# Historical simulation with component weight and ghosted scenarios

## Xinyi Liu

#### Need to know

• This paper proposes two simple mechanisms that can work together for a complex portfolio: "ghosted" scenarios scheme and short-term and long-term component weighting scheme.
• The "ghosted" scenarios scheme is a  technique that increases the number of scenarios simulated by HS and makes interaction between the two tails possible.
• The component weighting scheme  balances the importance of both short-run and long-run information.

#### Abstract

ABSTRACT

Historical simulation (HS) is a popular value-at-risk (VaR) approach that has the advantage of being intuitive and easy to implement. However, its response to most recent news has been too slow, its two "tails" (upper and lower) cannot learn from each other and it is not robust if there is insufficient data. In this paper, we put forward two strategies for improving HS in these weak areas with only minor additional computational costs. The first strategy is a "ghosted" scenario and the second is a two-component (short-run and long-run) exponentially weighted moving average scheme. The VaR is then calculated according to the empirical distribution of the two-component weighted real and ghosted scenarios.