Commodity futures prices for platinum rose to $928.50 per ounce, gaining 0.9%, supported by automotive sector demand recovery and supply constraints from South African mines. The U.S. 30-year Treasury bond futures edged only 0.08% lower in September. The long bond futures remained within the 110-01 to 127-22 trading range, which has been in place since December 2023. Where, \({\rm{\alpha }}\) is the mean regression rate, \({\rm{\nu }}\) is the volatility, \(E\) is the spot price long-term mean, \({f}_{t}\) is a triangular function representing seasonality (see Eq. 8 below for details), \(\beta =E-\frac{{\nu }^{2}}{2{\rm{\alpha }}}\) , \({B}_{Y,t}\) is the standard Brownian process. Consider a futures contract with a maturity time of T , its price is \({F}_{t,T}\) at time t, which is given by the following equation (Schwartz, 1997 ): Wheat futures dropped 0.7% to $6.19 per bushel, pulling commodity futures prices lower in the grains segment. Traders attribute this to higher-than-expected export volumes from the Black Sea region.