Consider an eight-month forward contract on a stock with a price of $98/share. The delivery date is eight monthshence. The firm is expected to pay a $1.80/share dividend in four months time. Riskless zero coupon interest rates(continuously compounded) for diferent maturities are as follows: 4 months 4%, 8 months 4.5%. The theoretical forwardprice (to the nearest cent)is: A.99.15 B.99.18 C.100.98 D.96.20

• 远期价格计算公式为 $F = S e^{r(T-t)}$，其中 $S$ 为标的资产当前价格，$r$ 为无风险利率，$T$ 为到期时间，$t$ 为当前时间。

远期价格计算

• 标的资产当前价格：$98
• 无风险利率：4个月 4%，8个月 4.5%
• 到期时间：8个月
• 当前时间：0个月
• 连续复利计算：$e^{0.04 \times 0.25} \approx 1.0408$，$e^{0.045 \times 0.6667} \approx 1.0456$

计算过程

1. 计算4个月后的远期价格：
   • 考虑4个月后的1.80美元股息，调整后的当前价格 $S = 98 - 1.80 = 96.20$
   • 4个月后的远期价格 $F_4 = 96.20 \times e^{0.04 \times 0.25} \approx 96.20 \times 1.0408 \approx 100.07$
2. 计算8个月后的远期价格：
   • 8个月后的远期价格 $F_8 = 100.07 \times e^{0.045 \times 0.6667} \approx 100.07 \times 1.0456 \approx 104.58$

结论

• 根据计算，8个月后的远期价格约为 $104.58，最接近的选项是 C.100.98。