Read e-book online A Benchmark Approach to Quantitative Finance PDF

By Eckhard Platen, David Heath

ISBN-10: 3540262121

ISBN-13: 9783540262121

A framework for monetary industry modeling, the benchmark strategy extends past common hazard impartial pricing idea. It allows a unified remedy of portfolio optimization, by-product pricing, built-in danger administration and coverage chance modeling. This ebook offers the required mathematical instruments, by way of a radical advent to monetary modeling lower than the benchmark process, explaining a number of quantitative tools for the reasonable pricing and hedging of derivatives.

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Extra info for A Benchmark Approach to Quantitative Finance

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5). Characteristic functions are often used to analyze and characterize properties of random variables. They are closely related to Fourier transforms of the corresponding density function. A characteristic function φX (θ) uniquely determines the density function fX (x) of a continuous random variable X. 83) see Lukacs (1960). We mentioned at the end of Sect. 2 that the SGH distribution covers logreturn distributions for a number of important asset price models. 84) for θ ∈ . Recall that Kλ is the modified Bessel function of the third kind with index λ.

In addition, if X is S-measurable, then are deterministic E(X Y | S) = X E(Y | S). s. The conditional expectation E(X | S) is in some sense obtained by smoothing X over the events in S. Thus the finer the information set S, the more E(X | S) resembles the random variable X. 3 Moments of Random Variables 35 Least-Squares Estimate Let S ⊂ A be a given sigma-algebra and X a square integrable random variable on (Ω, A, P ). 72) for all S-measurable, square integrable random variables Y . Consequently, E(X | S) is the least-squares estimate or best forecast for X amongst the random variables Y which are S-measurable.

23) Symmetric Generalized Hyperbolic Distribution (*) Various authors have proposed asset price models with log-returns that relate to the rich class of symmetric generalized hyperbolic (SGH) distributions. This class of distributions was extensively examined by Barndorff-Nielsen (1977), see Hurst & Platen (1997) for a study on log-returns. We shall use this class later on to identify the distribution that fits best observed log-returns. 24) for x ∈ , where λ ∈ and α, δ ≥ 0. We set α = 0 if λ ≥ 0 and δ = 0 if λ ≤ 0.

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A Benchmark Approach to Quantitative Finance by Eckhard Platen, David Heath


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