Forwards versus futures under random interest rates
Question
If interest rates are stochastic rather than deterministic, how does the futures price of an asset compare with its forward price, and what causes the difference?
Short answer
They differ whenever the asset is correlated with interest rates: futures exceed forwards when the correlation is positive and fall below them when it is negative. Futures are marked to market daily, so gains are reinvested and losses financed at the prevailing rate. With positive correlation, gains arrive when rates are high and losses when rates are low, which benefits the long futures holder and pushes the futures price up. With deterministic rates the two prices coincide.
Adapted from Zhou, A Practical Guide to Quantitative Finance Interviews, sec. 6.4 Other Finance Questions, 'Forward and futures', p.166; question and answer rewritten by SelfMadeQuant.com.
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Open the worked solutionLessons behind this question
- Forward and Futures Prices: Cost-of-Carry, Known Income, and Continuous Yields
- Covariance and Correlation
- Exponential Growth, Decay, and Continuous Compounding
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