Futures Price calculation

 

Formula for Cost of Carry:

The cost of carry for a futures price can be represented as:

$$\text{Futures Price} = \text{Spot Price} + \text{Cost of Carry}$$

Where:

$$\text{Cost of Carry} = \text{Interest Cost} - \text{Dividend Yield} \text{ (for stock indices)}$$

Example:

Let's say you are looking at the Nifty index, which is currently trading at a spot price of 10,000. The interest rate is 6% per year, and the dividend yield of the index is 2% per year. We want to calculate the futures price for a contract expiring in three months.

1. Interest Cost Calculation:

   • Annual interest rate: 6%
   • For three months (1/4th of the year), the interest cost is:
   $$6\% \times \frac{1}{4} = 1.5\%$$

2. Dividend Yield Calculation:

   • Annual dividend yield: 2%
   • For three months, the dividend impact would be:
   $$2\% \times \frac{1}{4} = 0.5\%$$

3. Net Cost of Carry:

   • Net cost of carry for three months:
   $$\text{Net Cost of Carry} = 1.5\% - 0.5\% = 1\%$$

4. Calculating the Futures Price:

   $$\text{Futures Price} = 10,000 + (10,000 \times 1\%) = 10,100$$