# The Gamma Riddle

I have reserved two signed free copies of my book: How to Calculate Options Prices and Their Greeks for the first two persons solving this puzzle with the right argumentation. Good luck!

Dear Options addicts, experts, traders, nerds and others being interested in option theory,

I got very positive feedback on the vega riddle I posted in December and therefore I decided to come up with another riddle.

The following situation is the case:

I am long the 50 call once at 25% volatility, with expiry in 112 days

I am short the 50 call twice at 25% volatility, with expiry in 235 days

The underlying is a non dividend paying asset and interest rate is set at 0%, the underlying trades at 50 and stays at 50

We know that at inception of the trade we will be short gamma and short to expiry for the shortdated option we will be long gamma in the combination.

My question to you is:

1. How many days before expiry for the short dated option are we having a flat(tish) gamma position in this combination?

The underlying has stayed at 50 for quite some time, so most probably volatility would have come off to 15%.

2. How many days before expiry for the short dated option are we having a flat(tish) gamma position when volatility would have dropped towards 15%?

I know this sounds like a horrific exercise, but I think if you know the distributions, you will be able to ponder on it and find the solution.

I have reserved two signed free copies of my book: How to Calculate Options Prices and Their Greeks, for the first two persons solving this riddle.

Good luck!

Best regards,

Pierino