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Option price data are used as inputs for model calibration, risk-neutral density estimation and many other financial applications. The presence of arbitrage in option price data can lead to poor performance or even failure of these tasks, making pre-processing of the data to eliminate arbitrage necessary. Most attention in the relevant literature has been devoted to arbitrage-free smoothing and filtering (i.e. removing) of data. In contrast to smoothing, which typically changes nearly all data, or filtering, which truncates data, we propose to repair data by only necessary and minimal changes. We formulate the data repair as a linear programming (LP) problem, where the no-arbitrage relations are constraints, and the objective is to minimise prices changes within their bid and ask price bounds. Through empirical studies, we show that the proposed arbitrage repair method gives sparse perturbations on data, and is fast when applied to real world large-scale problems due to the LP formulation. In addition, we show that removing arbitrage from prices data by our repair method can improve model calibration with enhanced robustness and reduced calibration error.
This paper presents simple formulae for the local variance gamma model of Carr and Nadtochiy, extended with a piecewise-linear local variance function. The new formulae allow to calibrate the model efficiently to market option quotes. On a small set
In this paper, we give a numerical method for pricing long maturity, path dependent options by using the Markov property for each underlying asset. This enables us to approximate a path dependent option by using some kinds of plain vanillas. We give
Adaptive wave model for financial option pricing is proposed, as a high-complexity alternative to the standard Black--Scholes model. The new option-pricing model, representing a controlled Brownian motion, includes two wave-type approaches: nonlinear
Recently, a novel adaptive wave model for financial option pricing has been proposed in the form of adaptive nonlinear Schr{o}dinger (NLS) equation [Ivancevic a], as a high-complexity alternative to the linear Black-Scholes-Merton model [Black-Schole
A nonlinear wave alternative for the standard Black-Scholes option-pricing model is presented. The adaptive-wave model, representing controlled Brownian behavior of financial markets, is formally defined by adaptive nonlinear Schrodinger (NLS) equati