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EdisonCruise
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Joined: September 15th, 2012, 4:22 am

How to price European put option with short selling cost?

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?
Last edited by EdisonCruise on March 18th, 2015, 11:00 pm, edited 1 time in total.
 
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LocalVolatility
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How to price European put option with short selling cost?

March 19th, 2015, 7:29 am

(1) Yes, you can price the repo like a continuous dividend yield.(2) The same holds true for calls as you are able to receive the repo on you long position.(3) So by (2) it makes no difference.
 
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EdisonCruise
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Posts: 102
Joined: September 15th, 2012, 4:22 am

How to price European put option with short selling cost?

March 19th, 2015, 3:05 pm

Thank you for your reply. The assumption here is the situation in practice, where no repo can receive in the long stock position. The market is not liquid. Some policy imposes a restriction on borrowing stock by a high short selling rate. So I doubt if there is a put-call parity in this case, which can be independent of pricing model.
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