Matching the Risk-Free Rate to an Option’s Expiry

Summary

The document explains how to choose a risk-free interest rate when valuing options with different expiration dates. Because the rate discounts the option’s future payoff, the suggested input is the rate on a risk-free instrument, such as a Treasury security, with a maturity close to the option’s expiry.

If no published instrument has an exact matching maturity, the rate can be approximated by interpolating between rates for nearby maturities. The answer characterizes this as a rough method and notes that more sophisticated approaches are available, without specifying them. It also says that interest rates generally have a small effect on option value, except for long-dated options that are deep in the money. No pricing example or comparison of interpolation methods is provided, so the guidance is a practical rule of thumb rather than a complete treatment of yield curves, compounding conventions, or instrument-specific discounting.

Key ideas

• Choose a risk-free rate whose instrument maturity is close to the option’s expiry.
• Interpolate between nearby published rates when no exact maturity is available.
• Treat simple interpolation as an approximation rather than a full yield curve method.
• The rate may matter more for long-dated, deep in-the-money options.

Tags

# how to compute the risk free rate for a given maturity of an option contract?


# how to compute the risk free rate for a given maturity of an option contract?












i'm working on options with different maturities. I need to correspond a risk free rate for each maturity. What rate should i consider as risk free rate? thank you.

## Answer by D Stanley (score 1, accepted)

https://quant.stackexchange.com/a/25271

The risk free rate is used to get the present value of future payoff, so you should use the rate of a risk-free instrument (e.g. a Treasury note) that has roughly the same maturity of the option you are valuing.

If you option expires in a time that does not have an exact Treasury instrument, you can get a rough approximation by interpolating between two published rates. There are more sophisticated methods, but for option valuation the interest rate is generally a small factor, other than for long-dated deep in-the-money options.

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.