题目
A market maker sells (writes) $50 million face value of call options on underlying bonds when the interest rate is 4.0%. At this 4.0% rate level, the DV01 (dollar value of an '01) of the option, per 100 face value, is $0.030. At this 4.0% rate level, the DV01 (per 100 face value) of the underlying bond is $0.070. What is the market maker's hedge transaction?
选项
A.Short $50.0 million face amount of underling bonds
B.Short $50 million face amount of call options on bond
C.Long $21.4 million face amount of underlying bonds
D.Long $50.0 million face amount of underlying bonds
答案
C
解析
F = $50 million × 0.030/0.070 = $21.429 million face amount of underlying bond.F(B)=-F(A)×DV01(A)/DV01(B); in this case, F(B) = -(-50) × 0.030/0.070 = + 21.429 indicates LONG (+) bonds.As the market maker will lose on the call options, if rates decrease, the market maker should purchase (go long) the underlying bonds, which will gain as rates decrease to offset.If the market maker goes long $21.429 the underlyling bonds, they key is that the market maker is neutral with respect to dollar duration:On the written options: 0.030/100 × 50 million = 0.0150 = a loss of $15,000 per each basis point decline; hedged by:On the long bonds: 0.070/100 × 21.429 million = 0.0150 = a gain of $15,000 per each basis point decline.F = $50 million × 0.030/0.070 = $21.429万美元基础债券面额。F（B）＝-F（A）×DV01（A）/ DV01（B）； 在这种情况下，F（B）=-（-50）×0.030 / 0.070 = 21.429表示买入债券。由于做市商在看涨期权头寸上遭受损失，因此如果利率降低，则做市商应购买（长期）基础债券，随着利率的降低抵消其收益。如果做市商做空基础债券$ 21.429，他们的关键是做市商在美元期限上保持中立：承兑期权：0.030 / 100×5000万= 0.0150 =每个基点下降损失15,000美元; 对冲：对于多头债券：0.070 / 100×214.2百万= 0.0150 =每个基点下跌获得$ 15,000的收益。