题目
A market maker sells (writes) $100 million face value of call options on underlying bonds when the interest rate is 4.0%. The price of the call options is $3.0 million and their (modified) duration is 80.0 years. At the same 4.0% rate, as the underlying bonds pay a 4.0% coupon, the price of the underlying happens to equal $100 par with a duration of 7.0 years. What is the market maker's hedge transaction?
选项
A.Short $12.9 million of underlying bond
B.Short $24.0 million of underlying bond
C.Long $24.0 million of underlying bond
D.Long $34.3 million of underlying bond
答案
D
解析
The DV01 of the written call options, DV01 = P×D/10000 = 3 million×80/10000 = $24,000 or $240 per 100 face.To hedge, the market marker should buy P = DV01×10,000/D = 240 × 10,000 / 7 = $342,857 per 100 face or $34.285 million in the underlying bond.卖出看涨期权的DV01，DV01 = P×D / 10000 = 300万×80/10000 = 24,000美元或每100张面240美元。为了进行套期保值，市场参与者应该购买P = DV01×10,000 / D = 240×10,000 / 7 =每100张面342,857美元或相关债券的3,488.5万美元。