Download PDF by Eckhard Platen: A Benchmark Approach to Quantitative Finance (Finance)

By Eckhard Platen

ISBN-10: 0195300572

ISBN-13: 9780195300574

The benchmark process presents a common framework for monetary marketplace modeling, which extends past the normal risk-neutral pricing conception. It allows a unified remedy of portfolio optimization, by-product pricing, built-in chance administration and coverage chance modeling. The lifestyles of an an identical risk-neutral pricing degree isn't required. in its place, it ends up in pricing formulae with admire to the real-world likelihood degree. This yields vital modeling freedom which seems to be worthwhile for the derivation of reasonable, parsimonious industry types. the 1st a part of the publication describes the mandatory instruments from chance conception, records, stochastic calculus and the speculation of stochastic differential equations with jumps. the second one half is dedicated to monetary modeling by the benchmark strategy. a variety of quantitative tools for the real-world pricing and hedging of derivatives are defined. the overall framework is used to supply an realizing of the character of stochastic volatility. The publication is meant for a large viewers that comes with quantitative analysts, postgraduate scholars and practitioners in finance, economics and coverage. It goals to be a self-contained, obtainable yet mathematically rigorous advent to quantitative finance for readers that experience an inexpensive mathematical or quantitative history. eventually, the ebook should still stimulate curiosity within the benchmark process via describing a few of its strength and large applicability.

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To illustrate certain typical SGH densities we shall describe four special cases of the SGH density in the sequel. These coincide with log-return densities of important asset price models suggested in the literature. Student t Density (*) Praetz (1972) and Blattberg & Gonedes (1974) proposed for log-returns a Student t density with degrees of freedom n > 0. This is also the log-return density that arises from observations over long periods of time generated by the minimal market model (MMM), which will be derived in Chap.

29) i,j=1 The matrix Cov(X) = Cov(X, X) is called the autocovariance matrix of the vector X. 4 Joint Distributions and Random Vectors 45 If X = (X1 , X2 , . . , Xn ) is an n-dimensional vector, A = [Ai,j ]n,m i,j=1 a deterministic n × m matrix and b = (b1 , b2 , . . 30) Cov(Y , Y ) = A Cov(X, X) A . 31) and For example, if X is a vector of n independent random variables with variance Var(Xi ) = 1, i ∈ {1, 2, . . 32) where I is the identity matrix or unit matrix and we have for Y = AX + b the autocovariance matrix Cov(Y , Y ) = A A .

I − 1, i + 1, . . , n}. ,xn →+∞ FX1 ,X2 ,··· ,Xn (x1 , x2 , . . , xn ) = 1. 37) 46 1 Preliminaries from Probability Theory In addition, FX1 ,X2 ,··· ,Xn is non-decreasing and continuous from the right in xi for i ∈ {1, 2, . . , n}. For any permutation {i1 , i2 , . . , in } of the set {1, 2, . . , n} we have FXi1 ,Xi2 ,··· ,Xin (xi1 , xi2 , . . , xin ) = FX1 ,X2 ,··· ,Xn (x1 , x2 , . . , xn ). 38) Furthermore, if {i1 , i2 , . . , ik } is any subset of the set {1, 2, . . , n}, then the marginal distribution FXi1 ,Xi2 ,··· ,Xik for k ∈ {1, 2, .

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A Benchmark Approach to Quantitative Finance (Finance) by Eckhard Platen

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