A dynamic equilibrium model for U-shaped pricing kernels. Issue 5 (4th May 2018)

• Record Type: Journal Article
• Authors: Yamazaki, Akira
• Is Part Of: Quantitative finance. Volume 18:Issue 5(2018)
• Page Start: 851
• Page End: 875
• Publication Date: 2018-05-04
• Subjects: Stock index -- U-shaped pricing kernel -- Stochastic activity rate -- Aggregate consumption -- Physical distribution -- Risk-neutral distribution -- Realized variance; Finance -- Periodicals; Business mathematics -- Periodicals; Finance -- Mathematical models -- Periodicals; Investments -- Mathematics -- Periodicals; Economics -- Periodicals; Finances -- Modèles mathématiques -- Périodiques; 332.015118
• DOI: 10.1080/14697688.2017.1388535
• Languages: English
• ISSNs: 1469-7688

Abstract

Abstract : This paper proposes a dynamic equilibrium model that can provide a unified explanation for the stylized facts observed in stock index markets such as the fat tails of the risk-neutral return distribution relative to the physical distribution, negative expected returns on deep OTM call options and negative realized variance risk premiums. In particular, we focus on the U-shaped pricing kernel against the stock index return, which is closely related to the negative call returns. We assume that the stock index return follows a time-changed Lévy process and that a representative investor has power utility over the aggregate consumption that forms a linear regression of the stock index return and its stochastic activity rate. This model offers a macroeconomic interpretation of the stylized facts from the perspective of the sensitivity of the activity rate and stock index return on aggregate consumption as well as the investor's risk aversion.