The most widely used Delta-normal method which is one of VaR measuring tools is based on two main assumptions. First, return distributions of underlying risk factors are normal. Second, relations between instrument values and underlying risk factors are linear. The first assumption is close to reality. But whether the second assumption is realistic depends on instruments. If instruments have non-linear payoff structures such as options, their movements can not be fully explained without considering higher-order changes. Hence ignoring higher-order changes may come to being exposed to higher-order risks and VaRs computed by the Delta-only approach come out over(under)valued. To overcome this problem partly is to focus on the second-order change like gamma or dollar convexity. This study analyzes if KOSPI200 call option and 3 year corporate bond have significant VaR changes caused by gamma or dollar convexity and introduces modified Delta-normal methods.
