Long put, long theta

I've got a spread expiring this month, and one of the legs is a long put, and according to Td waterhouse analytics, it's long theta.... Wtf?

I'm only talking about the leg, not the positon

 

Is it very deep in the money?

Often when puts are very deep in the money the BS curve crosses below the payoff so if you sell it you sell it for less than the intrinsic (payoff) hence it makes sense to just keep it and earn the time value.

 

hey,

yeah it is actually, delta ~0.99 - 1.0

I didn't know that could happen.

I'm sure there's a reasonable explanation, it just doesn't make sense to me at this time though.

 

I remember reading something about close to expiration, theta can reverse itself for ITM options. It has to do with the carry cost versus the volatility.

 

I see, I'll try to find some info on it then...

thanks!

 

For European style options ITM puts can trade for less than parity - due to cost of carry.

So if your put is euro - the positive theta may represent the difference between the discount and parity.

 

Yep, agree with donnap...

If there's cost of carry, your roll down can overwhelm the optionality aspect. Same reason why some ITM options can have delta > 1.

 

A simple explanation is that european style options are priced on a forward.

Thus, if interest rates are around 10% , spot is 100 and the one year put strike is 200, european option is priced on a forward around 110 (100*(1+10%)) .

Hence intrinsic value is 200-100=100 but the one year put value is 200-110=90

 

Options exhibit deltas>1 only if foreign interest rates are negative or there are storage costs.

 

It's just a function of the cost of carry (CoC), however that CoC arises (including the examples you cite). If CoC > risk-free rate, delta of an option can be > 1.