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Author: Gilles Boya Publisher: ISBN: Category : Languages : en Pages : 11
Book Description
The aim of this article is to provide tools to calibrate a smooth local volatility surface in the presence of jumps. First we provide techniques to approximate the value of European options in a local volatility model with jumps, then we propose a quick and robust fixed point algorithm combined with this method to build smooth local volatility surfaces.
Author: Gilles Boya Publisher: ISBN: Category : Languages : en Pages : 11
Book Description
The aim of this article is to provide tools to calibrate a smooth local volatility surface in the presence of jumps. First we provide techniques to approximate the value of European options in a local volatility model with jumps, then we propose a quick and robust fixed point algorithm combined with this method to build smooth local volatility surfaces.
Author: Adil Reghai Publisher: ISBN: Category : Languages : en Pages : 14
Book Description
This paper explores a powerful calibration technique of local volatility models based on the fixed point algorithm. It proves to be more robust and generic than the standard Dupire Approach. We also show how to dramatically increase the performance of Monte Carlo simulations by means of techniques borrowed from quantum physics. In particular, we use operator theory combined with fast discrete random generation to construct fast, efficient and robust algorithms for production purposes. This contribution is an engineering piece of work.
Author: Konstantinos Skindilias Publisher: ISBN: Category : Languages : en Pages : 20
Book Description
We propose a methodology to calibrate the local volatility function under a continuous time setting. For this purpose, we used the Markov chain approximation method built on the well-established idea of local consistency. The chain was designed to approximate jump-diffusions coupled with a local volatility function. We found that this method outperforms traditional numerical algorithms that require time discretization. Furthermore, we showed that a local volatility jump-diffusion model outperformed the in- and out-of-sample pricing that the market practitioners benchmark, namely the Practitioners Black-Scholes, in turbulent periods during which at-the-money implied volatilities have risen substantially. As in previous literature concerning local volatility estimation, we represent the local volatility function using a space-time cubic spline.
Author: Hamza Guennoun Publisher: ISBN: Category : Languages : en Pages : 22
Book Description
In this paper, we study the calibration to market call prices C^{mkt}(t;K) of a local volatility model enhanced with jumps. Instead of giving an exact calibration condition on the local volatility, we introduce an approximate process S_t^ epsilon satisfying a well-defined nonlinear McKean SDE driven by a Cox process, such that E[(S_t^ epsilon - K) _ ] converges to C^{mkt}(t;K) as epsilon goes to 0 for all (t;K). This implies that the particle method, applied to the process S_t^ epsilon, which is used for the calibration of the local volatility, converges numerically. We illustrate the accuracy of our calibration algorithm with various numerical experiments. Finally, we extend this model by allowing jumps in the local volatility.
Author: Cheng Wang Publisher: ISBN: Category : Languages : en Pages : 96
Book Description
This thesis proposes an optimization formulation to ensure accuracy and stability in the local volatility function calibration. The unknown local volatility function is represented by kernel splines. The proposed optimization formulation minimizes calibration error and an L1 norm of the vector of coefficients for the kernel splines. The L1 norm regularization forces some coefficients to be zero at the termination of optimization. The complexity of local volatility function model is determined by the number of nonzero coefficients. Thus by using a regularization parameter, the proposed formulation balances the calibration accuracy with the model complexity. In the context of the support vector regression for function based on finite observations, this corresponds to balance the generalization error with the number of support vectors. In this thesis we also propose a trust region method to determine the coefficient vector in the proposed optimization formulation. In this algorithm, the main computation of each iteration is reduced to solving a standard trust region subproblem.
Author: Ali Hirsa Publisher: Academic Press ISBN: 0123846838 Category : Business & Economics Languages : en Pages : 456
Book Description
An Introduction to the Mathematics of Financial Derivatives is a popular, intuitive text that eases the transition between basic summaries of financial engineering to more advanced treatments using stochastic calculus. Requiring only a basic knowledge of calculus and probability, it takes readers on a tour of advanced financial engineering. This classic title has been revised by Ali Hirsa, who accentuates its well-known strengths while introducing new subjects, updating others, and bringing new continuity to the whole. Popular with readers because it emphasizes intuition and common sense, An Introduction to the Mathematics of Financial Derivatives remains the only "introductory" text that can appeal to people outside the mathematics and physics communities as it explains the hows and whys of practical finance problems. Facilitates readers' understanding of underlying mathematical and theoretical models by presenting a mixture of theory and applications with hands-on learning Presented intuitively, breaking up complex mathematics concepts into easily understood notions Encourages use of discrete chapters as complementary readings on different topics, offering flexibility in learning and teaching
Author: Lorenzo Bergomi Publisher: CRC Press ISBN: 1482244071 Category : Business & Economics Languages : en Pages : 520
Book Description
Packed with insights, Lorenzo Bergomi's Stochastic Volatility Modeling explains how stochastic volatility is used to address issues arising in the modeling of derivatives, including:Which trading issues do we tackle with stochastic volatility? How do we design models and assess their relevance? How do we tell which models are usable and when does c
Author: Turinici M. Gabriel Publisher: ISBN: Category : Languages : en Pages :
Book Description
We document the calibration of the local volatility in terms of local and implied instantaneous variances; we first explore the theoretical properties of the method for a particular class of volatilities. We confirm the theoretical results through a numerical procedure which uses a Gauss-Newton style approximation of the Hessian in the framework of a sequential quadratic programming (SQP) approach. The procedure performs well on benchmarks from the literature and on FOREX data.
Author: Gilles Boya
Author: Gilles Boya
Author: Adil Reghai
Author: Konstantinos Skindilias
Author: Hamza Guennoun
Author: Cheng Wang
Author: Ali Hirsa
Author: Jian Geng
Author: Lorenzo Bergomi
Author: Changhong He
Author: Turinici M. Gabriel