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Equity Futures

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Equity Future/Forward Valuation

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FinPricing provides valuation models for the following equity futures and forwards:

• Equity Futures
• VIX Futures
• Equity Forwards
• Equity Forwards with Foreign Dividends
• Equity Quanto Forwards
• Equity Composite Forwards
• Equity Basket Forwards
• Equity Asian (Average) Forwards
• Check FinPricing valuation models
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An Equity Forward contract is an agreement between two counterparties to buy a specific number of equity stocks, stock index or basket at a given price (called strike price) at a given date. For any forward contract no cash changes hands until the maturity of the contract. Equity forward contracts are cash settled in most cases. At maturity, the two counterparties exchange a cashflow equivalent to the difference between the stock closing price and the strike price. Equity forward contract is traded over the counter (OTC) instead of exchange market.

Unlike Equity Forward, an Equity Futures contract traded over the organized exchange. In this contract parties commit to buy or sell a specified amount of an individual equity or a basket of equities or an equity index at an agreed contract price on a specified date. Generally there are two types of Equity Futures: Index Future and Stock Future. Stock markets Index Futures are futures contracts used to replicate the performance of an underlying stock market index. They can be used for hedging against an existing equity position, or speculating on future movements of the index. Indices for futures include well-established indices such as S&P 500, FTSE 100, DAX, CAC 40 and other G12 country indices. Indices for OTC products are broadly similar, but offer more flexibility.

Single-stock futures are exchange-traded futures contracts based on an individual underlying security rather than a stock index. Their performance is similar to that of the underlying equity itself, although as futures contracts they are usually traded with greater leverage. Another difference is that holders of long positions in single stock futures typically do not receive dividends and holders of short positions do not pay dividends. Single-stock futures may be cash-settled or physically settled by the transfer of the underlying stocks at expiration, although in the United States only physical settlement is used to avoid speculation in the market.

A future takes place on an organized exchange where the all of the contract’s terms and conditions, except price, are formalized. The future’s standardization helps to create liquidity in the marketplace enabling participants to close out positions before expiration. Equity forward contract is traded over the counter (OTC). They are customized to meet the user’s special needs. Forwards have credit risk, but futures do not because a clearing house guarantees against default risk.

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2. Equity Future and Forward Valuation

Equity futures prices are usually quoted in the same way as equity prices quoted in the underlying cash market by exchanges. A pricing model is mainly used to calculate risk for a future contract, although it is utilized for computing both price and risk for a forward.

The theoretical value of a future/forward depends on the dividend model assumption. There are two types of dividends: dividend yield (continuous dividend) or discrete dividend.

The future/forward price under dividend yield assumption is given by

Discrete Dividend

The future/forward price under discrete dividend assumption can be expressed as

Practical Notes

• Equity future/forward price formula is very simple under dividend yield assumption. Unfortunately there is no or almost no dividend yield existing in the market, although sometimes people may convert discrete dividends into dividend yields for analytic tractability purpose.
• Almost all dividends in the market are discrete.
• One key factor for pricing any equity products is to correctly calculate equity forward taking all discrete dividends into account.