Modeling Financial Market Movement with Winning Streaks: Sticky Maximum Process

Abstract

Winning streaks appear frequently in all financial markets including equity, commodity, foreign exchange, real estate, etc. Most stochastic process models for financial market data in the current literature focus on stylized facts such as fat-tailedness relative to normality, volatility clustering, mean reversion. However, none of existing financial models captures the pervasive feature of persistent extremes: financial indices frequently report record highs or lows in concentrated periods of time. The lack of persistent extremes in a quantitative model for asset pricing can have grave impact on the valuation and risk management of financial instruments. The new model in this paper enables us to measure and assess the impact of persistent extremes on financial derivatives and to more accurately predict option values. In addition, the model in this paper reveals a paradox that investors who bet on the growth of financial market may be worse off with pervasive winning streaks in the market. This model in this paper describes the phenomenon of market overreaction at the macro level, which complements existing behavior finance literature on this subject that explain market reactions by psychological reasoning and evidence. The paper also explores the possibility of using the model for measuring the tendency of overbought stocks and indices.