Stochastic Volatility Modeling based on Doubly Truncated Cauchy Distribution and Bayesian Estimation for Chinese Stock Market

In order to measure the uncertainty of financial asset returns in the stock market, this paper presents a new model, called SV-dt C model, a stochastic volatility(SV) model assuming that the stock return has a doubly truncated Cauchy distribution, which takes into account the high peak and fat tail of the empirical distribution simultaneously. Under the Bayesian framework, a prior and posterior analysis for the parameters is made and Markov Chain Monte Carlo(MCMC) is used for computing the posterior estimates of the model parameters and forecasting in the empirical application of Shanghai Stock Exchange Composite Index(SSECI) with respect to the proposed SV-dt C model and two classic SV-N(SV model with Normal distribution)and SV-T(SV model with Student-t distribution) models. The empirical analysis shows that the proposed SV-dt C model has better performance by model checking, including independence test(Projection correlation test), Kolmogorov-Smirnov test(K-S test) and Q-Q plot. Additionally, deviance information criterion(DIC) also shows that the proposed model has a significant improvement in model fit over the others.

Optimal Quota-Share and Excess-of-Loss Reinsurance and Investment with Heston’s Stochastic Volatility Model

An optimal quota-share and excess-of-loss reinsurance and investment problem is studied for an insurer who is allowed to invest in a risk-free asset and a risky asset.Especially the price process of the risky asset is governed by Heston's stochastic volatility(SV)model.With the objective of maximizing the expected index utility of the terminal wealth of the insurance company,by using the classical tools of stochastic optimal control,the explicit expressions for optimal strategies and optimal value functions are derived.An interesting conclusion is found that it is better to buy one reinsurance than two under the assumption of this paper.Moreover,some numerical simulations and sensitivity analysis are provided.

Comparative Study of Volatility Forecasting Models： The Case of Malaysia, Indonesia, Hong Kong and Japan Stock Markets

This paper aims to investigate the effectiveness of four volatility forecasting models, i.e. Exponential Weighted Moving Average （EWMA）, Autoregressive Integrated Moving Average （ARIMA） and Generalized Auto-Regressive Conditional Heteroscedastic （GARCH）, in four stock markets Indonesia, Malaysia, Japan and Hong Kong. Using monthly closing stock index prices collected from 1 st January 1998 to 31 st December 2015 for the four selected countries, results obtained confirm that volatility in developed markets is not necessarily always lower than the volatility in emerging markets. Among all the three models, GARCH （1, l） model is found to be the best forecasting model for stock markets in Malaysia, Indonesia, and Japan, while EWMA model is found to be the best forecasting model for Hong Kong stock market. The outperformance of GARCH （1, 1） found supports again what is found in Minkah （2007）.

Study of Volatility Stochastic Processes in the Context of Solvency Forecasting for Sri Lankan Life Insurers

The main business of Life Insurers is Long Term contractual obligations with a typical lifetime of 20 - 40 years. Therefore, the Solvency metric is defined by the adequacy of capital to service the cash flow requirements arising from the said obligations. The main component inducing volatility in Capital is market sensitive Assets, such as Bonds and Equity. Bond and Equity prices in Sri Lanka are highly sensitive to macro-economic elements such as investor sentiment, political stability, policy environment, economic growth, fiscal stimulus, utility environment and in the case of Equity, societal sentiment on certain companies and industries. Therefore, if an entity is to accurately forecast the impact on solvency through asset valuation, the impact of macro-economic variables on asset pricing must be modelled mathematically. This paper explores mathematical, actuarial and statistical concepts such as Brownian motion, Markov Processes, Derivation and Integration as well as Probability theorems such as the Probability Density Function in determining the optimum mathematical model which depicts the accurate relationship between macro-economic variables and asset pricing.

Market Risk Evaluation on Single Futures Contract:SV-CVaR Model and Its Application on Cu00 Data

A new stochastic volatility（SV）method to estimate the conditional value at risk（CVaR）is put forward.Firstly,it makes use of SV model to forecast the volatility of return.Secondly,the Markov chain Monte Carlo（MCMC）simulation and Gibbs sampling have been used to estimate the parameters in the SV model.Thirdly,in this model,CVaR calculation is immediate.In this way,the SV-CVaR model overcomes the drawbacks of the generalized autoregressive conditional heteroscedasticity value at risk（GARCH-VaR）model.Empirical study suggests that this model is better than GARCH-VaR model in this field.

