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Semi-static hedging of guarantees in variable annuities under exponential lévy modelsPang, Long-fung., 彭朗峯. January 2010 (has links)
published_or_final_version / Statistics and Actuarial Science / Master / Master of Philosophy
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Stochastic volatility models: calibration, pricing and hedgingPoklewski-Koziell, Warrick 01 October 2012 (has links)
Stochastic volatility models have long provided a popular alternative to the Black-
Scholes-Merton framework. They provide, in a self-consistent way, an explanation
for the presence of implied volatility smiles/skews seen in practice. Incorporating
jumps into the stochastic volatility framework gives further freedom to nancial
mathematicians to t both the short and long end of the implied volatility surface.
We present three stochastic volatility models here - the Heston model, the Bates
model and the SVJJ model. The latter two models incorporate jumps in the stock
price process and, in the case of the SVJJ model, jumps in the volatility process. We
analyse the e ects that the di erent model parameters have on the implied volatility
surface as well as the returns distribution. We also present pricing techniques for
determining vanilla European option prices under the dynamics of the three models.
These include the fast Fourier transform (FFT) framework of Carr and Madan as
well as two Monte Carlo pricing methods. Making use of the FFT pricing framework,
we present calibration techniques for tting the models to option data. Speci cally,
we examine the use of the genetic algorithm, adaptive simulated annealing and a
MATLAB optimisation routine for tting the models to option data via a leastsquares
calibration routine. We favour the genetic algorithm and make use of it in
tting the three models to ALSI and S&P 500 option data. The last section of the
dissertation provides hedging techniques for the models via the calculation of option
price sensitivities. We nd that a delta, vega and gamma hedging scheme provides
the best results for the Heston model. The inclusion of jumps in the stock price and
volatility processes, however, worsens the performance of this scheme. MATLAB
code for some of the routines implemented is provided in the appendix.
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A study on options hedge against purchase cost fluctuation in supply contracts.January 2008 (has links)
He, Huifen. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 44-48). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Motivation --- p.1 / Chapter 1.2 --- Literature Review --- p.4 / Chapter 1.2.1 --- Supply Contracts under Price Uncertainty --- p.5 / Chapter 1.2.2 --- Dual Sourcing --- p.6 / Chapter 1.2.3 --- Risk Aversion in Inventory Management --- p.6 / Chapter 1.2.4 --- Hedging Operational Risk Using Financial Instruments --- p.7 / Chapter 1.2.5 --- Financial Literature --- p.9 / Chapter 1.3 --- Organization of the Thesis --- p.10 / Chapter 2 --- A Risk-Neutral Model --- p.12 / Chapter 2.1 --- Framework and Assumptions --- p.12 / Chapter 2.2 --- "Price, Forward and Convenience Yield" --- p.14 / Chapter 2.2.1 --- Stochastic Model of Price --- p.14 / Chapter 2.2.2 --- Marginal Convenience Yield --- p.16 / Chapter 2.3 --- Optimality Equations --- p.17 / Chapter 2.4 --- The Structure of the Optimal Policy --- p.21 / Chapter 2.4.1 --- One-period. Optimal Hedge Decision Rule --- p.21 / Chapter 2.4.2 --- One-period Optimal Orderings Decision Rule --- p.23 / Chapter 2.4.3 --- Optimal Policy --- p.24 / Chapter 3 --- A Risk-Averse Model --- p.28 / Chapter 3.1 --- Risk Aversion Modeling and Utility Function --- p.28 / Chapter 3.2 --- Multi-Period Inventory Modelling --- p.31 / Chapter 3.3 --- Exponential Utility Model --- p.33 / Chapter 3.4 --- Optimal Ordering and Hedging Policy for Multi-Period Problem --- p.37 / Chapter 4 --- Conclusion and Future Research --- p.40 / Bibliography --- p.44 / Chapter A --- Appendix --- p.49 / Chapter A.l --- Notation --- p.49 / Chapter A.2 --- K-Concavity --- p.50
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Asymmetric effect of basis on hedging in Chinese metal market.January 2009 (has links)
