Choosing Interest Rates for Option Pricing and Discounting

Summary

The note considers which Treasury maturity to use as an interest-rate input when pricing options. Responses suggest matching the rate tenor to the option’s maturity, while also distinguishing the role of rates in different parts of a derivatives valuation. One answer says the relevant tenor should be close to the option’s term, framing it as an opportunity cost of tying up capital.

Another response cautions that a single generic risk-free rate may not serve every purpose: the forward price may reflect cost of capital, while discounting may use the cost of collateral, such as overnight indexed swap rates for over-the-counter trades. The material is brief and consists of competing short comments rather than a complete pricing framework. It does not explain how to construct curves, handle dividends or borrow costs, or choose inputs for a particular market convention, so the distinctions are guidance rather than a full implementation method.

Key ideas

• The suggested rate tenor should broadly match the option’s time to expiry.
• Forward pricing and discounting can use different rate concepts.
• Collateral cost may determine discounting in collateralized over-the-counter derivatives.
• The short responses do not provide a complete rate-curve construction or option-pricing procedure.

Tags

# Which interest rates to use for options pricing?


# Which interest rates to use for options pricing?












I am looking at the historical treasury interest rates and am uncertain which rates would be best to use for options pricing.

Should I use 1 month, 6 month, 2 year?

See: http://www.treasury.gov/resource-center/data-chart-center/interest-rates/Pages/Historic-LongTerm-Rate-Data-Visualization.aspx

## Answer by user15229 (score 1)

https://quant.stackexchange.com/a/16407

> This is why the rate used is the risk-free rate.

Except its not. Cost of capital is used for the forward (price of total return swap), cost of collateral (OIS for OTC, box rates for listed) is used for the discounting.

## Answer by john (score 0)

https://quant.stackexchange.com/a/15700

the length of rate which closest corresponds to the maturity of the option. This will be true opportunity cost of having capital tied up in option positions with regard to the risk free rate.

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