Random Interest Rate Research Articles

Robust risk‐sensitive control

SummaryWe introduce arisk‐sensitivegeneralization of the mixed control problem for linear stochastic systems with additive noise. Two criteria ofexponential‐quadraticform are used to generalise the usual quadratic criteria. The solutions are found in a linear state‐feedback form for both the finite and the infinite horizon formulations in terms of coupled Riccati differential and algebraic equations. A change of measures for both criteria and completion of squares method is used to derive the solutions, and explicit sufficient conditions for the admissibility of controls are derived. An application to the problem ofrobustportfolio control in a market with random interest rate subject to a disturbance is also given.

Correlation Financial Option Pricing Model and Computer Simulation under a Stochastic Interest Rate

With the continuous expansion of the consumer interest rate market today, the risks brought by interest rate fluctuations have had a huge and far-reaching impact on the financial markets of many countries and it is becoming more and more important to simulate the pricing of financial options. In the traditional pricing model of financial options, the pricing standard of the pricing model is generally set as a financial product with random disturbance characteristics and the market price of its transaction does not follow the arbitrage principle of financial product pricing. It is easy to generate errors and cause risks, and the accuracy of traditional financial option pricing models is not high, and the simulation time is long, which greatly reduces the rate of financial transactions. To improve the accuracy of option pricing models, this paper uses computer simulation technology to simulate the pricing of correlated financial options under stochastic interest rates. From the four aspects of error, risk parameters, success rate, and simulation time, it is tested to observe the influence of computer simulation technology on the financial option pricing model. The final results show that by using computer simulation technology, the error of the correlation financial option pricing model under the random interest rate is reduced, the success rate is improved, the risk parameter is reduced by 3.03%, and the simulation time is reduced by 0.605 seconds.

Sustainable Construction and Financing—Asset-Backed Securitization of Expressway’s Usufruct with Redeemable Rights

Asset-backed securitization will greatly promote the sustainability of infrastructure construction and financing. However, there are quite limited researches conducted in this field. Given the project characteristics of infrastructure project securities, this paper proposes the issuance steps of redeemable asset-backed notes (ABN) based on the infrastructure project’s usufruct as the basic asset. Taking the expressway franchise as an example, the issuing scale and coupon rate of the redeemable ABN are determined by the expected cash flow of the expressway, the term structure of random interest rates, and the option-adjusted spread (OAS). In addition, this research analyzes the duration, convexity, and OAS.

Option pricing formulas with random interest rate under uncertainty theory

Option pricing formulas with random interest rate under uncertainty theory

Put Options with Linear Investment for Hull-White Interest Rates

We derive a Put Option price associated with selling strategy of the underlying security in a random interest rate environment. This extends Put Option pricing under linear investment strategy from the Black-Scholes setting to Hull-White stochastic interest rate model. As an application, Call Option price for the linear investment strategy in the Hull-White model is established. Our results address recent emergence of developing dynamic investment strategies for the purpose of reducing the investor risk exposure associated with European-type options.

AnnuityRIR: an R-package to approximate the value of an annuity according to the non-central moments of the capitalization factor

The aim of this paper is to design the package of the R statistical software called “Annuity Random Interest Rate”, referred hereinafter as AnnuityRIR, in order to calculate the value of an n-annuity with payments of one unit each when the interest rate is random. To do this, we have employed different approaches; the two main methodologies treated in this study consider that all non-central moments of the capitalization factor are known, or contrarily some of them are unknown. Consequently, five different approaches have been developed and the practical application of the proposed methods is reflected in this paper by pricing an annuity with a random risk-free interest rate during the last ten years. The version is available from CRAN: https://cran.r-project.org/web/packages/AnnuityRIR/index.html.

Linear predictor of the discounted renewal aggregate claims with dependent inter-occurrence times

In this paper we derive the first two moments and a linear predictor of the compound discounted renewal aggregate claims when taking into account dependence within the inter-occurrence times. Using specific mixtures of exponential distributions to define the dependence structure between the inter-occurrence times, we compare the accuracy of the proposed linear predictor to the simulated value of that sum.Keywords: Discounted compound renewal aggregate sums; moments; Archimedean copula; random interest rate; linear predictor

Optimal Investment Strategy under Stochastic Interest Rates

We study how firms’ management can make effective investment decision under the influence of random interest rates. We define the threshold interest rate value below which investment can be effectively done and above which investment is not optimal. We use a stochastic differential equation with alternating drift to find the optimal investment policy under stochastic interest rate. One of our results indicated that, the optimal condition for investment expansion is when the interest rate is low and the profit level is high. Also, there exists the threshold interest rate value which forms the basis for investment decision of a company. Moreover, we revealed that it is not optimal for the managers to plan for firm’s business expansion when is already making extremely high profits. At the end we were able to confirm that business is generally more stable when the interest rates are lower than those when they are high. Since firms in emerging economies suffer most from interest rate fluctuations, they need more effective investment strategies. Monetary policy makers of such economies need to ensure low interest rates in order to promote firms’ investment and therefore boost the general economy.

On the short-maturity behaviour of the implied volatility skew for random strike options and applications to option pricing approximation

In this paper, we propose a general technique to develop first- and second-order closed-form approximation formulas for short-maturity options with random strikes. Our method is based on a change of numeraire and on Malliavin calculus techniques, which allow us to study the corresponding short-maturity implied volatility skew and to obtain simple closed-form approximation formulas depending on the derivative operator. The numerical analysis shows that these formulas are extremely accurate and improve some previous approaches for two-asset and three-asset spread options such as Kirk’s formula or the decomposition method presented in Alòs et al. [Energy Risk, 2011, 9, 52–57]. This methodology is not model-dependent, and it can be applied to the case of random interest rates and volatilities.

