Optimal Asset Allocation for CRRA and CARA Insurers under the Vasicek Interest Rate Model

This paper considers the reinsurance-investment problem with interest rate risks under constant relative risk aversion and constant absolute risk aversion preferences, respectively. Stochastic control theory and dynamic programming principle are applied to investigate the optimal proportional reinsurance-investment strategy for an insurer under the Vasicek stochastic interest rate model. Solving the corresponding Hamilton-Jacobi-Bellman equation via the Legendre transform approach, the optimal premium allocation strategies maximizing the expected utilities of terminal wealth are derived. In addition, several sensitivity analyses and numerical illustrations are given to analyze the impacts of different risk preferences and interest rate fluctuation on the optimal strategies. We find that the asset allocation and reinsurance ratio of the insurer are correlated with risk preference coefficient and interest rate fluctuation, and the insurance company may adjust the reinsurance-investment strategy to deal with interest rate risk.

Pricing and hedging bond options and sinking-fund bonds under the CIR model

<abstract><p>This article derives simple closed-form solutions for computing Greeks of zero-coupon and coupon-bearing bond options under the CIR interest rate model, which are shown to be accurate, easy to implement, and computationally highly efficient. These novel analytical solutions allow us to extend the literature in two other directions. First, the static hedging portfolio approach is used for pricing and hedging American-style plain-vanilla zero-coupon bond options under the CIR model. Second, we derive analytically the comparative static properties of sinking-fund bonds under the same interest rate modeling setup.</p></abstract>

Lévy Interest Rate Models with a Long Memory

This article proposes an interest rate model ruled by mean reverting Lévy processes with a sub-exponential memory of their sample path. This feature is achieved by considering an Ornstein–Uhlenbeck process in which the exponential decaying kernel is replaced by a Mittag–Leffler function. Based on a representation in term of an infinite dimensional Markov processes, we present the main characteristics of bonds and short-term rates in this setting. Their dynamics under risk neutral and forward measures are studied. Finally, bond options are valued with a discretization scheme and a discrete Fourier’s transform.

A New Algorithm for Approximate Maximum Likelihood Estimation in Sub-fractional Chan-Karolyi-Longstaff-Sanders Model

The paper introduces several approximate maximum likelihood estimators of the parameters of the sub-fractional Chan-Karolyi-Longstaff-Sanders (CKLS) interest rate model and obtains their rates of convergence. A new algorithm inspired by Newton-Cotes formula is presented to improve the accuracy of estimation. The estimators are useful for simulation of interest rates. The proposed new algorithm could be useful for other stochastic computation. It also proposes a generalization of the CKLS interest rate model with sub-fractional Brownian motion drivers which preserves medium range memory.

Nonparametric estimation and specification testing of a two-factor interest rate model

Nonparametric estimation and specification testing of a two-factor interest rate model

Nonparametric estimation and specification testing of a two-factor interest rate model

Nonparametric estimation and specification testing of a two-factor interest rate model

Pricing of Embedded Options in Bank Deposits and Loans Based on Jump-Diffusion Interest Rate Model

The marketization of interest rate is an inevitable requirement for China’s financial reform and joining the WTO to connect with the international financial market. It is also an important link to improve the marketization degree of China’s financial system. The marketization of interest rate in China is gradually advancing according to its preset mode. In the process of interest rate marketization, an unavoidable problem is that while the interest rate marketization gives the commercial banks the autonomy of capital pricing, the fluctuation of interest rate is more and more frequent. However, due to the fluctuation of interest rate, the loan as the main assets of commercial banks will be prepayed by borrowers, and the time deposit as the main liabilities of commercial banks will be withdrawn by depositors in advance; that is, embedded options are implied in asset liability items, which makes it difficult for commercial banks to accurately calculate the actual interest margin of deposits and loans and manage the interest rate risk. Therefore, it is of great significance to identify and price such embedded option value. On the basis of identifying and decomposing the embedded options in deposit and loan of commercial banks, according to the change characteristics of deposit and loan interest rate of Chinese commercial banks, this paper chooses jump-diffusion interest rate model to describe the change of benchmark interest rate of deposit and loan in China and demonstrates the advantages of this model compared with other models. Based on Monte Carlo simulation technology, the embedded options of five-year fixed deposit and ten-year prepayable loan in China are priced. On this basis, it points out that the real interest margin of commercial bank’s deposit and loan should be the nominal interest margin minus the value of deposit and loan’s embedded options. In the process of interest rate risk management, we should pay attention to the existence of embedded options and carry out effective management.