Early exercise premium method for pricing American options under the J-model

Background:This study develops a new model called J-am for pricing American options and for determining the related early exercise boundary(EEB).This model is based on a closed-form solution J-formula for pricing European options,defined in the study by Jerbi(Quantitative Finance,15:2041-2052,2015).The J-am pricing formula is a solution of the Black&Scholes(BS)PDE with an additional function called f as a second member and with limit conditions adapted to the American option context.The aforesaid function f represents the cash flows resulting from an early exercise of the option.Methods:This study develops the theoretical formulas of the early exercise premium value related to three American option pricing models called J-am,BS-am,and Heston-am models.These three models are based on the J-formula by Jerbi(Quantitative Finance,15:2041-2052,2015),BS model,and Heston(Rev Financ Stud,6:327-343,1993)model,respectively.This study performs a general algorithm leading to the EEB and to the American option price for the three models.Results:After implementing the algorithms,we compare the three aforesaid models in terms of pricing and the EEB curve.In particular,we examine the equivalence between J-am and Heston-am as an extension of the equivalence studied by Jerbi(Quantitative Finance,15:2041-2052,2015).This equivalence is interesting since it can reduce a bi-dimensional model to an equivalent uni-dimensional model.Conclusions:We deduce that our model J-am exactly fits the Heston-am one for certain parameters values to be optimized and that all the theoretical results conform with the empirical studies.The required CPU time to compute the solution is significantly less in the case of the J-am model compared with to the Heston-am model.

The Quadratic-Form Representation of the Pre-Averaging Estimator

Volatility forecasts are central to many financial issues, including empirical asset pricing finance and risk management. In this paper, I derive a new quadratic-form representation of the pre-averaging volatility estimator of Jacod et al. （2009）, which allows for the theoretical analysis of its forecasting performance.

Stochastic PDEs for large portfolios with general mean-reverting volatility processes

We consider a structural stochastic volatility model for the loss from a large portfolio of credit risky assets.Both the asset value and the volatility processes are correlated through systemic Brownian motions,with default determined by the asset value reaching a lower boundary.We prove that if our volatility models are picked from a class of mean-reverting diffusions,the system converges as the portfolio becomes large and,when the vol-of-vol function satisfies certain regularity and boundedness conditions,the limit of the empirical measure process has a density given in terms of a solution to a stochastic initial-boundary value problem on a half-space.The problem is defined in a special weighted Sobolev space.Regularity results are established for solutions to this problem,and then we show that there exists a unique solution.In contrast to the CIR volatility setting covered by the existing literature,our results hold even when the systemic Brownian motions are taken to be correlated.

Stochastic Volatility Model and Technical Analysis of Stock Price

In the stock market, some popular technical analysis indicators （e.g. Bollinger Bands, RSI, ROC, ...） are widely used by traders. They use the daily （hourly, weekly, ...） stock prices as samples of certain statistics and use the observed relative frequency to show the validity of those well-known indicators. However, those samples are not independent, so the classical sample survey theory does not apply. In earlier research, we discussed the law of large numbers related to those observations when one assumes Black-Scholes＇ stock price model. In this paper, we extend the above results to the more popular stochastic volatility model.

Empirical Evidence of the Leverage Effect in a Stochastic Volatility Model： A Realized Volatility Approach

Increasing attention has been focused on the analysis of the realized volatil- ity, which can be treated as a proxy for the true volatility. In this paper, we study the potential use of the realized volatility as a proxy in a stochastic volatility model estimation. We estimate the leveraged stochastic volatility model using the realized volatility computed from five popular methods across six sampling-frequency transaction data （from 1-min to 60- min） based on the trust region method. Availability of the realized volatility allows us to estimate the model parameters via the MLE and thus avoids computational challenge in the high dimensional integration. Six stock indices are considered in the empirical investigation. We discover some consistent findings and interesting patterns from the empirical results. In general, the significant leverage effect is consistently detected at each sampling frequency and the volatility persistence becomes weaker at the lower sampling frequency.

