开发者:上海品职教育科技有限公司 隐私政策详情

应用版本:4.2.11(IOS)｜3.2.5(安卓)APP下载

返回

ica.kiwi · 2024年07月23日

如果说5个月过去了，那么t和T的关系是什么样子的呢？这里我容易混淆。

  1. CFA III
  2. Derivative

NO.PZ2018113001000077

问题如下：

Marcus, who works for an investment management company, is asked to calculate what the gain would be in 6 months on a purchase of $2,000,000 vega notional of a one-year variance swap on the S&P 500 at a strike of 20% (quoted as annual volatility).

Now six months have passed, and the S&P 500 has experienced a realized volatility of 16%，The fair strike of a new 6-month variance swap on the S&P 500 will be 18%.

The annual interest rate is 2.00%

The current value of the variance swap is:

选项：

A.

-$5,445,544.500

B.

-$5,500,000.000

C.

$5,445,544.500

解释：

A is correct

中文解析：

本题考察的是variance swap。

需要求解的是variance swap在6个月时刻的value：

第一步，计算variance notional = $2,000,000/(2×20)=50,000

第二步，计算折现因子PVt (T)=1/[1 + (2.00% × 6/12)] = 0.990099

第三步，直接带入公式计算，VarSwapt= $50,000 × (0.990099) × [(6/12) × 256 + (6/12) × 324 – 400]= -$5,445,544.500.

如题。

添加评论
1 个答案

pzqa27 · 2024年07月23日

嗨，努力学习的PZer你好：


 那就用下面这个式子

$50,000 × (0.990099) × [(5/12) × 256 + (7/12) × 324 – 400]


先用5个月已经实现的波动率+7个月预期的波动率-约定的执行波动率

----------------------------------------------
努力的时光都是限量版，加油！

  • 1

    回答

  • 0

    关注

  • 75

    浏览
相关问题

NO.PZ2018113001000077 问题如下 Marcus, who works for investmentmanagement company, is asketo calculate whthe gain woulin 6 months ona purchase of $2,000,000 vega notionof a one-yevarianswon theS P 500 a strike of 20% (quoteannuvolatility).Now six months have passe anthe S P500 hexperiencea realizevolatility of 16%，Thefair strike of a new 6-month varianswon the S P 500 will 18%. The annuinterest rate is 2.00%The current value of the varianswis: A.-$5,445,544.500 B.-$5,500,000.000 C.$5,445,544.500 A is correct中文解析本题考察的是varianswap。需要求解的是varianswap在6个月时刻的value第一步，计算variannotion= $2,000,000/(2×20)=50,000第二步，计算折现因子PVt (T)=1/[1 + (2.00% × 6/12)] = 0.990099第三步，直接带入公式计算，VarSwapt= $50,000 × (0.990099) ×[(6/12) × 256 + (6/12) × 324 – 400]= -$5,445,544.500. 为什么是除以 （2*20）

2024-09-03 16:48 1 · 回答

NO.PZ2018113001000077问题如下 Marcus, who works for investmentmanagement company, is asketo calculate whthe gain woulin 6 months ona purchase of $2,000,000 vega notionof a one-yevarianswon theS P 500 a strike of 20% (quoteannuvolatility).Now six months have passe anthe S P500 hexperiencea realizevolatility of 16%，Thefair strike of a new 6-month varianswon the S P 500 will 18%. The annuinterest rate is 2.00%The current value of the varianswis: A.-$5,445,544.500B.-$5,500,000.000C.$5,445,544.500 A is correct中文解析本题考察的是varianswap。需要求解的是varianswap在6个月时刻的value第一步，计算variannotion= $2,000,000/(2×20)=50,000第二步，计算折现因子PVt (T)=1/[1 + (2.00% × 6/12)] = 0.990099第三步，直接带入公式计算，VarSwapt= $50,000 × (0.990099) ×[(6/12) × 256 + (6/12) × 324 – 400]= -$5,445,544.500. 题目中说的varianswap是6个月的，那么6个月后，这个swap就到期了，此时的value不是应该等于payment么？

2023-01-29 00:58 1 · 回答

NO.PZ2018113001000077问题如下 Marcus, who works for investmentmanagement company, is asketo calculate whthe gain woulin 6 months ona purchase of $2,000,000 vega notionof a one-yevarianswon theS P 500 a strike of 20% (quoteannuvolatility).Now six months have passe anthe S P500 hexperiencea realizevolatility of 16%，Thefair strike of a new 6-month varianswon the S P 500 will 18%. The annuinterest rate is 2.00%The current value of the varianswis: A.-$5,445,544.500 B.-$5,500,000.000 C.$5,445,544.500 A is correct中文解析本题考察的是varianswap。需要求解的是varianswap在6个月时刻的value第一步，计算variannotion= $2,000,000/(2×20)=50,000第二步，计算折现因子PVt (T)=1/[1 + (2.00% × 6/12)] = 0.990099第三步，直接带入公式计算，VarSwapt= $50,000 × (0.990099) ×[(6/12) × 256 + (6/12) × 324 – 400]= -$5,445,544.500. 我记得Vega Notional的含义是volatility变动1%的payoff。那么为什么不可以用Vega notional直接乘以volatility的变动求swap的value？即 PV{2,000,000 x [(16%/2 + 18%/2) - 20%]}

2022-04-05 18:14 2 · 回答

NO.PZ2018113001000077问题如下 Marcus, who works for investmentmanagement company, is asketo calculate whthe gain woulin 6 months ona purchase of $2,000,000 vega notionof a one-yevarianswon theS P 500 a strike of 20% (quoteannuvolatility).Now six months have passe anthe S P500 hexperiencea realizevolatility of 16%，Thefair strike of a new 6-month varianswon the S P 500 will 18%. The annuinterest rate is 2.00%The current value of the varianswis: A.-$5,445,544.500 B.-$5,500,000.000 C.$5,445,544.500 A is correct中文解析本题考察的是varianswap。需要求解的是varianswap在6个月时刻的value第一步，计算variannotion= $2,000,000/(2×20)=50,000第二步，计算折现因子PVt (T)=1/[1 + (2.00% × 6/12)] = 0.990099第三步，直接带入公式计算，VarSwapt= $50,000 × (0.990099) ×[(6/12) × 256 + (6/12) × 324 – 400]= -$5,445,544.500. 计算折现因子PVt (T)=1/[1 + (2.00% × 6/12)] = 0.990099折现因子可以用（1+2%）开平方计算吗

2022-03-19 20:55 1 · 回答