Modeling Financial Market Movement with Winning Streaks: Sticky Maximum Process

34 Pages Posted: 3 Apr 2020 Last revised: 8 Feb 2021

See all articles by Runhuan Feng

Runhuan Feng

University of Illinois at Urbana-Champaign

Pingping Jiang

Nankai University - School of Mathematical Sciences

Hans Volkmer

affiliation not provided to SSRN

Date Written: March 12, 2020

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: fi nancial indices frequently report record highs or lows in concentrated periods of time. In this paper, we apply the technique of time change with local time to capture the market anomaly of persistent extremes. The new model which is driven by a sticky processes with moving boundaries { running maxima enables us to measure and assess the impact of persistent extremes on fi nancial derivatives. Despite the time change construction, option prices are still solvable analytically. 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.

Keywords: sticky maximum process; sticky diffusion process; financial market movement; option valuation; stochastic process inference

JEL Classification: C51;G12

Suggested Citation

Feng, Runhuan and Jiang, Pingping and Volkmer, Hans, Modeling Financial Market Movement with Winning Streaks: Sticky Maximum Process (March 12, 2020). Available at SSRN: https://ssrn.com/abstract=3553389 or http://dx.doi.org/10.2139/ssrn.3553389

Runhuan Feng

University of Illinois at Urbana-Champaign ( email )

601 E John St
Champaign, IL 61820
United States

Pingping Jiang (Contact Author)

Nankai University - School of Mathematical Sciences ( email )

Weijin Road #94
Tianjin, 300071
China

Hans Volkmer

affiliation not provided to SSRN ( email )

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