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.

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 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.

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.

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 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.

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.

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.

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.