Equity Forward Contracts

An equity forward contract is an agreement between two parties to buy a pre-specified number of an equity stock (or stock index) at a given price at a given date.

• Notation

• F(0,T) = forward price for a contract initiated at time 0 and expiring in time T

• S0 = spot price of the underlying equity at time 0

• r = risk-free rate (rc indicates continuous compounding)

• δ = dividend yield (δc indicates continuous compounding)

• T = total time of the contract, where T of 1 year = 1 and T of six months = 0.5

• Equity Forward Contracts for Discrete Dividends

Price at initiation: F(0,T) = (S0 - PV(δ))(1+r)T

Value at time "t": Vt(0,T) = St - PV(δ) - PV[F(0,T)]

Remember, the price will represent the amount that the contract buyer will pay at contract expiration to acquire the underlying asset; alternatively, the value reflects a change to the intrinsic value of the contract (the spot price at time "t" minus the present value of the dividends, minus the present value of the price of the forward contract).

• Equity Forward Continuously Compounded Dividends

Price at initiation: F(0,T) = (S0e-δcT)ercT

Value at time "t": Vt(0,T) = Ste-δc(T-t) - F(0,T)e-δrc(T-t)

• The formulas for discrete and continuously compounding dividends, when pricing and valuing equity forward contracts, should lead to similar answers.