I'm trying to calculate the probability of a calendar spread resulting in a profit at expiration, when estimating it is modeled as a lognormal distribution, by getting:
P(a <= x <= b) = CDF(b) - CFA(a)
where a and b are the breakevens at expiration.
But there is something that I don't understand:
- Which value shall I use as variance? The IV of the ATM option for near expiration? The IV of the stock/index underneath?
- Does time really matter? I mean, since lognormal distribution (as defined in
numpylibraries) only requires mean and variance values, time does not matter unless you consider that volatility depends on t. If I get mean and variance for 2 calendars, one with front mont expiring in a week and another one expiring in a year, time should matter somehow, making the distribution PDF wider, and therefore affecting the results of the CDF. What am I missing here?