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By Andreas J. Grau

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

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The variance reduction uses the paths with antithetic variables and the geometric averaging Asian option as correction. 646. 1). 000 asset paths and use the result instead of an analytic formula for f (s). 5. 2. All values are computed using the same set of asset paths, the values in the column A (Reference MC) are values computed with a pure Monte Carlo method. The mean value is computed using 10,000 valuations with 10,000 asset paths simulations each. 001 with 95% confidence. 01 because the Monte Carlo method uses only 125 time steps for the averaging while the PDE method uses 4000.

3 Pricing Using Feature Extraction We denote by S = (St )t∈[0,tT ] the price process of an asset in the Black-Scholes model with constant volatility σ and risk-less interest rate r. Our aim is to price an option with a payoff P (S), S := {Sτ |τ ∈ I}, I ⊆ {t0 , t1 , . . , tT } at tT which may depend on the whole path history of S. The fair initial price of the option is given by Vt0 = e−rtT EQ [P (S)], where the expectation is taken under the risk-neutral measure given an initial asset price St0 .

The next section proceeds with an overview of the numerical methods currently used in the field of derivatives pricing. 1 Overview The challenge that remains after the introduction of the Black-Scholes framework is the efficient valuation of arbitrary derivatives. 20). In other cases, the derivation of a closed-form solution might be possible, but its evaluation still might be a challenge or the derivation too complex. In all these cases a numerical tool is required which can deliver accurate option prices.

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

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