Modeling Option Time Decay Across Overnight Market Closures

Summary

The document asks how Black–Scholes time should be counted when an exchange closes overnight. In theoretical use, time to expiry is expressed as a fraction of a year, so the model can represent any chosen interval rather than requiring a count of trading sessions. The passage does not prescribe a particular day-count basis or calendar convention.

For practical modeling, it presents alternative assumptions about how time value decays while the market is closed. A model could reduce time continuously, apply a discrete one-day reduction at a chosen point, or represent decay as concentrated after the market opens. The choice depends on the product, the trader’s analysis, and the intended use. These are modeling options, not empirical findings; the document offers no comparison, calibration method, or evidence establishing one decay pattern as generally superior.

Key ideas

• Black–Scholes time to expiry can be represented as a fractional year.
• Theoretical modeling does not require time to advance only during business hours.
• A practical model may represent overnight decay continuously or as a discrete step.
• Some products may be modeled with decay concentrated after the market opens.
• The document leaves the choice to product-specific analysis and trading goals.

Tags

# Over-night Black-Scholes


# Over-night Black-Scholes












I have a question for Black-Scholes. It is a continuous approach, but the real market closes every day. So for the Black-Scholes, how do we count the time effect of during the time when the market is closed? or do we just ignore that time and count the business day time?

## Answer by confused (score 1, accepted)

https://quant.stackexchange.com/a/57021

With theoretical modeling you just put in the number of days till expiration in years. If time to expiration is less than 1 year, it will just be some decimal. That means you can put in any time to expiration you want.

In practice, how you model the decay overnight depends on your own analysis, judgement, modeling, trading strategy etc.. You could do the same and have time to expiration continuously decrease linearly. Or you can just immediately decay it by a day (non linear). Sometimes the product may not decay much overnight, but decay quickly 30 minutes after open - which makes sense for this type of modeling. It just depends on your situation and goals.

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