Optimal investment and life insurance strategies in a mixed jump-diffusion framework

Abstract

This article investigates an optimal investment and life insurance strategies in a mixed jump-diffusion framework. The individual life insurance policyholder who has CRRA preferences. The market consists of riskless asset, a zero-coupon bond, a stock and life insurance. The instantaneous interest rate is modeled as the O-U model, while a zero-coupon bond with credit risk follows a BSDE and a risky asset be driven by MJD-fBm model. The problem is solved by the mixed jump diffusion fractional HJB SDE which satisfied the admissible strategy, then the closed form solution and optimal strategies are derived and the simulation of the various parameters are also given.     

A fractional version of the Cox–Ingersoll–Ross interest rate model and pricing double barrier option with Hurst index H∈(23,1)

In this work, we study the existence and uniqueness of the solution to a fractional version of the Cox–Ingersoll–Ross (fCIR) stochastic differential equation. The strong convergence of this equation is analyzed and according to it’s framework, we obtain the price of the double barrier option under transaction cost. Finally, we verify the effect of the parameters of the model on the value of the option.     

Robust portfolio choice for a defined contribution pension plan with stochastic income and interest rate

This paper considers a robust portfolio choice problem for a defined contribution pension plan with stochastic income and stochastic interest rate. The investment objective of the pension plan is to maximize the expected utility of the wealth at the retirement time. We assume that the financial market consists of a stock, a zero-coupon bond and a risk-free asset. And the member of defined contribution pension plan is ambiguity-averse, which means that the member is uncertain about the expected return rate of the bond and stock. Meanwhile, the member's ambiguity-aversion level toward these two financial assets is quite different. The closed-form expressions of the robust optimal investment strategy and the corresponding value function are derived by adopting the stochastic dynamic programming approach. Furthermore, the sensitive analysis of model parameters on the optimal investment strategy are presented. We find that the member's aversion on model ambiguity increases her hedging demand and has remarkable impact on the optimal investment strategy. Moreover, we demonstrate that ignoring model uncertainty will lead to significant utility loss for the ambiguity-averse member, and the model uncertainty about the stock dynamics implies greater effect on the outcome of the investment than the bond.     

The pricing of defaultable bonds under a regime-switching jump-diffusion model with stochastic default barrier

In this paper, we investigate the price for the zero-coupon defaultable bond under a structural form credit risk with regime switching. We model the value of a firm and the default threshold by two dependent regime-switching jump-diffusion processes, in which the Markov chain represents the states of an economy. The price is associated with the Laplace transform of the first passage time and the expected discounted ratio of the firm value to the default threshold at default. Closed-form results used for calculating the price are derived when the jump sizes follow a regime-switching double exponential distribution. We present some numerical results for the price of the zero-coupon defaultable bond via Gaver-Stehfest algorithm.     

Machine Learning Vasicek Model Calibration with Gaussian Processes

In this article, we calibrate the Vasicek interest rate model under the risk neutral measure by learning the model parameters using Gaussian processes for machine learning regression. The calibration is done by maximizing the likelihood of zero coupon bond log prices, using mean and covariance functions computed analytically, as well as likelihood derivatives with respect to the parameters. The maximization method used is the conjugate gradients. The only prices needed for calibration are zero coupon bond prices and the parameters are directly obtained in the arbitrage free risk neutral measure.     

Unspanned Macroeconomic Factors in the Yield Curve

In this article, we extract common factors from a cross-section of U.S. macro-variables and Treasury zero-coupon yields. We find that two macroeconomic factors have an important predictive content for government bond yields and excess returns. These factors are not spanned by the cross-section of yields and are well proxied by economic growth and real interest rates.     

收益率曲面预测及其在信用债投资组合管理中的应用

收益率曲线是信用债投资者的重要参考。在市场套利活动的作用下,跨期限和信用等级的债券收益率具有很强的内生联系,其变动规律具有整体性和连续性。以往研究将信用债收益率曲线拆分成无风险利率曲线和信用利差两个部分,前者关注期限的影响,后者关注信用等级的影响,但很少同时考虑两者的共同影响。本文在收益率曲线的基础上增加信用等级维度,将AAA+级到AA级收益率曲线视为一个相互关联的整体,定义为信用债的收益率曲面(Yield Surface)。相比收益率曲线,收益率曲面包含了跨等级的系统性预测信息,通过预测收益率曲面能够构建具有较高收益的投资管理策略。本文以中期票据市场为例,采用卷积神经网络模型预测1周后的收益率曲面,在此基础上计算债券的预测理论价格,发现该价格对未来交易价格的预测有显著作用。基于预测价差,本文提出了信用债投资管 理策略,应用该策略的投资组合能够获得显著的正收益。业绩归因分析发现,该策略取得的收益同时来 自投资组合在信用风险和久期风险上的暴露,预测价差可以刻画债券市场的“风险前沿”。本文采用了中债估值价格进行稳健性检验,主要结论均保持一致,具有较强的稳健性。     

