  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.
