogers (2002), Glasserman and Yu (2004b), Cerrato (2008). In this chapter, we start by sketching the work of Longstaff and Schwartz (2001) and subsequently present a modification for Bermudan callable interest rate derivatives that improves the lower bound values.3 This modification is an extension of the work presented in Piterbarg (2005) and Amin (2003); the basic idea is to use regressions for the holding and exercise values of the callable derivative.

11.1 PRICING AMERICAN OPTIONS USING ...

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