折现因子

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）

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. 如题。

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.-$5,445,544.500B.-$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？

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%]}