Calibration of the Volatility Surface

Non-parametric calibration of the local volatility surface for European options

In this paper, we explore a robust method for calibration of the local volatility surface for European options. Assuming the the volatility surface is smooth, we apply a second order Tikhonov regularization to the calibration problem. Additionally we propose a new approach for choosing the Tikhonov regularization parameter. Using the TAPENADE automatic differentiation tool in order to obtain ad...

B-spline techniques for volatility modeling

This paper is devoted to the application of B-splines to volatility modeling, specifically the calibration of the leverage function in stochastic local volatility models and the parameterization of an arbitrage-free implied volatility surface calibrated to sparse option data. We use an extension of classical B-splines obtained by including basis functions with infinite support. We first come ba...

Markov Functional Modeling of Equity, Commodity and other Assets

In this short note we show how to setup a one dimensional single asset model, e.g. equity model, which calibrates to a full (two dimensional) implied volatility surface. We show that the efficient calibration procedure used in LIBOR Markov functional models may be applied here too. In a addition to the calibration to a full volatility surface the model allows the calibration of the joint asset-...

Local volatility calibration using an adjoint proxy

We document the calibration of the local volatility in a framework similar to Coleman, Li and Verma. The quality of a surface is assessed through a functional to be optimized; the specificity of the approach is to separate the optimization (performed with any suitable optimization algorithm) from the computation of the functional where we use an adjoint (as in L. Jiang et. al.) to obtain an app...

THE FLORIDA STATE UNIVERSITY COLLEGE OF ARTS AND SCIENCES Calibration of a Local Volatility Surface using Tikhonov Regularization

Volatility Surface Calibration In Illiquid Market Environment

In this paper, we show the fragility of widely-used Stochastic Volatility Inspired (SVI) methodology. Especially, we highlight the sensitivity of SVI to the fitting penalty function. We compare different weight functions and propose to use a novel methodology, the implied vega weights. Moreover, we unveil the relationship between vega weights and the minimization task of observed and fitted pri...