On the calibration of the 3/2 model

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On the valuation of fader and discrete barrier options in Heston's Stochastic Volatility Model

We focus on closed-form option pricing in Hestons stochastic volatility model, in which closed-form formulas exist only for few option types. Most of these closed-form solutions are constructed from characteristic functions. We follow this approach and derive multivariate characteristic functions depending on at least two spot values for different points in time. The derived characteristic functions are used as building blocks to set up (semi-) analytical pricing formulas for exotic options with payoffs depending on finitely many spot values such as fader options and discretely monitored barrier options. We compare our result with different numerical methods and examine accuracy and computational times. --exotic options,Heston Model,Characteristic Function,Multidimensional Fast Fourier Transforms

Fast and Efficient Numerical Methods for an Extended Black-Scholes Model

An efficient linear solver plays an important role while solving partial differential equations (PDEs) and partial integro-differential equations (PIDEs) type mathematical models. In most cases, the efficiency depends on the stability and accuracy of the numerical scheme considered. In this article we consider a PIDE that arises in option pricing theory (financial problems) as well as in various scientific modeling and deal with two different topics. In the first part of the article, we study several iterative techniques (preconditioned) for the PIDE model. A wavelet basis and a Fourier sine basis have been used to design various preconditioners to improve the convergence criteria of iterative solvers. We implement a multigrid (MG) iterative method. In fact, we approximate the problem using a finite difference scheme, then implement a few preconditioned Krylov subspace methods as well as a MG method to speed up the computation. Then, in the second part in this study, we analyze the stability and the accuracy of two different one step schemes to approximate the model.Comment: 29 pages; 10 figure

Generalized Hyperbolic Distributions and Brazilian Data

The aim of this paper is to discuss the use of the Generalized Hyperbolic Distributions to fit Brazilian assets returns. Selected subclasses are compared regarding goodness of fit statistics and distances. Empirical results show that these distributions fit data well. Then we show how to use these distributions in value at risk estimation and derivative price computation.

On the valuation ofconstant barrier options under spectrally one-sided exponential L&evy models and Carr’s approximation for American puts.

This paper provides a general framework for pricing options with a constant barrier under spectrally one-sided exponential L&evy model, and uses it to implement ofCarr’s approximation for the value of the American put under this model. Simple analytic approximations for the exercise boundary and option value are obtained. c 2002 Elsevier Science B.V. All rights reservedAmerican options; Perpetual approximation; Spectrally negative exponential L&evy process;