Stock Returns, Volatility, and Cointegration among Chinese Stock Markets

This paper examines stockreturns, volatility, and cointegration among three Chinese stock marketsbeforeand afterHong Kong’sreturn to China. Theaverage daily returnsaremuch higherduring the first sub-period (from April1991 to June1997)and significantlyloweror even negativeduring the second sub-period (from July1997 to December2002). The mean adjusted changein volatilityis negativelyand significantly correlated with thelagged returns. This negative relation is mainly caused by a contemporaneous and significantly positive correlation between returnsand volatilityinthe firstsub-period. Thissignificant relationship disappears forthe Shanghai and Shenzhen Stock Exchanges and is even negative for the Hong Kong Stock Exchange during the second sub-period. Three Chinese stock markets arecointegrated over the entiresampleperiod and becomemore closelyrelated after Hong Kong’s return to China. Our results have important implications for both policy makers and individual investors.

PARAMETER ESTIMATION FOR A DISCRETELY OBSERVED STOCHASTIC VOLATILITY MODEL WITH JUMPS IN THE VOLATILITY

In this paper a stochastic volatility model is considered. That is, a log price process Y whichis given in terms of a volatility process V is studied. The latter is defined such that the logprice possesses some of the properties empirically observed by Barndorff-Nielsen & Jiang[6]. Inthe model there are two sets of unknown parameters, one set corresponding to the marginaldistribution of V and one to autocorrelation of V. Based on discrete time observations ofthe log price the authors discuss how to estimate the parameters appearing in the marginaldistribution and find the asymptotic properties.

A Heston local-stochastic volatility model for optimal investment-reinsurance strategy with a defaultable bond in an ambiguous environment

This study considers an optimal investment and reinsurance problem involving a defaultable security for an insurer in an ambiguous environment.In other words,the insurer is ambiguous about the insurance claim that is exponentially distributed with an uncertain rate parameter.The insurer can purchase proportional reinsurance and invest its wealth in three assets:a risk-free asset,a risky asset,the price process of which satisfies the Heston local-stochastic volatility model,and a defaultable corporate bond.For the optimal investment–reinsurance objective with a smooth ambiguity utility proposed by Klibanoff,P.,Marinacci,M.,and Mukerji,S.[A smooth model of decision making under ambiguity,Econometrica,2005,73(6):1849-1892],the equilibrium strategy is introduced and the extended Hamilton–Jacobi–Bellman equation is established through a stochastic control approach.However,the analytical solution of the strategy under the Heston local-stochastic volatility model cannot be obtained because of the complicated nonlinearity of the partial differential equation.In this study,we employ a perturbation method to derive an asymptotic solution for the post-and pre-default cases.In addition,we present a sensitivity analysis to explain the impact of model parameters on the equilibrium investment–reinsurance strategy.

The Numeric Characteristics of Chinese A-Share Market Index Volatility,Model Simulation,and Forecasting

This study investigates the basic numeric characteristics of Chinese A-share market index volatility (i.e.,the clustering,heteroscedasticity,and jumps) from the perspective of data mining.It presents a theoretical-empirical model based on these three major characteristics and conducts a maximum likelihood estimation to study Chinese A-share market return data empirically.Results show that,in full-sample or special periods,this model calibrates the A-share index volatility well and simulates in-sample volatility better than the four major empirical models adopted to study volatility.In out-of-sample forecasts,this model performs better than the other four models on the value-at-risk dates,which are the volatile days.This model can also decompose and explain the volatility of the Chinese A-share index.On the basis of GARCH,this study revises the volatility model proposed by Maheu and extends Engle’s research framework.Thus,this model is of theoretical significance.This model’s simulation and forecast functioning can contribute to regulatory expectation management and investment portfolio construction.

