Narrow Results

Compared with investing an ordinary options, investing the power options may possibly yield greater returns. On the one hand, the power option is the best choice for those who want to maximize the leverage of the underlying market movements. On the other hand, power options can also prevent the financial market changes caused by the sharp fluctuations of the underlying assets. In this paper, we investigate the power option pricing problem in which the price of the underlying asset follows the Ornstein–Uhlenbeck type of model involving an uncertain fractional differential equation. Based on critical value criterion, the pricing formulas of European power options are derived. Finally, some numerical experiments are performed to illustrate the results.

Option pricing under two stochastic volatility models, double Heston model and double Heston with three jumps, is done. Firstly, the efficiency of the second model is shown via FFT method, and numerical examples using power call options. Then it is shown that power option yields more premium income under the second model, double Heston with three jumps, than another one.