课后题

NO.PZ2018113001000052 问题如下 Olivia funmanager, sells $50,000 vega notionof a one-yevarianswon the S P 500 a strike of 20% (quoteannuvolatility).Now six months have passe anthe S P 500 hexperiencea realizevolatility of 16% (annualize. On the same y, the fair strike of a new six-month varianswon the S P 500 is 19%.The the current value of the varianswsolOlivia (note ththe annuinterest rate is 2.5%) is: A.$112,963 B.$ 998,653 C.$ 159,228 A is correct.Volatility strike on existing sw= 20.Varianstrike on existing sw= 20^2 = 400.Variannotion= Vega notional/(2*Strike)=50000/(2*20)=1250.Realizeol(0,6)^2 = 16^2 = 256.Implieol(6,12)^2 = 19^2 = 361.PVt(T) = 1/[1 + (2.5% × 6/12)] = 0.987654The current value of the swisVarSwapt = 1,250 × (0.987654) × [(6/12) × 256 + (6/12) × 361 – 400]= –$112,962.9263.Given thOlivia is short the varianswap, the mark-to-market value is positive for her, anit equals $112,963.中文解析本题考察的是对varianswap求value。直接带入公式计算即可。需要注意以下两点1. 该公式是站在long position的角度，而本题问的是short position，因此注意最后的结果需要加负号2. strike，implievolatility以及realizevolatility在代入计算时，不加百分号，只取百分号前面的数字。 请问题目中variance已经是Volatility的平方概念，为何公式里还是需要用平方计算？

NO.PZ2018113001000052 问题如下 Olivia funmanager, sells $50,000 vega notionof a one-yevarianswon the S P 500 a strike of 20% (quoteannuvolatility).Now six months have passe anthe S P 500 hexperiencea realizevolatility of 16% (annualize. On the same y, the fair strike of a new six-month varianswon the S P 500 is 19%.The the current value of the varianswsolOlivia (note ththe annuinterest rate is 2.5%) is: A.$112,963 B.$ 998,653 C.$ 159,228 A is correct.Volatility strike on existing sw= 20.Varianstrike on existing sw= 20^2 = 400.Variannotion= Vega notional/(2*Strike)=50000/(2*20)=1250.Realizeol(0,6)^2 = 16^2 = 256.Implieol(6,12)^2 = 19^2 = 361.PVt(T) = 1/[1 + (2.5% × 6/12)] = 0.987654The current value of the swisVarSwapt = 1,250 × (0.987654) × [(6/12) × 256 + (6/12) × 361 – 400]= –$112,962.9263.Given thOlivia is short the varianswap, the mark-to-market value is positive for her, anit equals $112,963.中文解析本题考察的是对varianswap求value。直接带入公式计算即可。需要注意以下两点1. 该公式是站在long position的角度，而本题问的是short position，因此注意最后的结果需要加负号2. strike，implievolatility以及realizevolatility在代入计算时，不加百分号，只取百分号前面的数字。 半年的折现率为什么不是用（1+2.5%）^0.5折现呢？

NO.PZ2018113001000052问题如下Olivia funmanager, sells $50,000 vega notionof a one-yevarianswon the S P 500 a strike of 20% (quoteannuvolatility).Now six months have passe anthe S P 500 hexperiencea realizevolatility of 16% (annualize. On the same y, the fair strike of a new six-month varianswon the S P 500 is 19%.The the current value of the varianswsolOlivia (note ththe annuinterest rate is 2.5%) is: A.$112,963 B.$ 998,653 C.$ 159,228 A is correct.Volatility strike on existing sw= 20.Varianstrike on existing sw= 20^2 = 400.Variannotion= Vega notional/(2*Strike)=50000/(2*20)=1250.Realizeol(0,6)^2 = 16^2 = 256.Implieol(6,12)^2 = 19^2 = 361.PVt(T) = 1/[1 + (2.5% × 6/12)] = 0.987654The current value of the swisVarSwapt = 1,250 × (0.987654) × [(6/12) × 256 + (6/12) × 361 – 400]= –$112,962.9263.Given thOlivia is short the varianswap, the mark-to-market value is positive for her, anit equals $112,963.中文解析本题考察的是对varianswap求value。直接带入公式variance  swapt=variance  notional×PVt(T)×{tT×[realize volatility(0，t)]2+T−tT×[implie volatility(t,T)]2}−strike2variance\;swap_t=variance\;notional\times PV_t\left(T\right)\times\left\{\frtT\times\left[realize;volatility\left(0，t\right)\right]^2+\frac{T-t}T\times\left[implie;volatility\left(t,T\right)\right]^2\right\}-strike^2varianceswapt​=variancenotional×PVt​(T)×{Tt​×[realizeolatility(0，t)]2+TT−t​×[implieolatility(t,T)]2}−strike2计算即可。需要注意以下两点1. 该公式是站在long position的角度，而本题问的是short position，因此注意最后的结果需要加负号2. strike，implievolatility以及realizevolatility在代入计算时，不加百分号，只取百分号前面的数字。 题目给的是 vega notion，不应该要除以（2*strike price）吗？为什么答案没有除以，而且题目也没有给strike price？

NO.PZ2018113001000052 $ 998,653 $ 159,228 A is correct. Volatility strike on existing sw= 20. Varianstrike on existing sw= 20^2 = 400. Variannotion= Vega notional/(2*Strike)=50000/(2*20)=1250. Realizeol(0,6)^2 = 16^2 = 256. Implieol(6,12)^2 = 19^2 = 361. PVt(T) = 1/[1 + (2.5% × 6/12)] = 0.987654 The current value of the swis VarSwapt = 1,250 × (0.987654) × [(6/12) × 256 + (6/12) × 361 – 400] = –$112,962.9263. Given thOlivia is short the varianswap, the mark-to-market value is positive for her, anit equals $112,963. 中文解析 本题考察的是对varianswap求value。 直接带入公式 variance  swapt=variance  notional×PVt(T)×{tT×[realize volatility(0，t)]2+T−tT×[implie volatility(t,T)]2}−strike2variance\;swap_t=variance\;notional\times PV_t\left(T\right)\times\left\{\frtT\times\left[realize;volatility\left(0，t\right)\right]^2+\frac{T-t}T\times\left[implie;volatility\left(t,T\right)\right]^2\right\}-strike^2varianceswapt​=variancenotional×PVt​(T)×{Tt​×[realizeolatility(0，t)]2+TT−t​×[implieolatility(t,T)]2}−strike2计算即可。 需要注意以下两点 1. 该公式是站在long position的角度，而本题问的是short position，因此注意最后的结果需要加负号 2. strike，implievolatility以及realizevolatility在代入计算时，不加百分号，只取百分号前面的数字。 算的结果是-112963, 怎么理解是盈利呢