Synergistic impacts of anthropogenic and biogenic emissions on summer surface O_3 in East Asia

A factor separation technique and an improved regional air quality model （RAQM） were applied to calculate synergistic contributions of anthropogenic volatile organic compounds （AVOCs）,biogenic volatile organic compounds （BVOCs） and nitrogen oxides （NOx） to daily maximum surface O3（O3DM） concentrations in East Asia in summer （June to August 2000）.The summer averaged synergistic impacts of AVOCs and NOx are dominant in most areas of North China,with a maximum of 60 ppbv,while those of BVOCs and NOx are notable only in some limited areas with high BVOC emissions in South China,with a maximum of 25 ppbv.This result implies that BVOCs contribute much less to summer averaged O3DM concentrations than AVOCs in most areas of East Asia at a coarse spatial resolution （1×1） although global emissions of BVOCs are much greater than those of AVOCs.Daily maximum total contributions of BVOCs can approach 20 ppbv in North China,but they can reach 40 ppbv in South China,approaching or exceeding those in some developed countries in Europe and North America.BVOC emissions in such special areas should be considered when O3 control measures are taken.Synergistic contributions among AVOCs,BVOCs and NOx significantly enhance O3 concentrations in the Beijing-Tianjin-Tangshan region and decrease them in some areas in South China.Thus,the total contributions of BVOCs to O3DM vary significantly from day to day and from location to location.This result suggests that O3 control measures obtained from episodic studies could be limited for long-term applications.

Robust M-estimate of GJR Model with High Frequency Data

In this paper, we study the GJR scaling model which embeds the intraday return processes into the daily GJR model and propose a class of robust M-estimates for it. The estimation procedures would be more efficient when high-frequency data is taken into the model. However, high-frequency data brings noises and outliers which may lead to big bias of the estimators. Therefore, robust estimates should be taken into consideration. Asymptotic results are derived from the robust M-estimates without the finite fourth moment of the innovations. A simulation study is carried out to assess the performance of the model and its estimates.Robust M-estimate of GJR model is also applied in predicting Va R for real financial time series.

Optimal Reinsurance and Investment Strategy with Delay in Heston’s SV Model

In this paper,we consider an optimal investment and proportional reinsurance problem with delay,in which the insurer’s surplus process is described by a jump-diffusion model.The insurer can buy proportional reinsurance to transfer part of the insurance claims risk.In addition to reinsurance,she also can invests her surplus in a financial market,which is consisted of a risk-free asset and a risky asset described by Heston’s stochastic volatility(SV)model.Considering the performance-related capital flow,the insurer’s wealth process is modeled by a stochastic differential delay equation.The insurer’s target is to find the optimal investment and proportional reinsurance strategy to maximize the expected exponential utility of combined terminal wealth.We explicitly derive the optimal strategy and the value function.Finally,we provide some numerical examples to illustrate our results.

SCHWARZ METHOD FOR FINANCIAL ENGINEERING

Schwarz method is put forward to solve second order backward stochastic di erential equations(2BSDEs)in this work.We will analyze uniqueness,convergence,stability and optimality of the proposed method.Moreover,several simulation results are presented to demonstrate the e ectiveness;several applications of the 2BSDEs are investigated.It is concluded from these results that the proposed the method is powerful to calculate the 2BSDEs listing from the nancial engineering.

PRICING CONVERTIBLE BONDS AND CHANGE OF PROBABILITY MEASURE

The changes of numeraire can be used as a very powerful tool in pricing contingent claims in the context of a complete market.By using the method of numeraire changes to evaluate convertible bonds when the value of firm,and those of zero-coupon bonds follow general adapted stochastic processes in this paper,using Ito theorem and Gisanov theorem.A closed-form solution is derived under the stochastic volatility by using fast Fourier transforms.

Multi-period Bank Hedging with Interest Rate Futures

In this paper, a model for multi-period bank hedging with interest rate futures is set up. Formulas for the optimal dynamic multi-period bank and static bank hedge ratio are derived. The described model offers the potential benefits of： （1） although these formulas are developed for the case of direct sheet balance multi-period hedging, the framework used is sufficiently flexible so that these formulas can be applied to bank loan or deposit multi-period hedging situations respectively. （2） Periodic modification and updating of the interest rate futures position, as suggested by interest rates, throughout the bank hedging horizons. （3） This paper examines a situation in which the return of loan, the interest rate of deposit and the equity capital of bank, and interest rate futures prices are cointergrated, Multi-period bank hedging formulas are derived under three-dimensional stochastic volatility model. However, empirical research is required for validating this model.