随机利率下的增额寿险模型

以即时给付的增额寿险为研究对象,在保证利率恒正的情况下,考虑到不同性质的信息对利率的影响,对利率的随机性采用带Poisson跳的反射Brown运动建模,给出了一次缴清净保费、净均衡年保费和连续缴费方式下S时刻责任准备金的一般表达式.     

Pricing currency derivatives with Markov-modulated Lévy dynamics

Using a Lévy process we generalize formulas in Bo et al. (2010) for the Esscher transform parameters for the log-normal distribution which ensure that the martingale condition holds for the discounted foreign exchange rate. Using these values of the parameters we find a risk-neural measure and provide new formulas for the distribution of jumps, the mean jump size, and the Poisson process intensity with respect to this measure. The formulas for a European call foreign exchange option are also derived. We apply these formulas to the case of the log-double exponential distribution of jumps. We provide numerical simulations for the European call foreign exchange option prices with different parameters.     

Heavy tail and light tail of Cox-Ingersoll-Ross processes with regime-switching

This study aims to investigate the tail behavior of Cox-Ingersoll-Ross(CIR) processes with regime switching. An essential difference shown in this study between CIR processes with and without regime switching is that the stationary distribution of those with regime switching may be heavy-tailed. We first provide sharp criteria to justify the existence of a stationary distribution for the CIR process with regime switching, which is applied to study the long-term returns of interest rates. Then, we provide a criterion to identify whether this distribution is heavy-tailed. Our results provide theoretical evidence of the existence of regime switching for interest-rate models based on empirical evidence of a heavy-tailed distribution.     

CIR框架下的投资组合效用微分博弈(英文)

建立了Cox-Ingersoll-Ross随机利率下的关于两个投资者的投资组合效用微分博弈模型.市场利率具有CIR动力,博弈双方存在唯一的损益函数,损益函数取决于投资者的投资组合财富.一方选择动态投资组合策略以最大化损益函数,而另一方则最小化损益函数.运用随机控制理论,在一般的效用函数下得到了基于效用的博弈双方的最优策略.特别考虑了常数相对风险厌恶情形,获得了显示的最优投资组合策略和博弈值.最后给出了数值例子和仿真结果以说明本文的结论.     

An overview of Brownian and non-Brownian FCLTs for the single-server queue

We review functional central limit theorems (FCLTs) for the queue-content process in a single-server queue with finite waiting room and the first-come first-served service discipline. We emphasize alternatives to the familiar heavy-traffic FCLTs with reflected Brownian motion (RBM) limit process that arise with heavy-tailed probability distributions and strong dependence. Just as for the familiar convergence to RBM, the alternative FCLTs are obtained by applying the continuous mapping theorem with the reflection map to previously established FCLTs for partial sums. We consider a discrete-time model and first assume that the cumulative net-input process has stationary and independent increments, with jumps up allowed to have infinite variance or even infinite mean. For essentially a single model, the queue must be in heavy traffic and the limit is a reflected stable process, whose steady-state distribution can be calculated by numerically inverting its Laplace transform. For a sequence of models, the queue need not be in heavy traffic, and the limit can be a general reflected Lévy process. When the Lévy process representing the net input has no negative jumps, the steady-state distribution of the reflected Lévy process again can be calculated by numerically inverting its Laplace transform. We also establish FCLTs for the queue-content process when the input process is a superposition of many independent component arrival processes, each of which may exhibit complex dependence. Then the limiting input process is a Gaussian process. When the limiting net-input process is also a Gaussian process and there is unlimited waiting room, the steady-state distribution of the limiting reflected Gaussian process can be conveniently approximated. This revised version was published online in June 2006 with corrections to the Cover Date.     

Efficient portfolio dependent on Cox-Ingersoll-Ross interest rate

We solve a certain problem of portfolio optimization in the case of asset price trends dependent on the bank interest rate governed by the Cox-Ingersoll-Ross dynamics. This work continues a series of papers where the interest rate was modeled by a linear stochastic differential equation with a constant volatility.     

Pricing Variance Swaps in a Hybrid Model of Stochastic Volatility and Interest Rate with Regime-Switching

In this paper, we consider the problem of pricing discretely-sampled variance swaps based on a hybrid model of stochastic volatility and stochastic interest rate with regime-switching. Our modeling framework extends the Heston stochastic volatility model by including the Cox-Ingersoll-Ross (CIR) stochastic interest rate model. In addition, certain model parameters in our model switch according to a continuous-time observable Markov chain process. This enables our model to capture several macroeconomic issues such as alternating business cycles. A semi-closed form pricing formula for variance swaps is derived. The pricing formula is assessed through numerical implementation, where we validate our pricing formula against the Monte Carlo simulation. The impact of incorporating regime-switching for pricing variance swaps is also discussed, where variance swaps prices with and without regime-switching effects are examined in our model. We also explore the economic consequence for the prices of variance swaps by allowing the Heston-CIR model to switch across three different regimes.     

分段时变参数CIR模型及其实证研究

经济环境总体是变化的,但在一定阶段会保持局部稳定.鉴于此,提出了分段时变参数CIR模型的构想,并用它来建模短期利率与汇率.给出了CIR模型设定检验的广义残差拟合优度检验法,用之来检验模型的时变性.用数值模拟和实证分析来验证分段时变参数CIR模型进行利率、汇率建模的可行性和合理性.数值模拟表明,两组符合CIR(Cox-Ingersoll-Ross)模型的数据合在一起不一定还符合CIR模型.通过对短期国库券利率和加拿大元与美元汇率数据的实证分析,发现用分段时变参数CIR模型来描述短期利(汇)率比一般的固定常数CIR模型更加合理.     

Enhancing credit default swap valuation with meshfree methods

In this paper, we apply the meshfree radial basis function (RBF) interpolation to numerically approximate zero-coupon bond prices and survival probabilities in order to price credit default swap (CDS) contracts. We assume that the interest rate follows a Cox-Ingersoll-Ross process while the default intensity is described by the Exponential-Vasicek model. Several numerical experiments are conducted to evaluate the approximations by the RBF interpolation for one- and two-factor models. The results are compared with those estimated by the finite difference method (FDM). We find that the RBF interpolation achieves more accurate and computationally efficient results than the FDM. Our results also suggest that the correlation between factors does not have a significant impact on CDS spreads.