Reading through Taleb's Dynamic Hedging, when I came across this part:
Theta, Interest Carry, and Self-Financing Strategies
Traders eliminate the interest costs of holding the premium to compute the theta because the carry of an option should be neutral to a trader who funds himself. In other words, if the trader incurs carry costs, the price of the theta will be increased by the interest paid on the premium, making it totally neutral. Thus, if interest rates are 20%, theta will be lower by 20% of the total premium (the option will have a lower price because of the present-value effect) but the carry costs of holding the option will offset these savings. It is assumed that the trader has borrowed the money to buy the option and that he would pay the difference in higher interest.
Many traders erroneously factor the premium costs in the theta computation.
As a convention, in this book, theta includes no premium costs.
In the derivation of an option value through a self-financing strategy, the seller of the option is supposed to buy an interest-yielding instrument. This is equivalent to the option trader funding himself from his firm by paying for negative balances and earning interest on positive ones.
I'm a bit confused. Does the standard BSM formula for theta have the interest costs for holding the premium or not? If so, what exactly is being removed? Would appreciate some general explanation of what he's talking about, thanks.
