How to price European put option with short selling cost?
Posted: March 18th, 2015, 2:47 pm
One sells a European put option and wants to hedge it by short selling the stock. If he does not own any stock, then he need to borrow it at a high rate L, say 10% p.a. from the borrower. He cannot get any money from short selling, which is different from the BS assumption. How to price this European put option?(1) I think under the black-scholes-merton framework, for European put pricing, the short selling cost is somewhat like a dividend in stock option or the cost of carry. Am I correct?(2) If one sells a call option, he needs to buy the stock to hedge the position. He can borrow money at risk free rate r, which is much smaller than short selling cost L. Then what is the put call parity in this case? (3) If the put option price is quoted by a market maker and he has already sold some call option, he must delta-hedge the call options by holding certain amount of stock. In such a case, if he wants to sell put option, the put price can be cheaper, because he doesn't need to borrow stock at a high rate. Then how to calcuate the implied volatility from put option price quoted from market?