Stock Market Futures

An operation with futures can be defined as a contract or agreement between two parts in which they commit to Exchange an asset, physical or financial, at an established price and at a future pre-established date at the signing of the resolution.

For the buyer, the contract of futures means the obligation of having to buy the underlying asset at a future price at the date of expire and for the salesman, it supposes the obligation to sell such underlying asset at the future price at the same date of expire.

In futures two positions distinguished themselves, in whose losses or profits will depend on the relation between the future price (agreed at the present) and the price of liquidation (price of the underlying asset at the market and on the date of expire):

Long position (buying):

• If the future price is < than the liquidation price, the buyer obtains a profit.
• If the futures price is > than the liquidation price, the buyer has a loss.

Short position (selling):

• If the futures price is > than the liquidation price, the salesman has a loss.

A key element on the contract of futures will be then the determination of the futures price. This will be calculated in base on the cash price of the underlying asset plus the net financial cost; financial cost that will mark the difference between today (day the contract is agreed) and the date of expire of the contract.

So then, it will depend on the underlying asset defined on the contract. As a way of example we present the case of the shares and the bonds.

Forward price of a share:

• FW= PC (1 + ti)- d (1 + t’ I’)
• Where FW= forward price
• PC= Cash quoting of the share
• I = Rate free of risk
• D = Dividends paid before expiration
• T= time until expiration

And it pays dividends during the contract period; the person who accorded on the futures contract will no perceive the dividends in question.

Before this situation, you will have to deduce its impact from the futures price. If this is not done, the cash operation would result more efficient than the future operation and everybody would buy in cash until this effect would dilute  (arbitrage operation).

Forward price of a bond without the intermediate coupon payment:

• FW = (PC+ CC) (1 + it/360)- CCF)
• Where PC = Cash quoting of the bond
• CC = Running coupon of the bond in t  (synonymous of the accumulated interests)
• t = time till expiration
• i = Free of risk type of interest corresponding to t       
• CCF = Running coupon the day of expiration of the forward

Forward price of a bond paid with an intermediate coupon:    

FW= (PC +CC) (1 + it/360)-CCF- CC’ (1 + I’ t’/360)

• Where: CC’= Paid coupon in t’
• T’  = time until the expiration since the payment of the coupon
• I’  = Type of interest free of risk corresponding to t’  

In this case the intermediate coupon acts in the same way as with the payment of dividends of the shares. Those who have a future over a bond will not receive the coupon, so it must be discharged from the price.