债券定价的离散时间仿射模型群

一、引言传统的债券定价方法—未来现金流量贴现法 ,是由美国的威廉姆斯 (Ｗｉｌｌｉａｍｓ .ＪｏｈｎＨｅｎｒｙ)根据现值理论推导而来的 ,曾被广大投资者用来作为衡量债券投资价值的方法。然而 ,该模型由于贴现率的选取没有确定的标准 ,具有比较大的随意性 ,因而导致所计算的债券价格也表现出较大的随意性 ,逐渐暴露其不足之处。随着利率期限结构理论的不断发展 ,债券定价方法也相应地获得了很大的进展。尤其是最近十几年来出现了利率期限结构的随机过程无套利分析方法 ,该方法认为利率期限结构和债券价格同某些随机因素 (即状态变量 )相…     

A bivariate integer-valued long-memory model for high-frequency financial count data

We propose a bivariate integer-valued fractional integrated (BINFIMA) model to account for the long-memory property and apply the model to high-frequency stock transaction data. The BINFIMA model allows for both positive and negative correlations between the counts. The unconditional and conditional first- and second-order moments are given. The model is capable of capturing the covariance between and within intra-day time series of high-frequency transaction data due to macroeconomic news and news related to a specific stock. Empirically, it is found that Ericsson B has mean recursive process while AstraZeneca has long-memory property.     

EUROPEAN OPTION PRICING WITH GENERAL TRANSACTION COSTS AND SHORT-SELLING CONSTRAINTS

In this paper, we study the problem of European Option Pricing in a market with short-selling constraints and transaction costs having a very general form. We consider two types of proportional costs and a strictly positive fixed cost. We study the problem within the framework of the theory of stochastic impulse control. We show that determining the price of a European option involves calculating the value functions of two stochastic impulse control problems. We obtain explicit expressions for the quasi-variational inequalities satisfied by the value functions and derive the solution in the case where the parameters of the price processes are constants and the investor's utility function is linear. We use this result to obtain a price for a call option on the stock and prove that this price is a nontrivial lower bound on the hedging price of the call option in the presence of general transaction costs and short-selling constraints. We then consider the situation where the investor's utility function has a general form and characterize the value function as the pointwise limit of an increasing sequence of solutions to associated optimal stopping problems. We thereby devise a numerical procedure to calculate the option price in this general setting and implement the procedure to calculate the option price for the class of exponential utility functions. Finally, we carry out a qualitative investigation of the option prices for exponential and linear-power utility functions.     

Optimal Strategies for a Long-Term Static Investor

The optimal strategies for a long-term static investor are studied. Given a portfolio of a stock and a bond, we derive the optimal allocation of the capitals to maximize the expected long-term growth rate of a utility function of the wealth. When the bond has a constant interest rate, three models for the underlying stock price processes are studied: Heston model, 3/2 model, and jump diffusion model. We also study the optimal strategies for a portfolio in which the stock price process follows a Black-Scholes model and the bond process has a Vasicek interest rate that is correlated to the stock price.     

基于国际资本多重动机的全球系统性风险传染路径识别

本文采用最新一代的SRISK方法测度了G20国家605家金融机构的系统性风险,并设计提出了基于高维的时变参数外溢网状矩阵,识别了全球系统性风险的传染路径和传染源。研究发现,各国系统性风险呈现明显增强态势,在危机时刻具有较强同步性,尤其是新冠肺炎疫情期间各国系统性风险同步激增。而欧美等发达金融市场更容易成为全球系统性风险的风险源,其中,美国溢出指数显著高于其他国家,是全球系统性风险的主要输出方;反之,新兴经济体的金融市场成熟度与放开程度远不及欧美发达国家,因此,更多地扮演着风险吸收方角色。基于面板模型的实证结果表明,资本流动骤停强化了系统性风险跨国别传染的溢出效应和吸收效应;国际资本流动的套利和套汇动机则是影响全球系统性风险传染的两个重要渠道,特别是,债券市场暴涨所引发的套利行为对吸收效应和溢出效应的影响存在显著的非对称性,而汇率升值超调引发的套汇行为则会增强系统性风险的溢出效应和吸收效应。此外,套价动机并未对系统性风险传染产生影响,一个主要原因可能在于各国的股票市场相对债券市场较为封闭,这势必隔断了套价行为对系统性风险传染效应的影响。最后,基于全球研究结论提出中国防范外部系统性风险冲击的政策建议。     

Pricing options with credit risk in a reduced form model

This article investigates the valuation of European option with credit risk in a reduced form model. We assume that the interest rate follows the Vasicek model and the intensity of default is driven by a jump diffusion process. We obtain the closed form formula for the price of the option and provide some numerical illustrations of the results obtained.     

