Choosing Comparable Strikes for First-Generation Barrier Options

Summary

The document asks how to select comparable strikes for first-generation exotic options, including digital and single- or double-barrier contracts, when testing strategies across securities and products. The intended comparison is based on normalized likelihood of touch. A fixed percentage distance from spot is considered unsuitable because price scales differ across markets and instruments. The author asks whether a strike can be solved from a target theoretical value, since exotic contracts are often quoted in premium terms as a percentage of theoretical value under Black–Scholes assumptions.

No answer or implementation method is included, so the document does not establish that theoretical value uniquely normalizes touch likelihood or identify a standard strike-from-delta equivalent for barriers. It provides a framing of the comparability problem and a pricing convention from FX exotics, but no evidence, tests, or recommended calibration. A reader would need a model and a clearly defined probability measure and touch event to make strikes comparable.

Key ideas

• The goal is to compare barrier-option strikes across securities by normalizing the likelihood of touch.
• A fixed percentage distance from spot may not be comparable across markets or products.
• The author considers solving for strikes at a target theoretical value expressed under Black–Scholes assumptions.
• The document supplies no answer, implementation, or evidence that theoretical value alone normalizes touch probability.

Tags

# Is there an analogous strikeFromDelta implementation for 1st gen barrier options?


# Is there an analogous strikeFromDelta implementation for 1st gen barrier options?












I have a simple replication pricing implementation for 1st gen exotics (digitals, single and double barriers, etc.). In order to effectively test strategies I want to price "like" strikes across securities and products. Where "like" just infers that I've normalized the likelihood of touch for each security, product, etc.

Some options I could use are:

- % from spot: this won't scale well across markets, securities, products.





Since exotics are normally quoted in %TV (theoretical value) I was hoping there was a standard "solve for strike" given a specific %TV value. If not, are there any other common strategies? References appreciated.

Edit: TV is theoretical value. Also for reference a bit about option contracts in FX from a text I'm referencing:

> Exotic option contracts are priced in premium terms and the pricing is anchored by Theoretical Value (TV)—the CCY1% value of the exotic contract under Black-Scholes assumptions, specifically:

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