Su, Yiwen. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (p. 76-84). / Abstract also in Chinese. / Abstract --- p.i / Acknowledgement --- p.iii / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Literature Review --- p.9 / Chapter 2.1 --- Hedge Ratio Review --- p.9 / Chapter 2.2 --- Estimating the Hedge Ratio --- p.13 / Chapter 2.2.1 --- Static Hedge Ratio --- p.13 / Chapter 2.2.2 --- "Dynamic Hedge Ratio, Multivariate GARCH Frame-work and DCC Model" --- p.14 / Chapter 3 --- Futures Market Efficiency --- p.19 / Chapter 3.1 --- Market Efficiency and Cointegration Test --- p.20 / Chapter 4 --- Model Specifications and Hedging Strategy --- p.24 / Chapter 4.1 --- Model Specifications --- p.24 / Chapter 4.1.1 --- BGARCH-DCC Model --- p.25 / Chapter 4.1.2 --- Symmetric BGARCH-DCC Model --- p.28 / Chapter 4.1.3 --- Asymmetric BGARCH-DCC Model --- p.31 / Chapter 4.2 --- Hedge Ratio --- p.33 / Chapter 4.2.1 --- MV Hedge Ratio --- p.34 / Chapter 4.2.2 --- Zero-VaR Hedge Ratio --- p.35 / Chapter 4.3 --- Evaluation of Hedge Effectiveness --- p.38 / Chapter 5 --- Data Description and Empirical Results --- p.39 / Chapter 5.1 --- Preliminary Data Analysis --- p.39 / Chapter 5.2 --- Estimation Results --- p.42 / Chapter 5.3 --- Dynamic Hedging Performance --- p.53 / Chapter 6 --- Conclusion --- p.68 / Chapter A --- Equation Derivation --- p.72 / Bibliography --- p.76
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The Lévy beta: static hedging with index futures.January 2010 (has links)
Cheung, Kwan Hung Edwin. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 39-40). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- The Levy Process --- p.4 / Chapter 2.1 --- Levy-Khintchine representation --- p.5 / Chapter 2.2 --- Variance Gamma process --- p.6 / Chapter 3 --- Minimum-Variance Static Hedge with Index futures --- p.8 / Chapter 3.1 --- Capital Asset Pricing Model with static hedge --- p.10 / Chapter 3.2 --- Continuous CAPM under Levy process --- p.11 / Chapter 4 --- Option pricing under Levy process --- p.15 / Chapter 4.1 --- Option pricing under the fast Fourier transform --- p.16 / Chapter 4.2 --- The modified fast Fourier transform on call option price --- p.19 / Chapter 5 --- Empirical Results --- p.23 / Chapter 5.1 --- Proposed model for empirical studies --- p.25 / Chapter 5.2 --- Calibration Procedure and Estimates of Betas --- p.26 / Chapter 5.3 --- Hedging performance of Betas --- p.32 / Chapter 6 --- Conclusion --- p.37 / Bibliography --- p.39
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Asset pricing, hedging and portfolio optimizationFu, Jun, 付君 January 2012 (has links)
Starting from the most famous Black-Scholes 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 risk-neutral
distributions for the jump component.
Another strand of the extensions of the Black-Scholes 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 time-changed 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 risk-free 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 continuous-time regime-switching market is also presented. The
use of regime-switching 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 regime-switching risk when obtaining the risk-neutral 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 single-regime market, which is
complete. / published_or_final_version / Statistics and Actuarial Science / Doctoral / Doctor of Philosophy
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Hedging with derivatives and operational adjustments under asymmetric informationLiu, Yinghu 05 1900 (has links)
Firms can use financial derivatives to hedge risks and thereby decrease the probability
of bankruptcy and increase total expected tax shields. Firms also can adjust
their operational policies in response to fluctuations in prices, a strategy that is
often referred to as "operational hedging". In this paper, I investigate the relationship
between the optimal financial and operational hedging strategies for a
firm, which are endogenously determined together with its capital structure. This
allows me to examine how operational hedging affects debt capacity and total expected
tax shields and to make quantitative predictions about the relationship
between debt issues and hedging policies. I also model the effects of asymmetric
information about firms' investment opportunities on their financing and hedging
decisions. First, I examine the case in which both debt and hedging contracts
are observable. Then, I study the case in which firms' hedging activities are not
completely transparent. The models are tested using a data set compiled from the
annual reports of North American gold mining companies. Supporting evidence is
found for the key predictions of the model under asymmetric information.
