Answer-first summary for fast verification
Answer: a) 0.04
The basis is the difference between the spot and futures prices: \(B = S - F\). Its variance is \[ \mathrm{Var}(B)=\mathrm{Var}(S-F)=\sigma_S^2+\sigma_F^2-2\rho\sigma_S\sigma_F \] Given: - \(\sigma_S = 0.20\) - \(\sigma_F = 0.32\) - \(\rho = 0.80\) So: \[ \mathrm{Var}(B)=0.20^2+0.32^2-2(0.8)(0.20)(0.32) \] \[ =0.04+0.1024-0.1024=0.04 \] Therefore, the variance of the basis is **0.04**.
Author: Manit Arora
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Q-153.1. Assume the volatility (standard deviation) of the change in prices for the spot price of oil and the futures price, respectively, are 20% and 32%. The (coefficient of) correlation between changes in the two prices is 0.80. What is the variance of the basis?
A
a) 0.04
B
b) 0.08
C
c) 0.12
D
d) 0.16
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