Futures vs Forwards with Stochastic Rates

This interview question explores the pricing difference between futures and forward contracts when interest rates are not deterministic, and when the underlying asset tends to move in the same direction as rates. The candidate is asked to reason about how daily settlement and marking to market in a futures contract contrasts with a single settlement at maturity in a forward contract, even when they reference the same underlying and have the same nominal maturity. This type of reasoning is common in fixed income and derivatives interviews, especially for roles involving pricing, risk, and structuring of interest rate products.

To answer it well, a candidate needs familiarity with no-arbitrage pricing, stochastic interest rate environments, and the role of correlation between the underlying asset and interest rates. The key techniques involve tracking the timing of cash flows, understanding reinvestment or funding at random rates, and recognizing how convexity and correlation affect expected present values. Interviewers look for a clear, stepwise argument that links payoffs, daily settlement, and rate movements, rather than memorized statements, and for comfort translating qualitative correlation statements into pricing implications.

What it tests

The core structure governing this class of problems is the impact of timing and reinvestment of cash flows under stochastic interest rates. When a contract is marked to market (as with futures), interim gains and losses are realized and can be reinvested or financed at prevailing rates, which may themselves be random and correlated with the underlying asset. The difference in value between two contracts with identical payoffs at maturity (such as forwards and futures) arises when the timing of cash flows allows the holder to benefit from favorable interest rate movements. This effect is pronounced when the underlying asset's price and interest rates are correlated, because the timing of cash flows aligns with periods of advantageous rates, amplifying or diminishing the contract's value relative to a contract with a single settlement at maturity. The principle holds because the present value of a sequence of cash flows depends not just on their amount, but also on when they occur and the rates available at those times.