Futures versus forwards under stochastic rates
Question
How do futures contracts differ from forward contracts? When interest rates are random and the underlying's price is strongly positively correlated with them, which should be priced higher, the futures or the forward, and why?
Short answer
The futures price is higher. Futures are standardised, exchange-traded and marked to market daily; forwards are bespoke OTC deals settled once at maturity. With positive correlation, a long futures holder receives variation-margin gains when rates are high (reinvested at a high rate) and pays losses when rates are low (financed cheaply), an advantage the forward lacks, so the futures price exceeds the forward price. With deterministic rates the two coincide.
Adapted from OpenQuant; 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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