Why Opposite Currency Options May Not Form an Arbitrage

Summary

The document considers whether buying a CADUSD put and selling a USDCAD call could create an arbitrage because their quoted premiums and payoffs appear to leave a net credit. The question highlights that the currencies are inversely related and argues that the put might gain more as the exchange rate rises, while both options might expire worthless if it falls.

The answer identifies differing expiration dates as enough to invalidate the riskless arbitrage claim. With mismatched expiries, the positions do not necessarily settle against the same market state, leaving exposure to price movements and timing. The trade could still be profitable, but it can also lose money, so the apparent premium difference does not establish a guaranteed profit. The discussion is brief and does not quantify option values, conversion mechanics, or other contract differences; it focuses on expiry mismatch as the stated source of risk.

Key ideas

• Opposing currency pairs can make option payoffs appear to offset one another.
• A net premium credit alone does not establish an arbitrage.
• Different option expiration dates leave residual market risk.
• A trade with expiry mismatch may earn a profit, but it can also lose money.

Tags

# USDCAD options vs CADUSD options arbitrage?


# USDCAD options vs CADUSD options arbitrage?












I think I've found an arbitrage opportunity. Right now, I can do this (first via CME, second via SAXO) :

BUY CADUSD AMERICAN PUT 10200 STRIKE EXPIRING 16 MAR 2011 FOR 53 pips USD

SELL USDCAD EUROPEAN CALL 0.9805 STRIKE EXPIRING 16 MAR 2011 FOR 68 pips CAD

The first trade costs me 530 USD, the second one gives me 680 CAD, for a net profit of 163.52 USD (assuming USDCAD at 0.9805). Now:

- If USDCAD decreases (meaning CADUSD increases), both options expire worthless.

- If USDCAD increases (meaning CADUSD decreases), it appears that my long put gains value faster than my short call (just barely, due to the currency difference).

Is there something I'm not seeing here?

Of course, the prices I'm seeing might not be tradeable, and there are some minor expiration date issues, but, assuming I could do this, is it arbitrage?

## Answer by glyphard (score 1)

https://quant.stackexchange.com/a/618

the difference in the expiration dates is enough to explain the source of what appears to be arbitrage.

Given that there is a difference, it's not abritrage(riskless profit) because there is risk.

However, that doesn't mean that you can't make money doing thsi trade. It just means that you might lose as well(not riskless).

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