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Lesson 2: Forward Contracts I Part 1
Forward – Pricing and Valuation: Forward Contracts on Underlying with No Income, No Storage Cost
| Variables | Meanings |
|---|---|
| T: | delivery time |
| r: | risk-free interest rate for maturity T |
| S0: | Spot price today, t = 0 |
| F(0,T): | forward price today (t = 0) with expiration at t = T |
| Vt1 (0,T): | Value at t = t1of an existing LONG forward contract expiring at t = T established at t = 0 < t1 (is this less than t1) |
Forward Price:
Recall: FowardPrice = SpotPrice + {FV(cost) - FV(benefits)} for deferred transaction.
FV(cost) is the interest cost of borrowing (assuming no storage cost), FV(benefit) = zero (assuming no income from the underlying).
Thus, a synthetic forward contract cost is: F(0,T) = (amount borrowed) + interest cost
Therefore:
- Discrete compounding: F(0,T) = S0 (1+r)T [⇔ FV(Spot Price at t = 0)]
Because (S0 (1 + r)T - S0) is the interest cost, we obtain:
S0 + (S0 (1 + r)T - S0) = S0 (1 + r)T - Continuous compounding: F(0,T) = S0erT [⇔ FV(Spot Price at t = 0)]