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

How a forward's price is set once at inception while its value starts at zero, drifts with the spot price, time and interest rates, and ends as the settlement amount; how carry costs, income and two interest rates (for FX) change that valuation; and how zero rates, discount factors and implied forward rates are derived for interest rates, which have a term structure, and used to price forward rate agreements.

1. 1. Forward price versus forward value: inception and expirationThe forward price is fixed once at inception so that the contract is worth zero to both sides; at expiration the contract is worth exactly its settlement amount, $S_T - F_0(T)$ to the buyer.Free11 min
2. 2. Valuing a forward during its lifeBefore maturity, a long forward is worth the spot price today minus the present value of the forward price, discounted over the time left.Video · 6 min13 min
3. 3. Forwards on assets with costs and benefitsWhen holding the underlying brings income or costs, adjust the spot price by the present value of the remaining income (subtract) and costs (add), both at inception and when marking to market.12 min
4. 4. Pricing and valuing FX forwardsAn FX forward price is the spot rate adjusted by the interest rate differential between the two currencies, and its MTM value compares today's spot rate with the forward rate discounted at the current differential.Video · 6 min12 min
5. 5. Term structure: zero rates and discount factorsInterest rates differ by maturity, so interest rate derivatives are built from zero rates bootstrapped out of coupon bond prices, and their price equivalents, discount factors.13 min
6. 6. Implied forward ratesAn implied forward rate is the breakeven reinvestment rate that makes investing short and rolling over earn exactly the same as investing long, so it follows directly from two zero rates.Video · 6 min13 min
7. 7. Forward rate agreements (FRAs)An FRA fixes today the interest rate on a future notional deposit; at the fixing date the parties exchange the present value of the difference between the market reference rate and the agreed implied forward rate.Video · 6 min13 min