Futures Pricing — Cost of Carry Model

The theoretical fair price of a futures contract is derived from the cost of carry model:

F = S × e(r+q-d)×T (continuous compounding)
or simplified: F = S × (1 + r − d) × T

Where:

  • F = Fair futures price
  • S = Current spot price
  • r = Risk-free rate (e.g., T-bill rate)
  • d = Dividend yield of underlying
  • T = Time to expiry (in years)

Example: Nifty 50 = 23,000. Risk-free rate = 7% p.a. No dividends. Time to expiry = 1 month (1/12 year). Fair futures price = 23,000 × (1 + 0.07/12) = 23,134.

Basis and Convergence

Basis = Spot Price − Futures Price

At the start of a contract, basis is usually negative (futures > spot = contango) because of the cost of carry. As expiry approaches, the basis narrows and converges to zero at expiry — this is called convergence.

Basis risk arises when the change in spot and futures prices is not perfectly correlated — creating imperfect hedges.

Margin System

Initial Margin (SPAN Margin)

Both buyer and seller must deposit an Initial Margin upfront with the clearing corporation (NSCCL). This is calculated using the SPAN (Standard Portfolio Analysis of Risk) methodology based on worst-case scenario loss over a single day.

Maintenance Margin

The minimum margin level. If MTM losses bring the account below maintenance margin, a Margin Call is issued. The trader must top up to the Initial Margin level within a specified time, or the broker squares off the position.

Mark-to-Market (MTM)

At end of day, all positions are revalued at the Daily Settlement Price:

  • Gains → credited to margin account
  • Losses → debited from margin account

Hedging with Futures

A short hedge involves selling futures to protect against a price fall (used by investors holding the underlying).

A long hedge involves buying futures to lock in a purchase price (used by those planning to buy the underlying in the future).

Hedge Ratio: Number of contracts needed = Portfolio Value / (Futures Price × Lot Size)