Financing Risk in Put–Call Parity Arbitrage

Summary

Put–call parity can imply an arbitrage when the prices of a call, a put, the underlying, and the present value of the strike do not align. The document asks what could make such a trade fail beyond insufficient liquidity to assemble the positions. Its answer identifies financing risk: a trader may rely on stock borrow or repo financing whose term is shorter than the options’ maturity, leaving future funding costs uncertain while the position remains open.

The example combines a short stock position with options and explains that borrow availability or cost can change when the initial financing period ends. Changes in interest rates can also alter financing assumptions. These risks may erode the apparent arbitrage profit, so a parity discrepancy is not necessarily risk-free in practice. The discussion is brief and does not quantify the impact, describe hedging methods, or cover other potential risks; it also explicitly sets aside transaction costs in its framing.

Key ideas

• A put–call parity price discrepancy may not translate into a risk-free trade after financing costs.
• Short stock positions can depend on borrow or repo terms that expire before the options do.
• Borrow conditions may change during the life of the position and reduce its expected profit.
• Interest rate changes can also affect the financing assumptions behind an arbitrage.

Tags

# Risk of Put-Call-Parity in practice


# Risk of Put-Call-Parity in practice












When $C+PV(K) \ne P + S_0$, it's an opportunity for risk-free arbitrage (excluding cost).

In practice, what potential risk could make the arbitrage fail?

I know that failure to build complete arbitrage portfolio due to lack of liquidity of call, put or underlying security could be one. What else could it be?

## Answer by Michael T (score 3)

https://quant.stackexchange.com/a/40757

Financing Risk

e.g. You sell the stock short and buy the Call and sell the Put. Lets say you can only get a 1w repo borrow on the stock yet your options are 3m options. You have the risk after that week is up, that the stock goes special, so your financing costs erode the arbitrage. Similarly the Fed could cut causing your financing assumptions to change, and depending the term of the repo that could impact your arbitrage.

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