题目
Consider the risk of a long call on an asset with a notional amount of $1 million. The VaR of the underlying asset is 7.8%. If the option is a short-term at-the-money option, the VaR of the option position is slightly:
选项
A.Less than $39,000 when second-order terms are considered.
B.More than $39,000 when second-order terms are considered.
C.Less than $78,000 when second-order terms are considered.
D.More than $78,000 when second-order terms are considered.
答案
A
解析
An at-the-money option has a delta of about 0.5 and a positive gamma. VaR_option=|Δ|×VaR(dS)-1/2×Γ×VaR(dS)^2. Because the gamma is positive, so the risk is slightly lower than the linear VaR, which is 0.5×7.8%×1=39,000.平价期权的Delta约为0.5，gamma为正。VaR_option=|Δ|×VaR(dS)?1/2×Γ×VaR(dS)^2由于gammag为正，因此风险略低于线性VaR，0.5×7.8%×1=39,000