Choosing the Interest Rate for Black–Scholes Option Pricing

Summary

This document asks which interest rate belongs in a Black–Scholes option valuation, distinguishing a bank funding rate from a short rate associated with the underlying stock. The answers describe the theoretical input as a risk-free rate matched to the option’s maturity. One response suggests using a bank funding rate corresponding to the option tenor, while another points to rates inferred from Treasury instruments.

For shorter maturities, the discussion cites Treasury bill yields as a direct reference; for longer maturities, it describes deriving zero-coupon spot rates from coupon-bearing bonds through bootstrapping. The underlying idea is that the discount rate should reflect the term structure over the option’s life, rather than an unrelated stock-specific short rate. The replies offer general conventions and do not resolve how funding, collateral, dividends, or market-specific discount curves alter practice. In real pricing, the appropriate curve depends on the product and valuation framework, details the document does not develop.

Key ideas

• Black–Scholes theory uses a risk-free discount rate appropriate to the option’s maturity.
• The responses suggest tenor-matched bank funding or rates inferred from Treasury instruments.
• Treasury bill yields can inform short maturities, while longer zero-coupon rates may require bootstrapping.
• The document gives general guidance and does not address product-specific funding or collateral conventions.

Tags

# What rate should I passed into Black Scholes to calculate an option price?


# What rate should I passed into Black Scholes to calculate an option price?












I can think of at least two rates with different physical meanings to use.

- rate on assessed balance.

- short rate of the underlying stock

I understand that BS model is a theory and practice getts messy,but at least in theory which is the one that makes sense to use?

## Answer by eSurfsnake (score 3)

https://quant.stackexchange.com/a/39957

Usually the bank funding rate that corresponds to the length of the option - I.e., for a 3 month option probably the 3 month Fed Funds rate

## Answer by Hui (score -1)

https://quant.stackexchange.com/a/39960

BS model uses risk-free rate to price option. The most popular way of deriving risk-free rate from treasury zero-coupon yield curve based on the expiration of the option.

For options expiring within a year, you can directly use the yield from the treasury bills(expiring within a year). For longer than a year, zero coupon rates (or spot rates) have to be derived from coupon bonds through bootstrapping.

This is the way of bootstrapping: https://en.wikipedia.org/wiki/Bootstrapping_(finance)

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