Borrow fees for shorting

In a conversion, a pending dividend increases the premium of a put relative to the call. A higher carry cost increases the premium of a call, relative to the put.

When the underlying is hard to borrow, a higher borrow cost increases the premium of a put. I can't figure out what formula is used for this. Or is it the same as above except that instead of borrowing to buy the underlying (a debit) you're paying a debit elsewhere (to the lender)?

Simple explanation with an example would be appreciated :->)

 

Market makers can do naked shorting. I don't know the details of when they are allowed to do this but if they are doing a naked short to balance out the put option they sold you then borrow costs and borrow availability aren't an issue.

 

I do not have a formula for you. When I was short stock and I had to pay interest to carry the short as a market maker, and my software did not allow me to use negative interest, I would add a small dividend once a week until the IVOl of the puts and call converged. I find that paying a dividend and paying short borrow fees worked the same for me. I hope that helps.

 

I don't follow what naked shorting by market makers has to do with my question. Or for that matter, borrow availability which is a function of how many shares lenders have to loan. I'm curious as to the mechanism of how the price of a put increases as the borrow fee increases.

 

Why do you think this would happen? I may have misunderstood something.

 

Thanks for your reply. That makes sense but I'm still wondering about a formula.

Would it make sense to use a Reverse Conversion and reduce the interest earned from the short equity position? Of course, that wouldn't work in software that doesn't allow negative carry cost (for example, the borrow cost exceeds the interest earned).

Be that as it may, set the Reversal up with zero profit. Then reduce the interest earned by the borrow fee, yielding a non-zero number. Divide by two and adjust the call and the put by that amount so that the Reversal is back to zero. That would demonstrate the effect of the borrow fee. Yeh, I know, I'm out on a limb, guessing at a solution.