Advances in Mathematical Finance by Michael C. Fu, Robert A. Jarrow, Ju-Yi Yen, Robert J Elliott

By Michael C. Fu, Robert A. Jarrow, Ju-Yi Yen, Robert J Elliott

This self-contained quantity brings jointly a suite of chapters via one of the most exclusive researchers and practitioners within the fields of mathematical finance and monetary engineering. featuring cutting-edge advancements in concept and perform, the Festschrift is devoted to Dilip B. Madan at the party of his sixtieth birthday.

Specific issues lined include:

* conception and alertness of the Variance-Gamma process

* Lévy method pushed fixed-income and credit-risk versions, together with CDO pricing

* Numerical PDE and Monte Carlo methods

* Asset pricing and derivatives valuation and hedging

* Itô formulation for fractional Brownian motion

* Martingale characterization of asset rate bubbles

* software valuation for credits derivatives and portfolio management

Advances in Mathematical Finance is a important source for graduate scholars, researchers, and practitioners in mathematical finance and monetary engineering.

Contributors: H. Albrecher, D. C. Brody, P. Carr, E. Eberlein, R. J. Elliott, M. C. Fu, H. Geman, M. Heidari, A. Hirsa, L. P. Hughston, R. A. Jarrow, X. Jin, W. Kluge, S. A. Ladoucette, A. Macrina, D. B. Madan, F. Milne, M. Musiela, P. Protter, W. Schoutens, E. Seneta, ok. Shimbo, R. Sircar, J. van der Hoek, M.Yor, T. Zariphopoulou

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Example text

The estimation was successful for just the first two classes, the normal (m = 1), the symmetric stable (m = 2), and the fourth class, the VG (with m = 2). The remaining classes, including the NCP, each had three parameters. f. estimation methods. f. of the symmetric VG and the associated stochastic process. This introduction of the VG material is expressed, verbatim, as follows in both [15] and [16]: The fourth parametric class is motivated by the derivation of the t distribution proposed by Praetz (1972).

However, a digital option with payoff 1{ST >K} would lead to a biased estimator (identically zero). Thus, the IPA estimator for the gamma would be biased. Roughly speaking, if h is almost surely continuous with respect to the parameter of interest, then the IPA estimator will be unbiased. The call payoff function is continuous, with a “kink” at K, which leads to a discontinuity in its first derivative at K, just as for the digital option. The example above was in some sense the simplest, because S0 doesn’t appear anywhere else in the expression for St given by (5) except as a scale factor.

Dilip has always been an inspiration to us all and an ideal academic colleague, always energetic and enthusiastic and full of ideas, whether it be at the research meetings with students or during our regular lunch strolls to downtown College Park. As Dilip has told me numerous times in our discussions, on Wall Street there are really two main numerical models/techniques employed for pricing derivative securities: Monte Carlo simulation or numerical solution of partial differential equations. The former depends on the first fundamental theorem of asset pricing: the existence of a martingale measure so that the price can be expressed as the expectation of an appropriately discounted payoff function.

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