ON THE MOMENTS OF STOCHASTIC ANNUITIES

The interest (discount) rate of annuity is a random variable, which is called stochastic. For stochastic annuities, also known as annuities under random rates of interest, we derive some moments, moments inequalities, and moments limits. When the discount rates are bounded, a strong convergence result is given showing that a stochastic annuity converges to its mean value as the number of years tend to infinity. Hence, stochastic annuities satisfy a type of strong law of large numbers.

Reserve of Semi-Continuous Life Insurance Model under Random Interest Rate

In this paper, it aims at an n-year term increasing life insurance model, considers the factual statements and the bursting out things’ influence on interest rate, establishes the model for stochastic interest rate by Reflected Brownian motion associating with Poisson process, and gives the common expression of semi-continuous reserve and the expression in the suppose of Uniform distribution of death.

Optimal dividend policy with random interest rates

Several recent papers have studied the impact of macroeconomic shocks on the financial policies of firms. However, they only consider the case where these macroeconomic shocks affect the profitability of firms but not the financial markets conditions. We study the polar case where the profitability of firms is stationary, but interest rates and issuance costs are governed by an exogenous Markov chain. We characterize the optimal dividend policy and show that these two macroeconomic factors have opposing effects: all things being equal, firms distribute more dividends when interest rates are high and less when issuing costs are high.

Optimal Dividend Policy with Random Interest Rates

Several recent papers have studied the impact of macroeconomic shocks on the financial policies of firms. However they only consider the case where these macroeconomic shocks affect the profitability of firms but not the financial markets conditions. We study the polar case where the profitability of firms is stationary, but interest rates and issuance costs are governed by an exogenous Markov chain. We characterize the optimal dividend policy and show that these two macroeconomic factors have opposing effects: all things being equal, firms distribute more dividends when interest rates are high and less when issuing costs are high.

Tests of the performance of structural models in bankruptcy prediction

In this study we investigate the relative performance of six structural credit risk models in predicting bankruptcy. The six models studied (the Merton, Black-Cox, Leland-Toft, Longstaff-Schwartz, flat barrier and Geske models) cover nested assumptions, thereby allowing us to study the factors that affect the accuracy of bankruptcy prediction. Using data from the period 1983-2002 (prior to the Sarbanes-Oxley Act), we compare the performance of these models for various prediction horizons and identify the factors that have the most substantial prediction power of default. Our results suggest that the left-tail probability of equity return distribution plays the most crucial role in predicting default. Moreover, we find that recovery boundary and multi-period default are important factors, while random interest rates are not.

Uniform estimate on finite time ruin probabilities with random interest rate

We consider a discrete time risk model in which the net payout (insurance risk) { X k, k = 1,2, …} are assumed to take real values and belong to the heavy-tailed class L ∩ D and the discount factors (financial risk) { Y k, k = 1,2, …} concentrate on [θ, L], where 0 < θ < 1, L < ∞, { X k, k = 1,2, …}, and { Y k, k = 1,2, …} are assumed to be mutually independent. We investigate the asymptotic behavior of the ruin probability within a finite time horizon as the initial capital tends to infinity, and figure out that the convergence holds uniformly for all n ≥ 1, which is different from Tang Q H and Tsitsiashvili G (Adv Appl Prob, 2004, 36: 1278–1299).

Annuities Under Random Rates of Interest II

Some attempts were made to evaluate the future value (FV) of the expected value and the variance for various cash flows (CF). The motivation stemmed from some recursive formulas. This method does not apply directly to the evaluation of present values (PV). One can get some estimates for the PV using results about the FV. We will present a direct approach to evaluate the PV of both factors for some CF. It will turn to be similar to that used to evaluate the FV. Furthermore it makes it possible to study the PV of these CF directly, and may suggest a method to study some other CF as well.

Strong consistency of maximum likelihood estimators for a discrete-time random field HJM-type interest rate model

We consider a discrete time Heath–Jarrow–Morton-type forward interest rate model, where the interest rate curves are driven by a geometric spatial autoregression field. Strong consistency of maximum likelihood estimators is proved for stable and unstable no-arbitrage models containing a simple stochastic discounting factor.

Generalized Vanna-Volga Method and its Applications

We give a general treatment of the Vanna-Volga mark-to-market volatility smile correction in application to pricing of contracts with European exercise on a single underlying. The method remains applicable in cases of delayed or misaligned expiries and absolute dividends. It is also applied to cases of time-dependent instantaneous volatility, multiple underlying assets and random interest rates. We also offer computation of the underlying volatility from market data and most valuable correction using more than three traded options.

Random field forward interest rate models, market price of risk and their statistics

In this paper we consider discrete time forward interest rate models. In our approach, unlike in the classical Heath–Jarrow–Morton framework, the forward rate curves are driven by a random field. Hence we get a general interest rate structure. Our aim is to give an overview of our results in such a model on the following questions: no-arbitrage conditions, maximum likelihood estimation of the volatility, as well as the joint estimation of the parameters and the asymptotic behaviour of the estimators, relationship with continuous models. Finally we give discussion on the practical problems of the estimation and we show several numerical results on the statistics of such models.

AN EXTENSION OF THE BRODY–HUGHSTON–MACRINA APPROACH TO MODELING OF DEFAULTABLE BONDS

The innovative information-based framework for credit risk modeling, proposed recently by Brody, Hughston, and Macrina, is extended to a more general and practically important setup of random interest rates. We first introduce the market model, and we derive an explicit expression for defaultable bond price. Next, the dynamics of the information process and dynamics of defaultable bond are found for both deterministic and random interest rates. Finally, the valuation and hedging of derivative securities are briefly examined. In particular, the valuation formula for a European option on a defaultable bond is established.