Pricing Corridor Digital Options in Black–Scholes

Summary

The note asks whether a corridor digital option can be priced analytically in the Black–Scholes framework. The payoff is conditional on the underlying price staying within specified barriers, making the joint behavior of the running minimum and maximum relevant. The author suggests that a known joint distribution for Brownian motion’s extrema might provide a route to a formula and asks whether an existing reference covers the topic.

No pricing derivation, formula, or answer is included, so the text serves as a research question rather than a worked method. It identifies the connection between barrier-style path constraints and extrema distributions, but does not establish how to handle discounting, parameter choices, or implementation. The linked material is not summarized in the document, so its coverage and applicability cannot be assessed from this text alone.

Key ideas

• A corridor digital payoff depends on the price staying within barrier levels.
• The joint distribution of a process’s running minimum and maximum may help characterize the payoff.
• The question is posed in the Black–Scholes setting.
• The document supplies no formula, derivation, or answer to the pricing problem.

Tags

# Range options in BS


# Range options in BS












I know how barrier options are priced in Black-Scholes scheme.

I'm wondering if an analytical formula exists also for range (corridor) digital options i.e. options paying only if the price remains between an up and an out barrier.

I think that if the joint distribution for the minimum and the max of a Wiener is known, an analytical pricing formula should exists. Would this contain the relevant literature?

http://www.yats.com/doc/stochastic-processes-en.pdf

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.