Olivia.W🌸 · 2024年04月17日
NO.PZ2023040401000056
问题如下：
Three months ago, an investor took a long position of a forward contract that expires in six months. The forward contract was priced at $50, with a quarterly dividend of $3, and a semi-annual cost of $4. The risk-free interest rate is 3%. Now the underlying price is $48, what is the value of this forward contract:
选项：
A.-$0.6392.
$0.6022.
-$1.0459.
解释：
T=6/12=0.5; T-t= 3/12 = 0.25; t=3/12=0.25; St=48.
为什么这个semi-annual cost不是1/2*3/12
李坏_品职助教 · 2024年04月17日
嗨，爱思考的PZer你好：
题目说的是，3个月之前签订了一个期限为6个月的远期合约。也就是现在距离远期合约到期日还剩3个月了（也就是剩余期限是0.25年）。
时间线如下：
假设签订合约是0时刻，现在是站在0.25的时刻，合约到期日是0.5的时刻。
因为cost是每半年发生一次，恰好在到期日的时候是0.5年，会发生一笔4$的cost，所以把cost从0.5的时刻折现到现在0.25的时刻，就是4/(1+3%)^0.25
----------------------------------------------就算太阳没有迎着我们而来，我们正在朝着它而去，加油！
NO.PZ2023040401000056 问题如下 Three months ago, investor took a long position of a forwarcontrathexpires in six months. The forwarcontrawprice$50, with a quarterly vinof $3, ana semi-annucost of $4. The risk-free interest rate is 3%. Now the unrlying priis $48, whis the value of this forwarcontract: A.-$0.6392. B.$0.6022. C.-$1.0459. T=6/12=0.5; T-t=3/12 = 0.25; t=3/12=0.25; St=48. Three months ago, investor took a long position of a forwarcontrathexpires in six months. 这个现金流能帮忙画一个么 ，不太懂哪个是t时刻
NO.PZ2023040401000056 问题如下 Three months ago, investor took a long position of a forwarcontrathexpires in six months. The forwarcontrawprice$50, with a quarterly vinof $3, ana semi-annucost of $4. The risk-free interest rate is 3%. Now the unrlying priis $48, whis the value of this forwarcontract: A.-$0.6392. B.$0.6022. C.-$1.0459. T=6/12=0.5; T-t=3/12 = 0.25; t=3/12=0.25; St=48. 求远期估值时，是用t时的即期价格减去FP折现到t时间。题目中已经告知了t时的即期价格48。为什么不直接用？
NO.PZ2023040401000056 问题如下 Three months ago, investor took a long position of a forwarcontrathexpires in six months. The forwarcontrawprice$50, with a quarterly vinof $3, ana semi-annucost of $4. The risk-free interest rate is 3%. Now the unrlying priis $48, whis the value of this forwarcontract: A.-$0.6392. B.$0.6022. C.-$1.0459. T=6/12=0.5; T-t=3/12 = 0.25; t=3/12=0.25; St=48. 当期发的一笔算在内是因为价格已经是剔除了当期响后的原因么？
