Pricing double volatility barriers option under stochastic volatility

In this paper, we study a new type of barrier option, which is called 'double volatility barriers option'. Take the European up-and-out option as an example, the option will become worthless if the volatility of underlying asset becomes too high and reaches or exceeds the barrier. One advantage of this kind of option is to help option holders effectively control volatility risk. To price double volatility barriers option, we use the eigenfunction expansion method to approximate the solution to the partial differential equation that the option price satisfies. We also obtain the estimation formulae for model parameters by the martingale method and the numerical simulations of the option price are provided for the demonstration purpose.