Portfolio selection in Heston's stochastic volatility model using a contingent claim

      Department of Systems Engineering and Engineering Management
                             The Chinese University of Hong Kong
Speaker:  Yongmin Zhang, Nottingham Business School China
Title: Portfolio selection in Heston's stochastic volatility model using a contingent claim
Previous research has shown that in a continuous-time financial market, the price of the risky asset with two sources of uncertainty follows a Heston stochastic volatility model in which its excess return (over the risk free asset) during a given period is a function of its long-run expected nominal return plus a risk premium dependent on the correlation between two sources of risk. Under such conditions, since there is one risky asset being traded with two sources of uncertainty, the market is incomplete and no unique solution exists. In this paper, however, we show that when an investor's attitude to risk is specified, a unique Martingale measure can be determined. First, following Romano and Touzi, we show how to complete the market using a European option. Having completed the market, we then follow Karatzas et al making this created asset uninteresting to investors, to achieve a unique, closed-form solution for the portfolio strategy. 
We further investigate how the rate of change (adjustment speed) of weight on the risky asset depends on model parameters such as long run mean price volatility and volatility of price volatility. We find expected weight adjustment speed is slower when the long run mean volatility increases and both expectation and variance of adjustment speed increase with volatility of volatility. We also study the time-dependent path of mean and variance of the weight on the risky asset using numerical simulations. We find both mean and variance of time dependent weight decrease with increasing long run mean volatility and increase with volatility of volatility. Our results are robust with agreement from two simulation methods. Convergence tests are conducted for various number of simulation paths and time step sizes.  
Chair Professor in Finance at University of Nottingham Ningbo China and Director of Centre for Global Finance and International Finance Research Centre. He obtained his Ph.D. from University of Chicago in 1997. After his graduation, he worked as a research scientist at Research Foundation of State University of New York. From 2001 to 2007, he was a Ph.D. supervisor at State University of New York at Stony Brook and a principle investigator for U.S. Department of Energy research projects.  From 2007 to 2011, he has worked as a lead research analyst at J. P. Morgan, a risk management consultant at Wells Fargo, a Ph.D. supervisor in financial mathematics at Xi’an Jiaotong – Liverpool University, the academic director for Qinlan Program of Jiangsu Province. Since 2012, he has been a leader for “Global Finance Management” which is one of key disciplines in universities in Zhejiang Province. 
Prof. Zhang’s research areas span multiple disciplines including mathematics, finance and physics. He has authored more than 70 papers with 11 papers in highest ranking A*/A journals.  He was the first person who successfully conducted computer simulations for the first spherically diverging, hydro-dynamically unstable laboratory experiments of relevance to supernova.  This work was published in the world top 15 highest cited Astrophysical Journal. His paper on mixed asset allocation was one of top 10 most downloaded papers in Social Science Research Network in 2010. His mathematical models for managing mortgage assets of more than US$100 billion have been used in asset management systems in several top U. S. financial institutions. His research has been sponsored by various agencies including U. S. Department of Energy, National Natural Science Foundation of China, and British Foreign & Commonwealth Office.  His honours include: French U.A.P. Prize in mathematics, Hong Kong Wang Foundation Scholar, Outstanding Paper Award in 11th U.S. Annual Conference in Applied Mathematics, Individual Development Award from State University of New York, Who’s Who in Engineering Education, “Highly Talented Expert” title by Chinese Ministry of Education, Zhejiang  “1000 Talents” Expert and Qianjiang Distinguished Professor. 
This seminar is hosted by Prof. Duan Li.
Venue: Room 513,
      William M.W. Mong Engineering Building (ERB),
      (Engineering Building Complex Phase 2)
      The Chinese University of Hong Kong.
Friday, April 29, 2016 - 08:30 to 09:30