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Consistent Time Units for Option Pricing Inputs

Article Quant Q&A · Author: rajah9
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Summary

The document asks how to express time-sensitive inputs when using a closed-form option pricing approximation, specifically the Bjerksund–Stensland model. The question lists the risk-free rate, volatility, time to expiration, and cost of carry, and asks whether each should be scaled to an annual basis and whether other inputs need adjustment.

The accepted answer confirms the general rule: use the same time unit for all parameters. It does not give a detailed conversion procedure or independently discuss how volatility should be scaled, so readers must consult the model’s conventions and the referenced explanation for those details. The key practical lesson is dimensional consistency: inputs expressed over mismatched time units can make a pricing calculation inconsistent.

Key ideas

  • Use a consistent time unit across the parameters in an option pricing model.
  • The question concerns annualized rates, volatility, carry, and time to expiration.
  • The accepted answer confirms consistency but does not detail each conversion.

Tags

OptionsDerivatives pricingVolatility
Full text
# How to scale option pricing components in regard to time


# How to scale option pricing components in regard to time












I am looking at closed-form options approximations, in particular the Bjerksund-Stensland model.

I have run into a very basic question. How should I scale the input variables in regard to time? My assumptions would be:

- r (riskless interest rate) should be an annual rate, so if the 3-month T-bill yields 0.03%, then I should use .12.

- σ (variance) should be annual (and according to How to calculate future distribution of price using volatility?, variance scales with the square root of time.

- T (time to expiration) should be in years, so expiration in 83 days would be 83/365 (=0.227397) years.

- b (cost of carry) should be an annual rate.

Have I got that right? Are there other input variables that I will need to scale before plugging in?

## Answer by glyphard (score 1, accepted)

https://quant.stackexchange.com/a/1188

Yes, that's correct. (use the same time unit for all of the parameters)

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