CFA L1 / Deriv / M5. Forward Pricing
Module 5 · Derivatives

Pricing and Valuation of Forward Contracts

EN: No-arbitrage forward price and value during the contract's life.
VN: Giá forward không-arbitrage và giá trị qua thời gian.

1. Forward Price (No Income) Core

\[ F_0(T) = S_0 \cdot (1 + r)^{T} \]
Practice problem

Spot $80, r = 5% (annual), T = 6 months. Compute forward.

Show solution
F = 80 × (1.05)\(^{0.5}\)
= 80 × 1.0247
F ≈ $81.98

2. With Income (Dividends, Coupons) Core

\[ F_0(T) = (S_0 - PV_0(I)) \cdot (1 + r)^{T} \]

Or with continuous yield

\(F_0(T) = S_0 \cdot e^{(r - q) T}\) where q = continuous dividend yield.

Practice problem

Spot $100, r = 5%, T = 1 year, $4 dividend in 6 months. Compute forward.

Show solution
PV(div) = 4/1.05^0.5 ≈ 3.904
F = (100 − 3.904)(1.05)
F ≈ $100.90

3. With Storage Costs Core

\[ F_0(T) = (S_0 + PV_0(\text{costs})) \cdot (1 + r)^{T} \]
Practice problem

Commodity spot $50, r = 4%, storage cost PV = $1, T = 1 year. Compute forward.

Show solution
F = (50 + 1)(1.04)
F = $53.04

4. Value of a Forward During Its Life Core

\[ V_t(\text{long}) = \frac{F_t(T) - F_0(T)}{(1 + r)^{T - t}} \]

Components

  • Ft(T) Forward rate at time t for delivery at T (current market quote).
  • F0(T) Original locked-in forward price.
  • T − t Remaining time to delivery.

Long benefits when current forward > original; short is the negative of this.

Practice problem

Original forward locked at $100 (1 year). 6 months later, current 6-month forward = $103, r = 5% annual. Value to long?

Show solution
V = (103 − 100) / (1.05)\(^{0.5}\)
= 3 / 1.0247
V ≈ $2.93 to long
Practice problem

Spot price of a non-dividend stock is $100. Risk-free rate 5% (annual compounding). 1-year forward price?

Show solution
F = 100(1.05)¹
= $105