Single-stock Futures - Pricing

Pricing

Single stock futures values are priced by the market in accordance with the standard theoretical pricing model for forward and futures contracts, which is:

where F is the current (time t) cost of establishing a futures contract, S is the current price (spot price) of the underlying stock, r is the annualized risk-free interest rate, PV(Div) is the present value of an expected dividend, t is the present time, and T is the time when the contract expires.

When the risk-free rate is expressed as a continuous return, the contract price is:

where S is the stock price, PV(Div) is the Present value of any dividends generated by the underlying stock between T and t, r is the risk free rate expressed as a continuous return, and e is the base of the natural log. Note the value of r will be slightly different in the two equations. The relationship between continuous returns and annualized returns is rc = ln(1 + r).


The value of a futures contract is zero at the moment it is established, but changes thereafter until time T, at which point its value equals ST - Ft, i.e., the current cost of the stock minus the originally established cost of the futures contract.

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