Pricing and Valuation of Forward Contracts and for an Underlying with Varying Maturities

A forward locks in a delivery price today for a transaction at expiration. Its price is the locked-in delivery rate. Its value is the mark-to-market gain or loss to one side. Confusing the two is the most common exam trap in derivatives.

KEY: Price is the contractual delivery rate negotiated at initiation. Value is the present worth of the contract to a counterparty at any moment. Price is fixed. Value moves.

At initiation, the forward price is set so neither party pays the other. The contract starts at zero value.

Start with a trade you could do yourself. Borrow $100 at 4%, buy a stock that pays nothing, hold it for a year, and deliver it into a forward contract. You owe the lender $104 at expiration. The only forward price that leaves no free money on the table is $104. A higher price lets you run this trade for a sure profit. A lower price lets someone run it in reverse.

Common mistakes

• Confusing price with value at initiation. The price equals $S_0(1+r)^T$. The value is zero. Trap: computing $\$104$ and labeling it the contract's value.
• Forgetting to discount the locked-in price during the life. The mid-life value is $S_t - F_0(T)/(1+r)^{T-t}$, not $S_t - F_0(T)$. Trap: subtracting $104 from $108 directly and reporting $4.00 instead of $6.02.
• Sign errors on income and carry. Income (dividends, coupons) lowers the forward price. Storage costs raise it. Trap: adding the dividend yield in Example 3 gives 4,128.01 instead of 4,054.37.

Bottom line

• Forward price at initiation: $F_0(T) = (S_0 - I + C)(1+r)^T$, or $S_0 e^{(r_c - q)T}$ for a continuous yield. Value at initiation = 0.
• Value during life (long): $S_t - PV_t(I) + PV_t(C) - F_0(T)/(1+r)^{T-t}$. The locked-in price must be discounted first.
• Value at expiration (long): $S_T - F_0(T)$. The short's value is always the negative.
• Income (dividends, coupons, yields) lowers the forward price; storage costs raise it.

Exam shortcut

For mid-life value, always discount the locked-in price before subtracting from spot, and strip out any dividend still to be paid. At expiration, skip discounting entirely: $S_T - F_0$. For implied forwards, set the two financing strategies equal and solve algebraically (no memorization needed if you can write the no-arbitrage equation). Take the root equal to the gap, not the longer maturity.

The full lesson (about 3,511 words, 23 min read) adds 11 worked examples, all 7 common mistakes, a self-check, free in the app.

Learning objectives

• pricing and valuation of forwards

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