问一道题：NO.PZ2020011303000227 [ FRM I ]

问题如下：

A position is worth USD 1.5 million. A two-basis-point increase in all rates causes the value to decline by USD 1199.85 and a two-basis-point decrease in all rates cause the value to increase by USD 1200.15. Estimate the effective duration and effective convexity.

解释：

Effective duration is

0.5 ×(1,199.85 +1,200.15)/(1,500,000×0.0002)=4

Also: P⁺+P^－－2P= (P⁺－P^－)－(P－P^－) =1200.15－1195.85=3

so that effective convexity is 0.3/(1,500,000×0.0002²)=5