A hard-to-borrow stock trades at 50. The borrow costs 8% annually, the funding rate is 5%, and there are no dividends. What is the fair value of C - P for the 6-month 50-strike options, and which side trades higher?

A hard-to-borrow stock trades at 50. The borrow costs 8% annually, the funding rate is 5%, and there are no dividends. What is the fair value of C - P for the 6-month 50-strike options, and which side trades higher?

Approach: Treat the borrow fee as a continuous dividend yield paid away by the stock holder, then apply parity in its dividend form.

-0.726. A borrow cost of q = 8% acts exactly like a continuous dividend yield in put-call parity, so C - P = S*e^{-qT} - K*e^{-rT} = 50*e^{-0.04} - 50*e^{-0.025} = 48.039 - 48.765 = -0.726. The put trades 0.726 above the call at the same strike, which is the market quoting a forward price of 49.26 rather than the 51.27 a zero fee would give. A trader who sees calls and puts equal here is being handed a synthetic short at a level that ignores the fee, and the borrow desk collects that 0.726 over six months. On names where the fee moves daily the options market reprices the parity gap faster than the stock loan market reprices the rate.

Follow-up: If the borrow fee is quoted daily and can jump from 8% to 40% overnight, how would you quote the 6-month conversion?

Key concepts: borrow cost, put-call parity, forward price, synthetic short.