Applying the Parity Ratio When Pricing Third-Party Warrants

Summary

The document explains how to account for the parity ratio when using Black–Scholes to value a third-party warrant. Parity states how many warrants are needed to exercise the right to acquire one unit of the underlying. The answer converts the warrant price into the value of the equivalent option by multiplying it by the parity ratio, then applies the standard Black–Scholes call formula using the underlying price, strike, rate, and time to expiry.

This scaling addresses the warrant’s unit relationship to the underlying: the formula gives the value corresponding to the full share-level option, while parity translates between that value and an individual warrant. The response distinguishes this setup from warrants issued by a company on its own shares, where dilution may affect valuation. It provides a concise pricing relationship, but no worked numerical example or discussion of market-specific warrant terms and conventions.

Key ideas

• Parity specifies how many warrants correspond to one unit of the underlying at exercise.
• Multiply the warrant price by parity to obtain the equivalent option value for Black–Scholes pricing.
• Use the standard call formula with the underlying price, strike, interest rate, and time to expiry.
• The explanation concerns third-party warrants and does not address dilution from company-issued warrants.

Tags

# How to use the parity parameter when pricing third-party warrants with BS?


# How to use the parity parameter when pricing third-party warrants with BS?












I attempt a second basic question. Let me know if https://money.stackexchange.com/ would have been more suitable for that.

Third-party warrants are very similar to call options. One of their main characteristics is the parity as defined here:

> Parity: this represents the number of warrants needed to exercise the right on a given underlying. A parity of 10 on a call warrant on a share means that 10 call warrants need to be exercised at expiration in order to buy 1 share at the exercise price. (from https://wholesale.banking.societegenerale.com/en/news-insights/glossary/warrants/)

If I use the Black-Scholes formula to price a warrant, where is the parity supposed to appear?

Please note in "Options, Futures, and Other Derivatives, 5th edition", John C. Hull has a section p249 about "warrants issued by a company on its own stock". I think it is a different topic, as there is no dilution in third-party issued warrants.

## Answer by Sylvain Leroux (score 0, accepted)

https://quant.stackexchange.com/a/78422

My intuition is we can price a third-party warrant with price $c_w$ and parity ${parity}$ by pricing the equivalent option with price $c_o = c_w\times{parity}$.

$$c_w\times{parity}=N(d_1)S-N(d_2)Ke^{-r(T-t)},$$

$d_1$ and $d_2$ calculated as usual.

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