16. How is Futures Pricing Determined?
Introduction
Futures prices are not arbitrarily set. They are derived from the spot price of the underlying asset and adjusted for something called the cost of carry. This cost includes financing cost, dividends, and time left until expiry.
This pricing model is rooted in arbitrage-free pricing theory — ensuring that there are no “free profits” for traders due to price mismatch between futures and spot markets.
Theoretical Pricing Formula
Futures Price = Spot Price + Cost of Carry
Where: Cost of Carry = (Financing Cost – Expected Income or Dividend) × Time to Expiry
Or more precisely:
Futures Price = Spot Price × e^((r – d) × t)
Where:
- r = Risk-free interest rate
- d = Dividend yield (if any)
- t = Time to expiry in years
- e = Exponential function (2.718…)
In most practical cases, a simplified linear version is used for explanation.
What is Cost of Carry?
Cost of Carry refers to the net cost of holding (or carrying) the asset till the expiry of the futures contract. It includes:
| Component | Description |
|---|---|
| Interest Cost (r) | Opportunity cost of capital used to buy the asset (often the risk-free rate) |
| Storage/Insurance | Applicable in commodities or physical goods |
| Dividends (d) | If the underlying pays dividends, it reduces the futures price |
| Time to Expiry (t) | Longer the time, higher the carry cost (unless income offsets it) |
Real-World Example: Nifty Futures
Let’s assume:
- Nifty Spot Price = ₹22,000
- Risk-Free Rate = 6% per annum
- Dividend Yield = 1.5%
- Time to Expiry = 30 days = 30/365 = 0.082 years
Applying the formula:
Cost of Carry ≈ (7% of 2,800) – 20 = ₹196 – 20 = ₹176 Futures Price ≈ 2,800 + 176 = ₹2,976 (approx)
Key Takeaways
- Futures prices are mathematically linked to the spot price.
- Cost of carry determines the premium or discount on the contract.
- The longer the time to expiry, the greater the impact of carry.
- Dividends and interest rates both play a crucial role.
- Traders use the difference between spot and futures prices to identify arbitrage or mispricing opportunities.