Theta on Deep In The Money Puts (LOS 60.d) scenario, increase, contract, positive, five

PieMan

In reading on the five inputs of the BSM and their related Greeks, the test repeatedly comes back to the point that some deep in the money puts display positive theta (time value) as expiration of the contract draws closer. Does anyone know the rationale behind this? They make a big deal of it and I picture time value basically as a fuse that slowly burns out and I can't foresee a scenario where erosion of time would increase the value of the put all else held constant. Thanks in advance...



Edited 1 time(s). Last edit at Tuesday, February 1, 2011 at 08:39PM by EastCoastJ.

comp_sci_kid

Hi EastCoast,
You enter in a put agreement for Royal bank stock which expire in Dec 2011 with X=100

Lets now assume the Royal stock went down to 0 from July to Dec......You are now deep in the money my friend for the put of $100.

Will u wait till December to excersise or u have to do early in July...either way u are selling for 100$ BUT consider the time value of money? Certainly July 100 bucks is worth more than Dec100$. This is the only exception for brother Theta's view lol....

Momentum trader,
Toronto



Edited 1 time(s). Last edit at Wednesday, February 2, 2011 at 02:06PM by Dobenya.

luda002

as above..where delta=1 this is theoretically possible.

However, i think this theory is most relevant to fx options rather than equities/rates.

OmarAdnan

ohai Wrote:
-------------------------------------------------------
> OP, theta is change in the price of the option if
> time to maturity decreases, holding all else
> equal. If your option is extremely in the money,
> the option value will be close to intrinsic value
> (the difference between spot and strike). It
> doesn't matter if it's a call or a put. As time
> progresses towards expiration, your payoff becomes
> sooner and hence, it increases in value.
>

This is true. Imagine you have a 5-year put with a strike price of $100 on a company that is bankrupt (stock price = $0). Since the stock price remains $0, you have a guaranteed payment of $100, the present value of which is equal to 100/(1+r)^t. Therefore, as time progresses, this option becomes more valuable, meaning theta is positive.