MARKET RISK OF INVESTMENT IN US SUBPRIME CRISIS: COMPARISON OF A PURE DIFFUSION AND A PURE JUMP MODEL

Abstract

We consider the oldest financial model to estimate the market risk of investment underlying the world indexes and compare its risk management features with those of a newer model. Our concern is the risk underlying the world indexes in the recent US subprime crisis period. We illustrate how the recent variance gamma (VG) pure jump model is comparable with one of the earliest pure diffusion (Bachelier (BC)) model in estimating investment risk in financial markets using the tail risk measure value-at-risk (VaR) and its coherent version expected shortfall (ES). We observe that for pure jump VG model single quantile VaR is consistently a better performer across indexes; however for tail average risk measure ES, VG is not a consistently better performer; pure diffusion Bachelier model gives ES estimates which are often — not always — better than VG. This provides one more empirical indication that the combination of diffusion and jump is likely to be more effective in turbulent times, e.g., in US subprime crisis period.