How Stock Borrow Costs Affect Option Carry and Put-Call Parity
Summary
The note discusses how a short stock position can affect the carry embedded in an option strategy. In a short sale, the trader receives proceeds that may earn interest, while also paying a stock borrow fee. The net financing effect can reduce the effective carry rate and lower the forward price used to compare calls and puts. In a no-dividend setting, call and put premiums are related through carry, as illustrated by conversion and reversal positions.
The explanation is framed as a clarification of a passage in an options text, and it cautions that the relevant value may refer to a combined position rather than the option premium alone. It offers no numerical example or market data, and actual economics depend on borrow availability, fees, interest earned on collateral, and dividends. The note is useful for understanding financing effects, but its brief answer does not fully develop the pricing framework.
Key ideas
- A short sale generates proceeds that may earn interest while the borrowed shares incur a borrow fee.
- The net financing rate can change the forward price and the relative carry of calls and puts.
- Put-call parity links call and put premiums through financing and dividends.
- The effect of a stock position may concern a combined strategy rather than an option premium in isolation.
Tags
Full text
# How do short stock positions lower the value of calls and raise the value of puts? # How do short stock positions lower the value of calls and raise the value of puts? I'm reading Option Volatility and Pricing by Sheldon Natenberg who 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. How can holding a short stock position affect the interest rate on the option? ## Answer by Bob Baerker (score 1) https://quant.stackexchange.com/a/57603 The short answer? In the absence of a dividend, call premium exceeds put premium by the carry cost (look at the explanation of conversions and reversals). If you're short the stock, your receive interest on the proceeds. However, you pay a borrow cost to the lender of the stock, thereby "reducing the interest rate by the borrowing costs required to sell the stock short. " I'm not a fan of Natenberg's explanations. I'd guess that his statement might be part of a larger story about a position he's explaining, perhaps even a conversion or reversal, hence his wording "the value of a stock option will also depend on whether the trader has a long or short stock position." If so, don't confuse value with premium.
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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.