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Basics of Derivatives

Pricing of Futures Contracts

In this unit, we will learn to determine the future price of an asset. 

 

We know the futures instrument derives its value from its respective underlying. We also know that the futures instrument moves in sync with its underlying. If the underlying price falls, so would the futures price and vice versa. However, the underlying price and the futures price differ and they are not really the same. Say for example, Nifty Spot is at 17586 whereas the corresponding current month contract is trading at 17597. This difference in price between the futures price and the spot price is called the “basis” or spread. The basis is 9 points in our example. 

 

Pricing of a futures contract depends on the characteristics of the underlying asset. There is no single way to price futures contracts because different assets have different demand and supply patterns, different characteristics and cash flow patterns. Market participants use different models for pricing futures. The two popular models of futures pricing:

 

  • Cash and Carry model
  • Expectancy model

Cash and Carry Model

Let us understand this concept with an example.

 

There are two people - Ram & Arjun. Ram decides to buy a particular stock TCS in the spot market paying total amount and takes delivery of the share. On the other hand, Arjun decides to buy TCS in futures paying just the margin. 

What happens with Ram’s Position?

 

TCS shares are credited in his demat account. Now if TCS announces a dividend, Ram is entitled to that dividend, but simultaneously he loses out on the opportunity cost of the funds involved in buying those TCS shares in the spot market. He is basically forgoing the interest on those funds.

 

On the other hand, Arjun deploying just a small margin is holding a similar position in TCS. When dividend is announced Arjun is not entitled to this dividend as his demat account doesn’t have TCS shares.

 

We see that both Ram and Arjun are long on TCS but still their situation has few differences on account of opportunity cost of funds involved as well as dividends received. This is known as cost of carry

 

The Cash & Carry Model assumes that markets are perfectly efficient. This means there are no differences in the cash and futures price. No opportunity for arbitrage exists and investors are indifferent to the spot and futures market prices while they trade in the underlying asset. 

 

The model also assumes, that the contract is held till maturity, the price of a futures contract will be equal to the spot price plus the net cost incurred in carrying the asset till the maturity date of the futures contract.

 

Futures Price = Spot Price + (Carry Cost – Carry Return)

 

Here, Carry Cost refers to the cost of holding the asset till the futures contract matures. This could include storage cost, in case of commodities, interest paid to acquire and hold the asset, financing costs etc. 

 

Carry Return refers to any income derived from the asset while holding it like dividends, bonuses etc. A net of these two is called the net cost of carry.

 

The cost of carry model used for pricing futures is given by:

 

 

Where,

 

S- Spot price

 

r- cost of financing (using continuously compounded interest rate)

 

T- Time to expiry

 

e- 2.71828

 

Expectancy Model

According to the expectancy model, it is not the relationship between spot and futures prices but that of expected spot and futures prices, which moves the market. This is why market participants would enter futures contract and price the futures based upon their estimates of the future spot prices of the underlying assets. 

 

According to this model, 

  • Futures can trade at a premium or discount to the spot price of the underlying asset. 
  • Futures price give market participants an indication of the expected direction of movement of the spot price in the future.

For instance, if the futures price is higher than the spot price of an underlying asset, market participants may expect the spot price to go up in the near future. This expectedly rising market is called “Contango market”. 

 

Similarly, if the futures price is lower than the spot price of an asset, market participants may expect the spot price to come down in future. This expectedly falling market is called “Backwardation market

 

The difference between the spot and the futures price is known as Basis.

 

So, now that we have understood how futures contracts are priced. Next, let us discuss the different market participants in this futures market. 

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