Airbag options are a new structured product that has gained popularity among investors in the over-the-counter derivatives market. They offer protection against downside losses, similar to how an airbag protects in a car crash. Airbag options provide investors with downside risk protection in the event of a market “collision.” However, if the “collision” is too severe, the “airbag” can be punctured, leading to potential losses (this is known as a “knock-in” event).
Airbag options are path-dependent due to knock-in events, making traditional risk-neutral pricing formulas inapplicable because it’s challenging to determine when the underlying asset hits the barrier. Closed-form pricing formulas, like the Black-Scholes for European options, are usually unattainable for these options. This problem was addressed by proposing the first passage time approach, which describes the random hitting time and derives its distribution by studying the maximum distribution of a Brownian motion. This method simplifies pricing path-dependent options to calculating an expectation, making closed-form pricing formulas achievable.
Reference [1] studies airbag-type option pricing with continuous monitoring under the MEJD, DEJD, and Black-Scholes models using the first passage time approach. The authors pointed out,
In this paper, we consider the pricing of airbag options, an emerging derivative in the finance market but has few studies in the literature, especially from a mathematical point of view. In line with the idea of providing protection against downside risk, we further propose two new types of airbag options with enhanced downside risk protections compared to the original one, namely, the airbag-TB option and the airbag-ER option. Regarding the quantitative pricing methodology, we propose a pricing framework for the three types of airbag options under the MEJD, DEJD and BS models. Closed-form pricing formulas under the MEJD and DEJD models are obtained whereas fully analytical pricing formulas are derived for the BS model.
In short, closed-form solutions were developed to price airbag options, and the results were favourably comparable to those obtained from Monte Carlo simulations.
This is another important contribution to the literature on financial derivatives. Let us know what you think in the comments below or in the discussion forum.
References
[1] Zheng Liu, Xiaosong Qian, Jing Yao and Yinghui Dong, Pricing airbag option via first passage time approach, Quantitative Finance, July 2024.
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