The pricing and static hedging of multi-step double barrier options

As a sequel to Lee et al. (2022b), this paper explores the pricing of multi-step double barrier options with arbitrary European-type payoffs from a static hedging perspective. Using the reflection principle of Brownian motion, we develop how to construct an exact static hedging portfolio consisting of simple discrete barrier options under the Black–Scholes model. This equivalent conversion from continuous monitoring to discrete ones provides an efficient way of evaluating multi-step double barrier options, while overcoming the drawbacks of dynamic hedging. We illustrate our result with numerical examples, and extend it to other asset price dynamics such as jump diffusion. •This paper explores the pricing of multi-step double barrier options from a static hedging perspective.•We consider an arbitrary payoff structure at maturity for multi-step double barrier options.•How to construct a static hedging portfolio is illustrated through numerical examples.•The extensibility of the BS framework to other asset price dynamics with jumps is discussed.