Exercise 9.4 Consider the Schwartz model for the spot price of a commodity and its convenience yield.

(a) Simulate a trajectory of n = 503 daily values for the spot price and its convenience yield, using the parameters of Table 9.2. Take S(0) = 16 and δ(0) = 0.025.

(b) Use the trajectory simulated in

(a) to compute the value, every month (21 days), of five futures contracts with maturities of 2, 3, 6, 9, and 11 months. It means that in January, we have futures expiring in March, April, July, October and December. Next, in February, we have futures expiring in April, May, August, November, and January, and so on.
Assume a constant risk-free rate of 5%.

(c) Add independent Gaussian noises ε with variances 0.001h to each set of log-prices of the futures and plot the graphs.