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Pricing index futures given expected dividend yield

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Sunanda K. Chavan
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Pricing index futures given expected dividend yield - October 1st, 2010

If the dividend flow throughout the year is generally uniform, i.e. if there are few historical cases of clustering of dividends in any particular month, it is useful to calculate the annual dividend yield.

F = s (1+r-q) T

Where:

F: futures price

S: spot index value

r: cost of financing

q: expected dividend yield

T: holding period


Example

A two-month futures contract trades on the NSE.

The annual dividend yield on Nifty is 2% annualized. The spot value of Nifty 1200. What is the fair value of the futures contract?

Fair value = 1200(1+.015-0.02) 60/365 =Rs. 1224.35

The cost of carry model explicitly defines the relationship between the futures price and the related spot price.

As we know, the difference between the futures price and the spot price is called the basis.


Nuances

• As the date of expiration comes near, the basis reduces - there is a convergence of the futures price towards the spot price. On the date of expiration, the basis is zero.

If it is not, then there is an arbitrage opportunity. Arbitrage opportunities can also arise when the basis (difference between spot and futures price) or the spreads (difference between prices of two futures contracts) during the life of a contract are incorrect.

At a later stage we shall look at how these arbitrage opportunities can be exploited.

• There is nothing but cost-of-carry related arbitrage that drives the behavior of the futures price.

• Transactions costs are very important in the business of arbitrage.
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Rose Marry
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Re: Pricing index futures given expected dividend yield - April 16th, 2016

Quote:
Originally Posted by sunandaC View Post
If the dividend flow throughout the year is generally uniform, i.e. if there are few historical cases of clustering of dividends in any particular month, it is useful to calculate the annual dividend yield.

F = s (1+r-q) T

Where:

F: futures price

S: spot index value

r: cost of financing

q: expected dividend yield

T: holding period


Example

A two-month futures contract trades on the NSE.

The annual dividend yield on Nifty is 2% annualized. The spot value of Nifty 1200. What is the fair value of the futures contract?

Fair value = 1200(1+.015-0.02) 60/365 =Rs. 1224.35

The cost of carry model explicitly defines the relationship between the futures price and the related spot price.

As we know, the difference between the futures price and the spot price is called the basis.


Nuances

• As the date of expiration comes near, the basis reduces - there is a convergence of the futures price towards the spot price. On the date of expiration, the basis is zero.

If it is not, then there is an arbitrage opportunity. Arbitrage opportunities can also arise when the basis (difference between spot and futures price) or the spreads (difference between prices of two futures contracts) during the life of a contract are incorrect.

At a later stage we shall look at how these arbitrage opportunities can be exploited.

• There is nothing but cost-of-carry related arbitrage that drives the behavior of the futures price.

• Transactions costs are very important in the business of arbitrage.
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