基于EGARCH-M模型的沪深300股指期货跨期套利研究——一种修正的协整关系

现有的基于协整股指期货跨期套利策略主要利用GARCH模型进行建模。该模型忽略了杠杆效应的存在,也未考虑条件方差可能影响协整方程。在引入EGARCH-M模型进行套利研究的基础上,提出一种新的协整关系——修正的协整;利用沪深300股指期货合约的每分钟收盘价进行实证分析,结果表明:正态EGARCH-M模型对数据的拟合效果优于传统的GARCH模型,通过设定合理的交易机制可以获得良好的套利结果;非正态的EGARCH-M模型在拟合效果和捕捉套利机会方面都比正态模型具有更好的表现,且套利效果也有显著提高。     

Option pricing for a stochastic volatility Lévy model with stochastic interest rates

An alternative option pricing model under a forward measure is proposed, in which asset prices follow a stochastic volatility Lévy model with stochastic interest rate. The stochastic interest rate is driven by the Hull–White process. By using an approximate method, we find a formulation for the European option in term of the characteristic function of the tail probabilities.     

大连商品交易所大豆与豆粕期货价格之间的套利研究

摘　　要:本文对大连商品交易所大豆与豆粕期货价格之间的动态关系及套利交易进行了研究,研究结果表明,大豆与豆粕期货价格之间存在长期均衡关系,二个品种期货价格之间相互影响、相互作用。而样本内套利交易的模拟结果显示,无论是否考虑交易费用,多头套利交易的平均利润均大于零,且在统计上显著：而空头套利交易以及所有套利交易的平均利润虽然也大于零,但在统计上并不显著;而从样本外模拟结果来看,套利交易的平均利润并不显著。总体而言,大连商品交易所大豆与豆粕期货价格之间套利交易的赢利能力并不明显。     

Flexible Threshold Models for Modelling Interest Rate Volatility

This paper focuses on interest rate models with regime switching and extends previous nonlinear threshold models by relaxing the assumption of a fixed number of regimes. Instead we suggest automatic model determination through Bayesian inference via the reversible jump Markov Chain Monte Carlo (MCMC) algorithm. Moreover, we allow the thresholds in the volatility to be driven not only by the interest rate but also by other economic factors. We illustrate our methodology by applying it to interest rates and other economic factors of the American economy.     

Flexible Threshold Models for Modelling Interest Rate Volatility

This paper focuses on interest rate models with regime switching and extends previous nonlinear threshold models by relaxing the assumption of a fixed number of regimes. Instead we suggest automatic model determination through Bayesian inference via the reversible jump Markov Chain Monte Carlo (MCMC) algorithm. Moreover, we allow the thresholds in the volatility to be driven not only by the interest rate but also by other economic factors. We illustrate our methodology by applying it to interest rates and other economic factors of the American economy.     

Enhancing Estimation for Interest Rate Diffusion Models With Bond Prices

We consider improving estimating parameters of diffusion processes for interest rates by incorporating information in bond prices. This is designed to improve the estimation of the drift parameters, which are known to be subject to large estimation errors. It is shown that having the bond prices together with the short rates leads to more efficient estimation of all parameters for the interest rate models. It enhances the estimation efficiency of the maximum likelihood estimation based on the interest rate dynamics alone. The combined estimation based on the bond prices and the interest rate dynamics can also provide inference to the risk premium parameter. Simulation experiments were conducted to confirm the theoretical properties of the estimators concerned. We analyze the overnight Fed fund rates together with the U.S. Treasury bond prices. Supplementary materials for this article are available online.     

On the arbitrage price of European call options

We show that in a discrete price and discrete time model for option pricing, specifically that given by the Cox–Ross–Rubinstein model, the arbitrage price of a European call option can depend on parameters other than volatility (the standard deviation of the log asset price). We provide two theorems to illustrate this phenomenon. Our first theorem considers two securities with the same volatility so that at a specified time n₀, with probability near 1, the two securities are equal. If their call options differ, both the discounted securities will be martingales. Our second theorem considers two securities with the same volatility so that at times n = 0, ..., N ? 1 the securities are equal with probability near 1. If their call options differ, one of the discounted securities will be a martingale and the other discounted security will be a supermartingale.