Futures Pricing — Cost of Carry Model
Fair futures price = Spot × e^((r − q) × t) for continuous compounding, or Spot + Cost of Carry for simple. r is the risk-free rate, q is the dividend yield on ...
Cost of Carry Pricing
Fair futures price = Spot × e^((r − q) × t) for continuous compounding, or Spot + Cost of Carry for simple. r is the risk-free rate, q is the dividend yield on the underlying, t is time to expiry in years. Any material deviation creates a cash-and-carry arbitrage.
Holding a stock costs money (interest on the borrowing) but can pay dividends — so the fair forward price of a stock is today's price plus net carrying cost. For an index, the same logic applies using the index dividend yield. When actual futures trade above fair value, arbitrageurs sell the overpriced futures and simultaneously buy the underlying stocks (cash-and-carry arbitrage) → pushes futures back to fair value. When futures trade below fair value, reverse cash-and-carry (buy futures, sell stocks) closes the gap. This arbitrage mechanism is why futures rarely stray far from fair value for more than minutes in a liquid market like Nifty.
Interest cost to hold the underlying, minus dividend income
The price at which arbitrage nets to zero
Sell overpriced futures + buy underlying = risk-free profit
Buy underpriced futures + short underlying
A Practical Example
Nifty spot = 22,500. Risk-free rate r = 6%, dividend yield q = 1.5%, time to expiry t = 30/365.
Fair value = 22,500 × e^((0.06 − 0.015) × 30/365) = 22,500 × e^(0.00370) = 22,500 × 1.003702 ≈ 22,583.
Market futures = 22,640. Premium of 57 points above fair value.
Arbitrage: SELL futures @ 22,640 + BUY Nifty basket @ 22,500. On expiry, basis converges — arbitrageur captures ~57 × 25 = ₹1,425 per lot risk-free (minus transaction costs).
What Makes This Important
Cost of Carry Model (continuous compounding)
F = S × e^((r − q) × t)
Nifty Futures Fair Value
Frequently Asked Questions
Because prices compound continuously — that is the standard finance convention and is consistent with Black-Scholes. The simple formula S + S·(r − q)·T is an approximation that works for short tenors and small rates but drifts for longer tenors.
🧠 Quick Quiz
1 questions to check your understanding