Question

A market-maker in stock index forward contracts observes a one-month forward price of 2,765 on an index.

You are given:

• The index spot price is 2,757.
• The continuously compounded dividend yield on the index is 1%.
• The cost of carry is 2%.

Describe actions the market-maker could take to exploit an arbitrage opportunity, and calculate the resulting profit (per index unit) at the end of one month.

1. Sell observed forward, buy synthetic forward; Profit = 3.40

2. Sell observed forward, buy synthetic forward; Profit = 1.10

3. Buy observed forward, sell synthetic forward; Profit = 1.10

4. Buy observed forward, sell synthetic forward; Profit = 3.40

5. No arbitrage opportunity is available

Answer 1

Fair Value of any forward contract is FV,

S = Spot Price = 2757

c = cost of carry = 2%.

t = time = 01 Month = 01/12 = 0.0833 Year

=  2,761.59

As fair value is lower than the Actual future Index Value 2765.

So there is an arbitrage opportunity.

Here FV <  One-month forward price

So, the market maker should sell synthetic forward and buy on observed forward ,

Profit should be = Observed Value - Fair Value = 2765 - 2761.59 ~ 3.4

Ans : Buy observed forward, sell synthetic forward; Profit = 3.40

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