New PDF release: Applications of Least-Squares Regressions to Pricing and

By Andreas J. Grau

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For this regression estimate, we need to define our basis functions b1 (x), . . , bm (x). In this simple case we choose polynomials up to the power of two in x := StT such that b1 (StT ) = 1, b2 (StT ) = StT and b3 (StT ) = St2T . 5684                 in this particular case. 005712) . e. 005712 · s2 ) · 0 (log(s/St )+(r−(1/2)σ 0 1 − 2σ 2 tT √ e σs 2πtT 2 )t T) 2 ds. The last integral can now be evaluated with numerical methods. 1. 84. But, as we will see in the next section, in realistic settings with many paths and more regression basis functions the Feature Extraction method converges faster to the true solution and delivers more accurate estimates than the traditional Monte Carlo method.

With P j (Stj0 , Stj1 , Stj2 ) = max 100 − 1 3 2 Stji , 0 , j = 1, . . 3 Pricing Using Feature Extraction 39 which can already be used for a price estimate following the traditional Monte Carlo pricing method (cp. 8412. 5. For this regression estimate, we need to define our basis functions b1 (x), . . , bm (x). In this simple case we choose polynomials up to the power of two in x := StT such that b1 (StT ) = 1, b2 (StT ) = StT and b3 (StT ) = St2T . 5684                 in this particular case.

But, only a few options which have a moving average as a strike or as an underlying are actively traded [70]. More common is the moving average computation in issuer-call features of some fixed income securities [71]. Our algorithm can easily be adapted to these securities, so that we will only present the simple case of MWAOs. The foundation of almost any option pricing method is layed by the no-arbitrage framework introduced by Black and Scholes [17]. We presented the common methods for valution in this framework in Chapter 1.

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Applications of Least-Squares Regressions to Pricing and Hedging of Financial Derivatives by Andreas J. Grau


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