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How One-Touch Option Prices Relate to Binary Options

Article Quant Q&A · Author: tstudio
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Summary

The document compares a one-touch option, which pays when the underlying crosses a threshold at any time through maturity, with a binary option that pays when the underlying is above the threshold at maturity. It reports that the one-touch price is approximately twice the equivalent binary price.

The stated relationship is exact for a pure Wiener process, where it follows from the reflection principle. For lognormal underlying-price processes, the factor of two is described only as a useful approximation, not an identity. The document gives no derivation, pricing inputs, numerical example, or empirical evidence, so the approximation’s accuracy in particular market conditions cannot be assessed from this discussion.

Key ideas

  • A one-touch option pays upon reaching its threshold before or at maturity, while a binary option depends on the terminal price.
  • For a pure Wiener process, the one-touch price is exactly twice the equivalent binary price by the reflection principle.
  • For lognormal processes, the factor-of-two relationship is approximate rather than exact.
  • The document does not provide a derivation or quantify the approximation’s error.

Tags

OptionsDerivatives pricingVolatility
Full text
# Relation between one touch and binary option


# Relation between one touch and binary option












Is there a relation between the price of a one touch option and the price of a binary option?

By one touch option, I mean an option that pays off a fixed amount if the price of the underlying is above a certain threshold at any point in time before or at maturity.

By binary option, I mean an option that pays off a fixed amount if the price of the underlying is above a certain threshold at maturity.

## Answer by Dom (score 1)

https://quant.stackexchange.com/a/74058

The One Touch option is approximately twice the price of the equivalent Binary Option. This result can be shown to be exact if the underlying process is a pure Wiener process using the Reflection Principal. For lognormal processes this result is a good approximation but not exact.

## Answer by yu zhang (score -3)

https://quant.stackexchange.com/a/44509

One touch option is an American barrier digital

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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