Forward Contract

Summaries

1. Long position – agree to buy the financial or physical asset at the forward price (FP) at expiration (T).

2. Short position – agree to sell

3. For long position, at time t, if the spot price is more than the PV of FP, there is +ve value for the contract. Because you may short the asset at spot price and buy at expiration to earn:

V(t, long) = S(t) – FP/ (1+r)^(T-t)

Similarly,

V(t, short) = FP/(1+r)^(T-t) – S(t)

4. To prevent arbitrage, V(0) = 0, So S(0) = FP/(1+r)^T

This can be proved by cost-of-carry model.

5. This is based on frictionless market assumption:

1)      transaction cost is 0

2)      no restriction on short sales

3)      borrowing and lending can be done unlimited with risk-free rate

6. Equity forward price

V(t, long) = S(t) – PVD – FP/(1+r)^(T-t)

PVD is the PV of dividend. Since the stock has to be short at t, so the one who longs the contract receive no dividend. So have to subtract PVD. **** Make sure only dividend before the contract expires (T) is included.

Use 365 days or 12 months.

7. Equity forward contracts with continuous dividend (Useful for equity index)

d_c = continuous compounded yield of the index dividend

r_c = continuous compounded risk free rate   (r = exp(r_c) – 1  ***r_c<r)

Therefore,

FP = S(0)exp(-d_c*T)*exp(r_c*T)             

(??Approximation by exp(-d_c*T) ~ 1 – exp(d_c*T))

V(t,long) = S(t)/exp(d_c*(T-t)) – FP/exp(r_c*(T-t))

General strategy: Calculate the FP with the assumption of V(0) =0. And then calculate the V(t).