A reader posed an interesting question to us: Is an option priced based on calendar days or trading days? So, this week, we discuss how time to expiry is priced into an option and its implication for your trading strategy.

Does it matter?

Interest rate that is input into the Black Scholes Merton (BSM) model is based on calendar days. Therefore, it would be logical also to use calendar days for time to expiry. A supportive argument is that geo-political and macro-level events happen during weekends that impact volatility and must be priced into the options. But a compelling counterargument is that markets are closed on weekends. So, what should you do?

Take the next-week expiry 18700 call on the Nifty Index. With the index at 18675, the option price of 141 points consists of only time value. Based on calendar days, the option’s implied volatility is 11.21, and the corresponding time decay is 8.45. But if you use trading days, the implied volatility is 12.81, and the time decay is 10.35. Note that time decay and implied volatility compensate each other, given the time value of an option. This is because the time value is a function of time to expiry and implied volatility. For a given time value of an option, a longer time to expiry leads to lower implied volatility, and a shorter time to expiry leads to higher implied volatility. 

Time value of options
Longer time to expiry leads to lower implied volatility and shorter time to expiry leads to higher implied volatility

The choice of calendar or trading days for pricing options could have a bearing on two decisions — your choice of strike and whether to buy options on Fridays. Suppose you select the 18700, 18800 and 18900 (one near at-the-money and two out-of-the-money) strikes. Your objective is to pick the one with the lowest implied volatility. This would be the 18,900 strikes, whether you use calendar or trading days. This is because you are looking for relative cheapness between options. So, the choice of calendar or trading days does not impact your choice of strike.

What about buying options on Fridays? If you were to consider trading days, the loss from time decay will be larger for each day, but you will not lose time value on weekends. If you were to consider calendar days, you will lose less on weekdays, but you will also lose on weekends. So, it is difficult to argue which is better. That said, it is optimal to avoid initiating a long position on a call or a put on Friday unless you have a compelling reason to buy; you cannot close your position if a macro-level event bearing a negative outcome were to happen on a weekend.

Optional reading

Empirical evidence in the US suggests that weekend volatility is typically lower than weekdays, but significant enough to be included in pricing options. Suffice it to know that models developed to price such volatility are complex and require time and effort to be applied to exchange-traded options.

The author offers training programmes for individuals to manage their personal investments

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