Unlike options, that are just a right without an obligation, the futures are a right and an obligation. Futures are symmetric products as the buyer and the seller have the same set of rights and obligations. But how is the futures price determined and how do you decide at what futures you should put in your trade. That depends on the rate of interest and the time to expiry. Let us consider some situations to understand this point.

Futures Price Determination

Basic equation for the future's price

without cash flows during maturity

F

= future's price

100.99

S

= spot price

100.00

r

12.00%

(continuous)

T-t

= days to maturity

30

(365 days in year)

In the above illustration, if the spot price is Rs.100 and if you are looking at a 1-month future, then for a return of 12% annualized you need to sell the futures at a price of Rs.100.99. Of course, there is brokerage and statutory costs and that will impact but for now let us leave that out for simplicity. Let us only focus on the term to expiry of futures. What if the above conditions pertained to a 2-mont future instead of a 1 month future? What happens then? Check the calculation below:

Futures Price Determination

Basic equation for the future's price

without cash flows during maturity

F

= future's price

101.99

S

= spot price

100.00

r

12.00%

(continuous)

T-t

= days to maturity

60

(365 days in year)

In the above illustration, if the spot price is Rs.100 and if you are looking at a 2-month future instead of a 1 month future, then for a return of 12% annualized you need to sell the futures at a price of Rs.101.99. As you can see in the above illustration, you have to sell the 2 month future at a higher price for the same gain at the end of the year. That also explains why futures premium keeps going up as you go to 2 month and 3 month futures in India. Of course, there is brokerage and statutory costs and that will impact but for now let us leave that out for simplicity. Let us only focus on the term to expiry of futures. What if the above conditions pertained to a 3-month future instead of a 2 month future? What happens then? Check the calculation below:

Futures Price Determination

Basic equation for the future's price

without cash flows during maturity

F

= future's price

103.00

S

= spot price

100.00

r

12.00%

(continuous)

T-t

= days to maturity

90

(365 days in year)

In the above illustration, if the spot price is Rs.100 and if you are looking at a 3-month future instead of a 2 month future, then for a return of 12% annualized you need to sell the futures at a price of Rs.103.00. As you can see in the above illustration, you have to sell the 3 month future at a higher price for the same gain at the end of the year. That also explains why futures premium keeps going up as you go to 2 month and 3 month futures in India. Here of course, we assume that the interest rate remains the same and only the term to expiry changes. But in practice, the time to expiry and the interest rates keep moving and that makes it a lot more complicated.

Unlike options, that are just a right without an obligation, the futures are a right and an obligation. Futures are symmetric products as the buyer and the seller have the same set of rights and obligations. But how is the futures price determined and how do you decide at what futures you should put in your trade. That depends on the rate of interest and the time to expiry. Let us consider some situations to understand this point.

Futures Price DeterminationBasic equation for the future's price

without cash flows during maturity

F

= future's price

100.99

S

= spot price

100.00

r

12.00%

(continuous)

T-t

= days to maturity

30

(365 days in year)

In the above illustration, if the spot price is Rs.100 and if you are looking at a 1-month future, then for a return of 12% annualized you need to sell the futures at a price of Rs.100.99. Of course, there is brokerage and statutory costs and that will impact but for now let us leave that out for simplicity. Let us only focus on the term to expiry of futures. What if the above conditions pertained to a 2-mont future instead of a 1 month future? What happens then? Check the calculation below:

Futures Price DeterminationBasic equation for the future's price

without cash flows during maturity

F

= future's price

101.99

S

= spot price

100.00

r

12.00%

(continuous)

T-t

= days to maturity

60

(365 days in year)

In the above illustration, if the spot price is Rs.100 and if you are looking at a 2-month future instead of a 1 month future, then for a return of 12% annualized you need to sell the futures at a price of Rs.101.99. As you can see in the above illustration, you have to sell the 2 month future at a higher price for the same gain at the end of the year. That also explains why futures premium keeps going up as you go to 2 month and 3 month futures in India. Of course, there is brokerage and statutory costs and that will impact but for now let us leave that out for simplicity. Let us only focus on the term to expiry of futures. What if the above conditions pertained to a 3-month future instead of a 2 month future? What happens then? Check the calculation below:

Futures Price DeterminationBasic equation for the future's price

without cash flows during maturity

F

= future's price

103.00

S

= spot price

100.00

r

12.00%

(continuous)

T-t

= days to maturity

90

(365 days in year)

In the above illustration, if the spot price is Rs.100 and if you are looking at a 3-month future instead of a 2 month future, then for a return of 12% annualized you need to sell the futures at a price of Rs.103.00. As you can see in the above illustration, you have to sell the 3 month future at a higher price for the same gain at the end of the year. That also explains why futures premium keeps going up as you go to 2 month and 3 month futures in India. Here of course, we assume that the interest rate remains the same and only the term to expiry changes. But in practice, the time to expiry and the interest rates keep moving and that makes it a lot more complicated.