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No--arbitrage property provides a simple method for pricing financialderivatives. However, arbitrage opportunities exist among different markets invarious fields, even for a very short time. By knowing that an arbitrageproperty exists, we can adopt a financial trading strategy. This paperinvestigates the inverse option problems (IOP) in the extended Black--Scholesmodel. We identify the model coefficients from the measured data and attempt tofind arbitrage opportunities in different financial markets using a Bayesianinference approach, which is presented as an IOP solution. The posteriorprobability density function of the parameters is computed from the measureddata.The statistics of the unknown parameters are estimated by a Markov ChainMonte Carlo (MCMC) algorithm, which exploits the posterior state space. Theefficient sampling strategy of the MCMC algorithm enables us to solve inverseproblems by the Bayesian inference technique. Our numerical results indicatethat the Bayesian inference approach can simultaneously estimate the unknowntrend and volatility coefficients from the measured data.

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