Preprint Article Version 1 This version is not peer-reviewed

Parameters Identification for Inverse Option Problems Using Markov Chain Monte Carlo Methods

Version 1 : Received: 25 July 2019 / Approved: 28 July 2019 / Online: 28 July 2019 (16:17:51 CEST)

How to cite: Ota, Y.; Jiang, Y. Parameters Identification for Inverse Option Problems Using Markov Chain Monte Carlo Methods. Preprints 2019, 2019070318 (doi: 10.20944/preprints201907.0318.v1). Ota, Y.; Jiang, Y. Parameters Identification for Inverse Option Problems Using Markov Chain Monte Carlo Methods. Preprints 2019, 2019070318 (doi: 10.20944/preprints201907.0318.v1).

Abstract

This paper investigates the inverse option problems (IOP) in the extended Black--Scholes model arising in financial markets. We identify the volatility and the drift coefficient from the measured data in financial markets using a Bayesian inference approach, which is presented as an IOP solution. The posterior probability density function of the parameters is computed from the measured data. The statistics of the unknown parameters are estimated by a Markov Chain Monte Carlo (MCMC) algorithm, which exploits the posterior state space. The efficient sampling strategy of the MCMC algorithm enables us to solve inverse problems by the Bayesian inference technique. Our numerical results indicate that the Bayesian inference approach can simultaneously estimate the unknown trend and volatility coefficients from the measured data.

Subject Areas

inverse problem; option pricing; Bayesian inference approach

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