How Short-Stock Borrow Costs Affect Option Values

Summary

The document raises a question about the effect of stock borrowing costs on option valuation when a trader holds a short stock hedge. The cited explanation says that borrow costs act like a reduction in the effective interest rate: they lower the forward price, which tends to reduce call values and increase put values. The question asks for an arbitrage, replication, or hedging example to make that relationship clear.

However, the supplied text contains no answer or worked example, so it does not establish the derivation or specify the assumptions behind that interpretation. It serves as a prompt about how stock loan economics enter option pricing, rather than a complete pricing method. Any application would need to account for the borrowing rate and the market conventions relevant to the security and option being valued.

Key ideas

• Stock borrow costs can affect the forward price implied by a short stock hedge.
• A lower forward price is associated with lower call values and higher put values in the explanation cited.
• The document asks for a replication or arbitrage example but does not provide one.
• The pricing effect depends on the stock borrowing assumptions used.

Tags

# Do option values depend on whether a trader hedges with a long stock or short stock position?


# Do option values depend on whether a trader hedges with a long stock or short stock position?












Sheldon Natenburg in his book Option Volatility and Pricing in the chapter on Risk Management is trying to explain the effect of interest rates on options.

He says

> The value of a stock option will also depend on whether the trader has a long or short stock position. If a trader's option also includes a short stock position, he is effectively reducing the interest rate by the borrowing costs required to sell the stock short. This will reduce the forward price, thereby lowering the value of calls and raising the value of puts.

I understand that there is a cost to borrowing the stock but how does this "lower the interest rate"? Can someone show me this effect using an arbitrage/replication/hedging example?

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.