Pricing airbag option via first passage time approach
研究了空气包期权的定价问题，提出两种新型空气包期权，并在混合指数跳跃扩散等模型下推导出显式定价公式，通过蒙特卡洛模拟验证了公式的准确性和效率。
Airbag option is a new structured product that has been highly favored by investors in the over-the-counter derivatives market. It provides protections against the downside loss to investors like the ‘airbag’ in a car crash. In contrast with its popularity, there is little literature on the pricing of airbag options, especially from the mathematical finance point of view. In this paper, we study the pricing of airbag options using the first passage time approach. We propose two innovative new types of airbag options, namely airbag-TB and airbag-ER, which enhance the downside loss protections by integrating a time-varying barrier and early redemption features respectively in the payoffs. Explicit and closed-form pricing formulas for the original and the two new types of airbag options are derived under the mixed-exponential jump diffusion (MEJD) model, double exponential jump diffusion (DEJD) model and Black-Scholes (BS) model. In doing so, we significantly improve the Hybrid model proposed by Jaimungal and Sigloch (Incorporating risk and ambiguity aversion into a hybrid model of default. Math. Finance, 2012, 22, 57–81) by incorporating a stochastic redemption intensity model and more general underlying asset dynamics. We further demonstrate the performance of our pricing formulas and the two new types of airbag options with numerical examples based on Monte Carlo simulation, which verifies the accuracy and efficiency of our pricing formulas.