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By Andreas J. Grau

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Extra info for Applications of Least-Squares Regressions to Pricing and Hedging of Financial Derivatives

Example text

A. 1. With Stj0 = 100 and random numbers θi,j , j = 1 . . 2725 Now, we can compute the payoff of the Asian option for each paths. 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 .

4.

A. a. 1. With Stj0 = 100 and random numbers θi,j , j = 1 . . 2725 Now, we can compute the payoff of the Asian option for each paths. 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 .

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