Titlebook: Mathematical Finance - Bachelier Congress 2000; Selected Papers from Hélyette Geman,Dilip Madan,Ton Vorst Book 2002 Springer-Verlag Berlin

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Modern Finance Theory Within One Lifetime,on today is about the genesis of the present modern theory of finance in one academic lifetime — a rare phenomenon in the annals of any science. Although Bachelier’s basic breakthrough came in 1900, its scientic beginning must be placed at about 1950. Science is public knowledge. The treasures that

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Brownian Motion and the General Diffusion: Scale & Clock,is the standard Brownian motion .(1) starting at .(0) = 0. It lies at the back of Itô’s local representation . = .(.). + .(.). of the general 1-dimensional diffusion x with paths .(.) : . ≥ 0 and infinitesimal operator G = 1/2. .(.). ./. . + .(.)./., as suggested by the simplest example .(.) = .(0)

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Rare Events, Large Deviations,e probability of getting . heads in a row is clearly small, and for large . is very small. We know its exact value as 2. and in logarithmic scale we can write it as . .. While in this case the exact probability is easy to evaluate, there are many situations in which a direct exact calculation is imp

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Conquering the Greeks in Monte Carlo: Efficient Calculation of the Market Sensitivities and Hedge-Reters that drive the economic state-variables of the model, we perturb the vector of probabilities of simulated paths in a neighborhood of the uniform distribution. The resulting hedge-ratios (sensitivities with respect to input prices) are characterized in terms of statistical moments of simulated

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On the Term Structure of Futures and Forward Prices,t process as well as by a multidimensional Wiener process. Within an infinite dimensional HJM-type model for futures and forwards we study the properties of futures and forward convenience yield rates. For finite dimensional factor models, we develop a theory of affine term structures, which is show

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Spread Option Valuation and the Fast Fourier Transform,ansform technique introduced by Carr & Madan (1999) to a multi-factor setting. The method is applicable to models in which the joint characteristic function of the prices of the underlying assets forming the spread is known analytically. This enables us to incorporate stochasticity in the volatility

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