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

This self-contained quantity brings jointly a suite of chapters by means of essentially the most exclusive researchers and practitioners within the fields of mathematical finance and fiscal engineering. featuring cutting-edge advancements in idea and perform, the Festschrift is devoted to Dilip B. Madan at the celebration of his sixtieth birthday.

Specific themes lined include:

* conception and alertness of the Variance-Gamma process

* Lévy procedure pushed fixed-income and credit-risk types, 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 cost bubbles

* software valuation for credits derivatives and portfolio management

Advances in Mathematical Finance is a invaluable 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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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. Other parameters of interest include time t, the interest rate r, and the VG parameters (θ, σ, ν), and these all make more complicated appearances in St , both directly through (5) and indirectly through Xt , where in the latter case the chain rule would be applied.

Geb, 10:212–225,1968. 30. A. Tjetjep and E. Seneta. Skewed normal variance-mean models for asset pricing and the method of moments. International Statistical Review, 74: 109–126, 2006. Variance-Gamma and Monte Carlo Michael C. Fu Robert H. edu Summary. The Variance-Gamma (VG) process was introduced by Dilip B. Madan and Eugene Seneta as a model for asset returns in a paper that appeared in 1990, and subsequently used for option pricing in a 1991 paper by Dilip and Frank Milne. This paper serves as a tutorial overview of VG and Monte Carlo, including three methods for sequential simulation of the process, two bridge sampling methods, variance reduction via importance sampling, and estimation of the Greeks.

Of a standard normal distribution. The distribution of X is thus a normal with mixing on the variance, is symmetric about μ, and has the same form irrespective of the size of time increment t. It is long-tailed relative to the normal in the sense that its kurtosis value 3λσ 4 3+ (θ + σ 2 λ)2 exceeds that of the normal (whose kurtosis value is 3). When the NCP distribution is symmetrized about the origin by putting μ = 0, it has a simple real characteristic function of closed form. The NCP process from the structure (3) clearly has jump components (the ξi s are regarded as “shocks” arriving at Poisson rate), and through the Brownian process add-on θ1/2 b(t) in (3), has obviously a Gaussian component.

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