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:

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:

ComponentDescription
Interest Cost (r)Opportunity cost of capital used to buy the asset (often the risk-free rate)
Storage/InsuranceApplicable 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:

Applying the formula:

Cost of Carry ≈ (7% of 2,800) – 20 = ₹196 – 20 = ₹176 Futures Price ≈ 2,800 + 176 = ₹2,976 (approx)

Key Takeaways