Question

The current level of a stock is S₀ = 100. A forward contract on 1 share of this stock matures after six months. The continuously compounded interest rate is 5% per year. The stock generates a 1.9% dividend yield per year. Now a dealer quotes a forward price $102.31 for S.

(a) How would you arbitrage this quote?
(b) What would your arbitrage profits be?

Answer 1

To arbitrage this quote, you would borrow money to purchase the stock and enter into a forward contract. The arbitrage profits would be $2.31.

Step-by-step explanation:

To arbitrage this quote, you would undertake the following steps:

1. Borrow $100 at the continuous interest rate of 5% per year for six months. The amount borrowed would be $100 * e^(0.05 * 0.5) = $102.53.
2. Purchase one share of the stock for $100.
3. Enter into a forward contract to sell the stock for $102.31 after six months.
4. Hold the stock until it matures and then sell it for $102.31.
5. Repay the borrowed amount plus interest, which would be $102.53 * e^(-0.05 * 0.5) = $100.

The arbitrage profits would be the selling price of the stock ($102.31) minus the purchase price of the stock ($100), which is $2.31.