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Hedging with derivatives and operational adjustments under asymmetric informationLiu, Yinghu 05 1900 (has links)
Firms can use financial derivatives to hedge risks and thereby decrease the probability
of bankruptcy and increase total expected tax shields. Firms also can adjust
their operational policies in response to fluctuations in prices, a strategy that is
often referred to as "operational hedging". In this paper, I investigate the relationship
between the optimal financial and operational hedging strategies for a
firm, which are endogenously determined together with its capital structure. This
allows me to examine how operational hedging affects debt capacity and total expected
tax shields and to make quantitative predictions about the relationship
between debt issues and hedging policies. I also model the effects of asymmetric
information about firms' investment opportunities on their financing and hedging
decisions. First, I examine the case in which both debt and hedging contracts
are observable. Then, I study the case in which firms' hedging activities are not
completely transparent. The models are tested using a data set compiled from the
annual reports of North American gold mining companies. Supporting evidence is
found for the key predictions of the model under asymmetric information. / Business, Sauder School of / Graduate
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Evaluation of hedging effectiveness of Hong Kong and U.S. stock index futures.January 2000 (has links)
by Wong Man Kit, Andy, Yu Miu Ki. / Thesis (M.B.A.)--Chinese University of Hong Kong, 2000. / Includes bibliographical references (leaves 53-54). / ABSTRACT --- p.ii / ACKNOWLEDGEMENT --- p.iii / TABLE OF CONTENTS --- p.iv / Chapter / Chapter I. --- INTRODUCTION --- p.1 / Credit Risk --- p.2 / Operational risk --- p.3 / Liquidity risk --- p.3 / Legal risk --- p.3 / Market Risk --- p.3 / Model risk --- p.4 / Chapter II. --- LITERATURE REVIEW --- p.5 / Value at Risk (VaR) --- p.5 / Minimum Variance --- p.7 / Dollar equivalence --- p.8 / Statistical Hedging --- p.8 / Risk and Return in an Imperfect Hedge --- p.8 / Expected return and standard deviation in a hedged position --- p.9 / Risk and Return in an actual hedge --- p.11 / Optimal Hedge Ratio --- p.13 / Deriving Optimal Hedge Ratio h* --- p.15 / Computing the minimum risk hedge ratio by regression --- p.16 / Basis Risk --- p.18 / Sources of Basis Risk --- p.19 / Variation in the equilibrium price relationship between cash and futures --- p.19 / "Random ""noise"" in the price process" --- p.19 / Mismatch between cash position and the underlying for the future --- p.20 / Hedging Effectiveness --- p.21 / Chapter III. --- DATA AND METHODOLOGY --- p.25 / Data --- p.25 / Data Collection --- p.25 / Data Selection --- p.25 / Data Manipulation --- p.26 / Methodology --- p.27 / Part I: The Selection of the Portfolios --- p.27 / Part II: The Determination of the Hedge Ratio --- p.28 / Part III: Hedged vs. Unhedged --- p.29 / Part IV: Data Analysis & Comparison --- p.31 / Chapter IV. --- FINDINGS --- p.35 / High volatility of Hong Kong market --- p.35 / Manipulation of institutional investors --- p.36 / Hong Kong financial market are less mature --- p.36 / Less efficient information flow --- p.37 / Less Sophisticated Investors --- p.38 / Results and Discussion --- p.39 / Empirical Results --- p.40 / Explanation for the differences --- p.42 / Limitations --- p.47 / Learning Period --- p.47 / Cross Hedging --- p.47 / Mismatch between the futures and the underlying index --- p.48 / Missing Stock Data in the S&P500 --- p.49 / Chapter V. --- CONCLUSION --- p.50 / Tradeoff between risk and return --- p.50 / Hedge Effectiveness --- p.51 / BIBLIOGRAPHY --- p.53
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