问题如下:
A trader is looking for an arbitrage opportunity relating to a bond futures based on following information:
- Quoted futures price=103
- Conversion factor=1.02
- One month remaining to expiration, no coupon during this period
- Quoted bond price=108
- AI0=0.1
- AIT=0.15
- Annual compounded risk-free rate=0.2%
The arbitrage profit is closest to:
选项:
A.0.8965
B.2.9075
C.1.3253
解释:
B is correct.
考点:fixed-income futures定价
解析:
No-arbitrage futures price:
F0(T) =(108+0.1) (1 + 0.002)1/12-0.15=107.968
市场中的futures price=quoted futures price * CF=103*1.02=105.06
arbitrage profit应该是两个futures price之差的现值
所以arbitrage profit=
求No-arbitrage futures price画图:(该题合约期间没有coupon,所以PVC=0)
该提出的不严谨吧,题目中已知条件只说了合同还有1个月到期,但是没有说合同总长是多少(即T是多少),所以无法求得合理F0(T)啊,看助教画的图把T等于1/12更是不明白