Download or read book Smooth Calibration in Local Volatility with Jumps written by Gilles Boya and published by . This book was released on 2016 with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Local Volatility written by Adil Reghai and published by . This book was released on 2015 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Local Volatility Calibration During Turbulent Periods written by Konstantinos Skindilias and published by . This book was released on 2014 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Local Volatility Models Enhanced with Jumps written by Hamza Guennoun and published by . This book was released on 2016 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Stable Local Volatility Calibration Using Kernel Splines written by Cheng Wang and published by . This book was released on 2008 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book An Introduction to the Mathematics of Financial Derivatives written by Ali Hirsa and published by Academic Press. This book was released on 2013-12-18 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Download or read book Calibration of local volatility models and proper orthogonal decomposition reduced order modeling for stochastic volatility models written by Jian Geng and published by . This book was released on 2013 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Estimation of Volatilities Under a Merton s Jump diffusion Model and an Uncertain Volatility Model written by Changhong He and published by . This book was released on 2005 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Calibration of Local Volatility Using the Local and Implied Instantaneous Variance written by Turinici M. Gabriel and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Pricing and Calibration in Local Volatility Models Via Fast Quantization written by Giorgia Callegaro and published by . This book was released on 2017 with total page 13 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we propose the first calibration exercise based on quantization methods. Pricing and calibration are typically difficult tasks to accomplish: pricing should be fast and accurate, otherwise calibration cannot be performed efficiently. We apply in a local volatility context the recursive marginal quantization methodology to the pricing of vanilla and barrier options. A successful calibration of the Quadratic Normal Volatility model is performed in order to show the potentiality of the method in a concrete example, while a numerical exercise on barrier options shows that quantization overcomes Monte-Carlo methods.

Download or read book Calibrating the local volatility model written by and published by . This book was released on 2012 with total page 73 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Smart Expansion and Fast Calibration for Jump Diffusion written by Eric Benhamou and published by . This book was released on 2009 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Using Malliavin calculus techniques, we derive an analytical formula for the price of European options, for any model including local volatility and Poisson jump process. We show that the accuracy of the formula depends on the smoothness of the payoff function. Our approach relies on an asymptotic expansion related to small diffusion and small jump frequency/size. Our formula has excellent accuracy (the error on implied Black-Scholes volatilities for call option is smaller than 2 bp for various strikes and maturities). Additionally, model calibration becomes very rapid.

Download or read book Adjoint based Calibration of Local Volatility Models written by Andre Lörx and published by . This book was released on 2012 with total page 165 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Approximation and Calibration of Short term Implied Volatilities Under Jump diffusion Stochastic Volatility written by Alexey Medvedev and published by . This book was released on 2006 with total page 37 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Equity Derivatives and Hybrids written by Oliver Brockhaus and published by Springer. This book was released on 2016-04-29 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the development of the Black-Scholes model, research on equity derivatives has evolved rapidly to the point where it is now difficult to cut through the myriad of literature to find relevant material. Written by a quant with many years of experience in the field this book provides an up-to-date account of equity and equity-hybrid (equity-rates, equity-credit, equity-foreign exchange) derivatives modeling from a practitioner's perspective. The content reflects the requirements of practitioners in financial institutions: Quants will find a survey of state-of-the-art models and guidance on how to efficiently implement them with regards to market data representation, calibration, and sensitivity computation. Traders and structurers will learn about structured products, selection of the most appropriate models, as well as efficient hedging methods while risk managers will better understand market, credit, and model risk and find valuable information on advanced correlation concepts. Equity Derivatives and Hybrids provides exhaustive coverage of both market standard and new approaches, including: -Empirical properties of stock returns including autocorrelation and jumps -Dividend discount models -Non-Markovian and discrete-time volatility processes -Correlation skew modeling via copula as well as local and stochastic correlation factors -Hybrid modeling covering local and stochastic processes for interest rate, hazard rate, and volatility as well as closed form solutions -Credit, debt, and funding valuation adjustment (CVA, DVA, FVA) -Monte Carlo techniques for sensitivities including algorithmic differentiation, path recycling, as well as multilevel. Written in a highly accessible manner with examples, applications, research, and ideas throughout, this book provides a valuable resource for quantitative-minded practitioners and researchers.

Download or read book Calibration and Pricing Under a Stochastic Volatility Jump Diffusion Model with Time dependent Parameters written by and published by . This book was released on 2010 with total page 63 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Local Volatility Calibration by Optimal Transport written by Ivan Guo and published by . This book was released on 2018 with total page 13 pages. Available in PDF, EPUB and Kindle. Book excerpt: The calibration of volatility models from observable option prices is a fundamental problem in quantitative finance. The most common approach among industry practitioners is based on the celebrated Dupire's formula, which requires the knowledge of vanilla option prices for a continuum of strikes and maturities that can only be obtained via some form of price interpolation. In this paper, we propose a new local volatility calibration technique using the theory of optimal transport. We formulate a time continuous martingale optimal transport problem, which seeks a martingale diffusion process that matches the known densities of an asset price at two different dates, while minimizing a chosen cost function. Inspired by the seminal work of Benamou and Brenier, we formulate the problem as a convex optimization problem, derive its dual formulation, and solve it numerically via an augmented Lagrangian method and the alternative direction method of multipliers (ADMM) algorithm. The solution effectively reconstructs the dynamic of the asset price between the two dates by recovering the optimal local volatility function, without requiring any time interpolation of the option prices.