Quick, what's your trade?

Quantitative Finance Level 2

The stock is trading at $20. The European call on the $10 strike expiring in 1 months is actively trading at $9. What trade do you want to execute?

Need to know the dividends Buy the call Sell the call Need to know the interest rates Need to know the counterparty

1 solution

Calvin Lin Staff
Feb 10, 2015

Given that this strike is nearly 50% down, and we have 1 months to expiry, it is likely (but not always true) that the extrinsic value of the call is close to 0. Hence, let's focus on calculating the intrinsic value, which would be the bulk of the call's value.

Even though it appears that the intrinsic value is greater than the price of the call (IE $20 - 10 = 10 > 9$ ), because this is a European call, we have to know what the future value of the call is worth.

In particular, if the stock will be paying out a dividend in the month, then the future price of the stock will be much lower, and hence the intrinsic value might not be more than 9.

Hence, we must know about the dividend payment before we can determine if this is a good trade.

Borrow and short sell stock and receive $20 now. Spend $9 on the call. Invest $11 at risk free rate now and earn interest until expiration. At expiration exercise call and buy back stock for $10 with the money you collected by selling stock and return borrowed stock. Total expenditure: $9 now and the present value of $10 Total revenue: $20 Risk free profit from buying call = $1 + interest Correct answer is buy the call.

Denis Kelleher - 4 years, 10 months ago

As stated, you need to first check for dividends. Suppose that the stock has dividends of $2 that pay out the day before expiration, and that the stock stays at $20 till expiration day when it drops to $18 due to dividends.

This is what happens. The numerical value indicates money going in/out of your account: 1. You sold the stock for +$20.
2. You bought the call for -$9.
3. You have to pay the dividends on the stock for -$2.
4. You exercise the call and buy the stock for -$10.

As a end result, your bank account has -$1. The reason is that the forward price you are using would be the "stock - dividend" price, especially since this is a European call when you cannot exercise before the expiration date.

The difference with an American call, is that we could immediately exercise the call, and thus skip step 3 where we have to pay out the dividend on the ex-div date.

Calvin Lin Staff - 4 years, 10 months ago

Haha!! I asked my father! !!

Parth Lohomi - 6 years, 4 months ago

Quick, what's your trade?

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