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DFY1125 · 2024年11月19日

为什么本题用365天不是360天呢

  1. CFA II
  2. Derivative

NO.PZ2023041003000010

问题如下：

Assume that you own a dividend-paying stock currently worth $150. You plan to sell the stock in 250 days. In order to hedge against a possible price decline, you wish to take a short position in a forward contract that expires in 250 days. The risk-free rate is 5.25 percent. Over the next 250days, the stock will pay dividends according to the following schedule:

What is the forward price of a contract established today and expiring in 250 days?

It is now 100 days since you entered the forward contract. The stock price is $115. What is the value of the forward contract at this point?

选项：

A.

B.

C.

解释：

A. S0= $150

T = 250/365

r = 0.0525

PV(D,0,T) = $1.25/ + $1.25/ + $1.25/ = $3.69

F(0,T) = ($150.00 -$3.69) = $151.53

B.St = $115

F(0,T) = $151.53

t = 100/365

T = 250/365

T -t = 150/365

r = 0.0525

After 100 days, two dividends remain: the first one in 20 days, and the second one in 110 days.

PV(D,t,T) = $1.25/ + $1.25/ = $2.48

Vt (0,T) = $115.00 -$2.48 -$151.53/(1.0525)150/365 = -$35.86

A negative value is a gain to the short

老师好，如题，我看之前几道题算的时候都用360天的。为什么这题就用365呢

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1 个答案

李坏_品职助教 · 2024年11月19日

嗨，努力学习的PZer你好：


在衍生品这个科目中，基于过去的习惯，对于FRA和swap的定价和估值我们都是按照360天的单利来进行计算的，其余的都是按照365天的复利来计算的。关于这一点老师在基础课也做过说明：

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加油吧，让我们一起遇见更好的自己！

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NO.PZ2023041003000010问题如下 Assume thyou own avinpaying stocurrently worth $150. You plto sell the stoin 250ys. In orr to hee against a possible pricline, you wish to take ashort position in a forwarcontrathexpires in 250 ys. The risk-freerate is 5.25 percent. Over the next 250ys, the stowill pvinaccorng to the following schele:Whis theforwarpriof a contraestablishetoy anexpiring in 250 ys? It is now 100 yssinyou enterethe forwarcontract. The stopriis $115. Whis thevalue of the forwarcontrathis point? A.B.C. S0= $150T = 250/365r = 0.0525PV(0,T) = $1.25/ + $1.25/ + $1.25/ = $3.69F(0,T) = ($150.00-$3.69) = $151.53B.St = $115F(0,T) = $151.53t = 100/365T = 250/365T -t = 150/365r = 0.0525After 100 ys, twovin remain: the first one in 20 ys, anthe seconone in 110 ys.PV(t,T) = $1.25/ + $1.25/ = $2.48Vt(0,T) = $115.00 -$2.48 -$151.53/(1.0525)150/365 = -$35.86A negative valueis a gain to the short 答案完全看不懂写的什么，能详细一下这道题吗

2023-10-07 15:48 1 · 回答