Choosing Day-Count Conventions for Option and Swap Pricing
Summary
The document explains why pricing models need dates converted into year fractions. In Black–Scholes or Monte Carlo pricing, an option’s pricing date and expiry must be expressed as a time to maturity using a day-count convention. Swaps can use different conventions on their fixed and floating legs to calculate accrual periods and rates, which raises the question of which convention should govern the model’s time scale.
The answer emphasizes that conventions depend on the market and product. It suggests actual/365 is common for volatility markets, actual/360 for many swaps, and 30E/360 for some bonds. These are presented as informed generalizations rather than universal rules; the document does not give a definitive convention for a particular swap’s Monte Carlo clock. In practice, the relevant market convention must be identified, while each leg’s contractual convention continues to determine its accrual calculations.
Key ideas
- Pricing models express calendar dates as year fractions using a day-count convention.
- A swap’s contractual legs may use different conventions for accrual calculations.
- The answer suggests actual/365 for many volatility markets and actual/360 for many swap markets.
- Bond markets may use conventions such as 30E/360.
- Conventions vary by market and product, so the examples are not universal rules.
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Full text
# What day count convention for pricing # What day count convention for pricing Imagine looking at some equity implied vol surface on Bloomberg. You see a call implied volatility in the grid. Now you want to convert this vol into a price. For that, you will use Black-Scholes formula. And in this formula, the expiry is a number while a call as an expiry which is a date, and a pricing date. From these two dates and a day count convention (and a calendar) you can get the number you want to use a expiry in the Black-Scholes formula. Same if you want to price that call in a Monte-Carlo (MC) setting. (All dates appearing are converted, with the pricing date as basis/reference date, and a day-count convention, into real numbers etc.) What is this day count convention ? Now imagine I have a fixed VS floating vanilla swap. Both swap's legs have a day count convention used to compute the year fractions needed for the zero-coupons and the EURIBOR rates (let's say the swap is an ICE EURIBOR swap). And it can happen that these two day count conventions are different. Suppose they are different. And suppose that you price that swap in a short rate model. You diffuse the spot rate across both legs dates and for that you need to have real numbers at the end, as in the simple example, hence a day count convention (for the conversion) but for the swap you have two. Do you choose one of them for the MC ? If not, which day count convention is it ? ACT/365.25 FIXED ? (Keeping then legs' day count conventions only for "accounting" (i.e. computing year fractions).) To put it simple : how, in a MC setting, do you convert dates into real numbers ? As the MC price is a limit, I would say that any reasonable day count convention would suit, but which one do practitioners use ? ## Answer by river_rat (score 1) https://quant.stackexchange.com/a/79718 Every market and product has its own pricing conventions that participants are just expected to know. Would guess most vol markets are actual/365 for black-scholes day-count while most swap markets are actual/360. Bonds can be 30E/360 etc
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