Parameter estimation of uncertain stock model using residual method optimized by genetic algorithm: valuation of vulnerable European and barrier options

Stock markets around the world are growing rapidly, and vulnerability created by default risk of option holders has become a serious issue. In such circumstances, this paper suggests the pricing of vulnerable European and barrier options, when the underlying asset and asset held by the option writer follow the geometric Liu process and uncertain mean-reverting process, respectively. According to the uncertainty theory, we present closed-form analytic formulas of these option prices and use the residual method to estimate the model parameters. In order to estimate the model parameters, the genetic algorithm to solve the generalized moment estimation problem derived by the residual method is suggested. From the uncertain hypothesis test, we then evaluate whether the proposed uncertain stock models fit the observed data. Ultimately, based on the estimated parameters, we evaluate the effect of the vulnerable option parameters on its price.