Based on the extended Black-Scholes model to quantitatively study corporate bounds. The inversion study of drift rate can help us discover possible arbitrage opportunities, and thus produce an inverse problem worthy of discussion. Under the assumption that the drift rate to be inverted is a more general polynomial or trigonometric function and the given prior condition is Gaussion distribution, an inproved Markov chain Monte Carlo method based on Metropolis-Hastings criterion is given, which realizes the numerical inversion of drift rate parameters.