Incentives for Traders: Ideal and Heuristic Contracts (with Philip H. Dybvig)
Presented at University of Sydney; Southern Finance Association 2021 (accepted).
Admati and Pfleiderer (1997) show that linear contracts for portfolio managers do not create incentives for effort, because the manager can undo any increase in slope of the contract by choosing less portfolio risk. Dybvig, Farnsworth and Carpenter (2010) use the revelation principle to solve a portfolio agency problem, and they show that a compensation contract plus portfolio constraints can implement the constrained optimum. However, their model is abstract and the numerical solution is complex and is dependent on the exact model. For example, it is not even clear how to implement their strategy if the trader’s effort affects execution. We develop heuristic rules that do give incentives for effort and seem easier to implement, and they come close to the constrained optimum. The incentive for effort comes from compensation for taking an active position, and this makes it unattractive to choose low effort and play it safe by taking little risk.
The (Un)Importance of Small Jumps in Lévy Model Option Pricing (with Ales Cerny)
Presented at 8th General AMaMeF Conference, Amsterdam, the Netherlands; Bachelier World Congress 2018 (accepted), Dublin, Ireland; Scheduled for 7th National Annual Conference of Probability, Shandong, China
Option pricing literature argues that the behaviour of small jumps in a Geometric Lévy model is of paramount importance. This is evidently true for very short time horizons and very deep in- and out-of-the-money options. In this paper, we took the complementary view and asked what values of time to maturity and option moneyness in a Geometric Lévy model lead to option prices that are practically indistinguishable from the price of plain vanilla options in the Black-Scholes model. In other words, when the Lévy model in question can be replaced with a Brownian motion with minimal pricing error. We produced explicit tight bounds in the case of a Poisson jump process and related heuristic bounds for arbitrary Lévy process with exponentially decaying jump intensity. We tested the latter for tempered stable process of Boyarchenko and Levendorskii 2002.
Asset Pricing Model with underlying Time-Varying Lévy Processes
Presented at Stochastic and Computational Finance Conference 2015, Lisbon, Portugal; LSF Brownbag; Asian Quantitative Finance Conference, Osaka, Japan; FMA Asia/Pacific 2016, Ph.D. consortium, Sydney, Australia; Bachelier World Congress 2016, New York, US; 9th Summer School in Financial Mathematics, St. Petersburg, Russia; University of Glasgow (online)
This paper proposed a novel equilibrium asset pricing model under general jump diffusion framework, including time-varying nonparametric drift, volatility and jump intensity. The corresponding pricing kernel provides insights on option pricing, equity premium puzzle. The analytical solutions of equity premium and European call option are given as well. In addition, by combining Hodrick-Prescott filter and particle filters, I applied the proposed method on the S&P500 index, and found evidences supporting the proposed general jump diffusion asset pricing model. I further observed the clustering of volatility and jumps, though the clustering effects are more pronounced when the time-varying drift is negative.