Abstract: In this paper, we propose a new option named as digital power exchange option by adding an indicator function of the ratio of the two underlying assets prices (denoted power forms) to the payoff of the power exchange option. This proposed model can be used to avoid the risk caused by the excessive price deviation of two underlying assets. Based on the above work, we obtain the explicit pricing formulas of the digital power exchange option under the jump-diffusion model by choosing the different numeraire. Finally, we take some historical data of the adjusted closing prices of two real stocks to discuss the prices of the digital power exchange option.

Key words: digital power exchange option, avoid risk, jump-diffusion process, Esscher transform, numerical analysis