American Arbitrage
A finance question asked in Senior Trader Interview at Hudson River Trading
Joe has 2 call options on the underlying S with initial price S_0 = 24 and strike K = 21. One option is European and the other is American. A European option is one where you can only exercise it at expiry while an American option can be exercised any time. The European option is valued at 3.21 while the American option is valued at 3.15. You also have access to bonds with discount rate Z_0 = 0.9. The underlying pays no dividends. What is the arbitrage? Give the answer in the form of the initial credit you receive (round to 2 decimal points)
Try to solve this problem yourself before moving on to the solution below
.
.
.
.
.
.
Solution
American and European calls on non-dividend paying stocks should have the same value.
The rationale is as follows: if you can exercise the American option and gain S - K anytime, it must be worth at least the European call for there to be no arbitrage. We will short the European call and long the American call. If the call expires in-the-money, then both options have value S - K and we obtain 0, but we keep our 0.06. If the calls expire out-of-the-money, then both options have value 0 and we once against keep our 0.06.
.
.
😃 Over to you: Were you able to solve this?
👉 If you liked this post, don’t forget to leave a like ❤️. It helps more people discover this newsletter on Substack and tells us that you appreciate solving these weekly questions. The button is located towards the bottom of this email.
👉 If you love reading this newsletter, feel free to share it with friends!