4. Consider the following terms and conditions on a contract build on a stock X

Question

4. Consider the following terms and conditions on a contract build on a stock X currently selling at INR 1000. In a 6 months time the long forward position on X pays INR 1026.20. However, the long forward holder will only receive the asset from the short position exactly 2 months after the payment INR. 1026.20 is made at the end of 6th month. In between, the underlying asset pays a cash dividend of 10.50 exactly one month after the payment of INR 1026.20 is made. Let the continuously compounded interest rate is 4.25%. Ignoring all other transaction and other charges, answer the following: Explain how would you make transaction in the underlying and the forward (i.e. long or short) at different time points to create an arbitrage (if any) in the above offered contract. Or else, justify that the forward is fairly priced and there is no arbitrage possible.

Explanation / Answer

Forward price at the time of delivery 2 months later is 1026.20 e0.04252/12 = 1033.49 (long forward is 2 months prepaid).

The arbitrage free forward price must be 1000 e0.04258/12 10.50 e0.04251/12 = INR1018.20.

Arbitrage is INR 15.29.
At time t = 0, borrow 1000, buy the asset, take short position in the forward contract.

At delivery time 8 months after, your forward is obliged so you receive 1033.49. You have collected a dividend 10.50e0.425/12 = 10.54. and you repay the borrowed loan with 8 months continuous interest amounting to INR 1028.74. So you earn arbitrage profit INR 15.29 at the end of 8th month.

Related Questions

Navigate

• Browse (All)
• Browse 4
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.