Futures pricing

Q8.1: What determines the fair price of a derivative?
A: The fair price of a derivative is the price at which profitable arbitrage is infeasible. In
this sense, arbitrage (and arbitrage alone) determines the fair price of a derivative: this is
the price at which there are no profitable arbitrage opportunities. ••

Q8.2: What determines the fair price of an index futures product?
A: The pricing of index futures depends upon the spot index, the cost of carry, and expected
dividends. For simplicity, suppose no dividends are expected, suppose the spot
Nifty is at 1000 and suppose the one–month interest rate is 1.5%. Then the fair price of
an index futures contract that expires in a month is 1015. ••

Q8.3: What is ‘basis’?
A: The difference between the spot and the futures price is called the basis. When a Nifty
futures trades at 1015 and the spot Nifty is at 1000, “the basis” is said to be Rs.15 or 1.5%.
••
Q8.4: What is “basis risk”?
A: Basis risk is the risk that users of the futures market suffer, owing to unwanted fluctuations
of the basis. In the ideal futures market, the basis should reflect interest rates,
and interest rates alone. In reality, the basis fluctuates within a band. These fluctuations
reduce the usefulness of the futures market for hedgers and speculators. ••

Q8.5: What happens if the futures are trading at Rs.1025 instead
of Rs.1015?
A: This is an error in the futures price of Rs.10.
An arbitrageur can, in principle, capture the mispricing of Rs.10 using a series of

38 CHAPTER 8. FUTURES PRICING
transactions. He would (a) buy the spot Nifty, (b) sell the futures, and (c) hold till expiration.
This strategy is equivalent to risklessly lending money to the market at 2.5% per
month. As long as a person can borrow at 1.5%/month, he would be turning a profit of
1% per month by doing this arbitrage, without bearing any risk. ••

Q8.6: What happens if the futures are trading at Rs.1005 instead
of Rs.1015?
A: This is an error in the futures price of Rs.10.
An arbitrageur can, in principle, capture the mispricing of Rs.10 using a series of
transactions. He would (a) sell the spot Nifty, (b) buy the futures, and (c) hold till expiration.
This is equivalent to borrowing money from the market, using (Nifty) shares as
collateral, at 0.5% per month. As long as a person can lend at 1.5%/month, he would be
turning a profit of 1% per month by doing this arbitrage, without bearing any risk. ••

Q8.7: Are these pricing errors really captured by arbitrageurs?
A: In practice, arbitrageurs will suffer transactions costs in doing Nifty program trades.
The arbitrageur suffers one market impact cost in entering into a position on the Nifty
spot, and another market impact cost when exiting. As a thumb rule, transactions of a
million rupees suffer a one–way market impact cost of 0.1%, so the arbitrageur suffers a
cost of 0.2% or so on the roundtrip. Hence, the actual return is lower than the apparent
return by a factor of 0.2 percentage points or so. ••

Q8.8: What kinds of arbitrage opportunities will be found in
this fashion?
A: The international experience is that in the first six months of a new index futures
market, there are greater arbitrage opportunities that lie unexploited for relatively longer.
After that, the increasing size and sophistication of the arbitrageurs ensures that arbitrage
opportunities vanish very quickly. However, the international experience is that the glaring
arbitrage opportunities only go away when extremely large amounts of capital are
deployed into index arbitrage. See Peters (1985), Figlewski (1984), and Brenner et al.
(1990). ••

Q8.9: What kinds of interest–rates are likely to show up on the
index futures market – will they be like badla financing rates?
A: Arbitrage in the index futures market involves having the clearing corporation (NSCC)
as the legal counterparty on both legs of the transaction. Hence the credit risk involved
here will be equal to the credit risk of NSCC. This is in contrast with the risks of badla
financing. ••