Auxiliary Model-based Approximation Method Of The Option Pricing

This paper uses an approximate technique to solve the issue that many continuous-timeoption pricing models have no closed-form solutions. The paper first sets up an “auxiliary”model that has the closed-form solution and has high similarity to the true (but unknown) one.Then, by using risk compensation methods, the approximate closed-form solution of the truemodel is obtained.To be specific, the paper shows the procedure how to apply this approximate approach topricing options with stochastic volatility, barrier options and Asian options. For the optionswith stochastic volatility, choose the model with different underlying processes but the samepayoff function as the true one to be auxiliary. For barrier options, the auxiliary means themodel employed has different payoff function but has the same underlying process. For Asianoptions, the auxiliary model has the form that the underlying process and payoff function areboth different. Then, the PDE form which describes the price differences between theauxiliary and true model and the mispricing function are deduced by infinitesimal generator.Since this price difference could be expanded into power series, the closed-form expression isobtained. For Asian and barrier options, the solution can be simpler.Finally, the software matlab is used to derive approximate analytic solutions of thesethree option pricing models. By doing error analysis on the approximate solution and trueclosed-form solution of the affine stochastic volatility models and barrier option models, thefeasibility of this approximate method is verified. For Asian options and non-affine stochasticvolatility models, through comparing Monte Carlo simulation and the approximate solution,we conclude that our model is intuitive, simple to implement, has higher computationefficiency without losing accuracy.