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postgraduate thesis: Asset pricing, hedging and portfolio optimization
Title  Asset pricing, hedging and portfolio optimization 

Authors  
Advisors  Advisor(s):Yang, H 
Issue Date  2012 
Publisher  The University of Hong Kong (Pokfulam, Hong Kong) 
Abstract  Starting from the most famous BlackScholes model for the underlying asset
price, there has been a large variety of extensions made in recent decades.
One main strand is about the models which allow a jump component in the
asset price. The first topic of this thesis is about the study of jump risk
premium by an equilibrium approach. Different from others, this work provides
a more general result by modeling the underlying asset price as the ordinary
exponential of a L?vy process. For any given asset price process, the equity
premium, pricing kernel and an equilibrium option pricing formula can be
derived. Moreover, some empirical evidence such as the negative variance risk
premium, implied volatility smirk, and negative skewness risk premium can
be well explained by using the relation between the physical and riskneutral
distributions for the jump component.
Another strand of the extensions of the BlackScholes model is about the
models which can incorporate stochastic volatility in the asset price. The second
topic of this thesis is about the replication of exponential variance, where
the key risks are the ones induced by the stochastic volatility and moreover it
can be correlated with the returns of the asset, referred to as leverage effect.
A timechanged L?vy process is used to incorporate jumps, stochastic volatility
and leverage effect all together. The exponential variance can be robustly
replicated by European portfolios, without any specification of a model for the
stochastic volatility.
Beyond the above asset pricing and hedging, portfolio optimization is also
discussed. Based on the Merton (1969, 1971)'s reduced portfolio optimization
and the delta hedging problem, a portfolio of an option, the underlying stock
and a riskfree bond can be optimized in discrete time and its optimal solution
can be shown to be a mixture of the Merton's result and the delta hedging
strategy. The main approach is the elasticity approach, which has initially
been proposed in continuous time.
In addition to the above optimization problem in discrete time, the same
topic but in a continuoustime regimeswitching market is also presented. The
use of regimeswitching makes our market incomplete, and makes it difficult to
use some approaches which are applicable in complete market. To overcome
this challenge, two methods are provided. The first method is that we simply
do not price the regimeswitching risk when obtaining the riskneutral probability.
Then by the idea of elasticity, the utility maximization problem can be
formulated as a stochastic control problem with only a single control variable,
and explicit solutions can be obtained. The second method is to introduce
a functional operator to general value functions of stochastic control problem
in such a way that the optimal value function in our setting can be given by
the limit of a sequence of value functions defined by iterating the operator.
Hence the original problem can be deduced to an auxiliary optimization problem,
which can be solved as if we were in a singleregime market, which is
complete. 
Degree  Doctor of Philosophy 
Subject  Capital assets pricing model. Hedging (Finance)  Mathematical models. Portfolio management  Mathematical models. 
Dept/Program  Statistics and Actuarial Science 
DC Field  Value  Language 

dc.contributor.advisor  Yang, H   
dc.contributor.author  Fu, Jun   
dc.contributor.author  付君   
dc.date.issued  2012   
dc.description.abstract  Starting from the most famous BlackScholes model for the underlying asset price, there has been a large variety of extensions made in recent decades. One main strand is about the models which allow a jump component in the asset price. The first topic of this thesis is about the study of jump risk premium by an equilibrium approach. Different from others, this work provides a more general result by modeling the underlying asset price as the ordinary exponential of a L?vy process. For any given asset price process, the equity premium, pricing kernel and an equilibrium option pricing formula can be derived. Moreover, some empirical evidence such as the negative variance risk premium, implied volatility smirk, and negative skewness risk premium can be well explained by using the relation between the physical and riskneutral distributions for the jump component. Another strand of the extensions of the BlackScholes model is about the models which can incorporate stochastic volatility in the asset price. The second topic of this thesis is about the replication of exponential variance, where the key risks are the ones induced by the stochastic volatility and moreover it can be correlated with the returns of the asset, referred to as leverage effect. A timechanged L?vy process is used to incorporate jumps, stochastic volatility and leverage effect all together. The exponential variance can be robustly replicated by European portfolios, without any specification of a model for the stochastic volatility. Beyond the above asset pricing and hedging, portfolio optimization is also discussed. Based on the Merton (1969, 1971)'s reduced portfolio optimization and the delta hedging problem, a portfolio of an option, the underlying stock and a riskfree bond can be optimized in discrete time and its optimal solution can be shown to be a mixture of the Merton's result and the delta hedging strategy. The main approach is the elasticity approach, which has initially been proposed in continuous time. In addition to the above optimization problem in discrete time, the same topic but in a continuoustime regimeswitching market is also presented. The use of regimeswitching makes our market incomplete, and makes it difficult to use some approaches which are applicable in complete market. To overcome this challenge, two methods are provided. The first method is that we simply do not price the regimeswitching risk when obtaining the riskneutral probability. Then by the idea of elasticity, the utility maximization problem can be formulated as a stochastic control problem with only a single control variable, and explicit solutions can be obtained. The second method is to introduce a functional operator to general value functions of stochastic control problem in such a way that the optimal value function in our setting can be given by the limit of a sequence of value functions defined by iterating the operator. Hence the original problem can be deduced to an auxiliary optimization problem, which can be solved as if we were in a singleregime market, which is complete.   
dc.language  eng   
dc.publisher  The University of Hong Kong (Pokfulam, Hong Kong)   
dc.relation.ispartof  HKU Theses Online (HKUTO)   
dc.rights  The author retains all proprietary rights, (such as patent rights) and the right to use in future works.   
dc.rights  Creative Commons: Attribution 3.0 Hong Kong License   
dc.source.uri  http://hub.hku.hk/bib/B48199345   
dc.subject.lcsh  Capital assets pricing model.   
dc.subject.lcsh  Hedging (Finance)  Mathematical models.   
dc.subject.lcsh  Portfolio management  Mathematical models.   
dc.title  Asset pricing, hedging and portfolio optimization   
dc.type  PG_Thesis   
dc.identifier.hkul  b4819934   
dc.description.thesisname  Doctor of Philosophy   
dc.description.thesislevel  Doctoral   
dc.description.thesisdiscipline  Statistics and Actuarial Science   
dc.description.nature  published_or_final_version   
dc.identifier.doi  10.5353/th_b4819934   
dc.date.hkucongregation  2012   