Preprint Article Version 1 This version is not peer-reviewed

Bayesian Inference Approach to Inverse Problems in a Financial Mathematical Model

Version 1 : Received: 29 July 2019 / Approved: 31 July 2019 / Online: 31 July 2019 (11:53:47 CEST)

How to cite: Ota, Y.; Jiang, Y.; Nakamura, G.; Uesaka, M. Bayesian Inference Approach to Inverse Problems in a Financial Mathematical Model. Preprints 2019, 2019070356 (doi: 10.20944/preprints201907.0356.v1). Ota, Y.; Jiang, Y.; Nakamura, G.; Uesaka, M. Bayesian Inference Approach to Inverse Problems in a Financial Mathematical Model. Preprints 2019, 2019070356 (doi: 10.20944/preprints201907.0356.v1).

Abstract

This paper investigates an inverse problem of option pricing in the extended Black--Scholes model. We identify the model coefficients from the measured data and attempt to find arbitrage opportunities in financial markets using a Bayesian inference approach. The posterior probability density function of the parameters is computed from the measured data. The statistics of the unknown parameters are estimated by Markov Chain Monte Carlo (MCMC), which explores the posterior state space. The efficient sampling strategy of MCMC 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 drift and volatility coefficients from the measured data.

Subject Areas

inverse problem; option pricing; Bayesian inference approach.

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