Parameters identification for an inverse problem arising from a binary option using a Bayesian inference approach

TL;DR

This paper employs Bayesian inference and MCMC algorithms to identify unknown parameters in an inverse Black-Scholes model, enabling detection of arbitrage opportunities in financial markets.

Contribution

It introduces a Bayesian inference method with MCMC for solving inverse option problems and estimating model parameters from market data.

Findings

Successfully estimates trend and volatility coefficients

Demonstrates the effectiveness of Bayesian approach in inverse problems

Provides a practical framework for arbitrage detection

Abstract

No--arbitrage property provides a simple method for pricing financial derivatives. However, arbitrage opportunities exist among different markets in various fields, even for a very short time. By knowing that an arbitrage property exists, we can adopt a financial trading strategy. This paper investigates the inverse option problems (IOP) in the extended Black--Scholes model. We identify the model coefficients from the measured data and attempt to find arbitrage opportunities in different 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.