Academic literature on the topic 'STOCHASTIC INTEREST BOND'

In the considered bond market, there are N zero-coupon bonds transacted continuously, which will mature at equally spaced dates. A duration of bond portfolios under stochastic interest rate model is introduced, which provides a measurement for the interest rate risk. Then we consider an optimal bond investment term-structure management problem using this duration as a performance index, and with the short-term interest rate process satisfying some stochastic differential equation. Under some technique conditions, an optimal bond portfolio process is obtained.

Stochastic volatility of underlying assets has been shown to affect significantly the price of many financial derivatives. In particular, a fast mean-reverting factor of the stochastic volatility plays a major role in the pricing of options. This paper deals with the interest rate model dependence of the stochastic volatility impact on defaultable interest rate derivatives. We obtain an asymptotic formula of the price of defaultable bonds and bond options based on a quadratic term structure model and investigate the stochastic volatility and default risk effects and compare the results with those of the Vasicek model.

We study power exchange options written on zero-coupon bonds under a stochastic string term-structure framework. Closed-form expressions for pricing and hedging bond power exchange options are obtained and, as particular cases, the corresponding expressions for call power options and constant underlying elasticity in strikes (CUES) options. Sufficient conditions for the equivalence of the European and the American versions of bond power exchange options are provided and the put-call parity relation for European bond power exchange options is established. Finally, we consider several applications of our results including duration and convexity measures for bond power exchange options, pricing extendable/accelerable maturity zero-coupon bonds, options to price a zero-coupon bond off of a shifted term-structure, and options on interest rates and rate spreads. In particular, we show that standard formulas for interest rate caplets and floorlets in a LIBOR market model can be obtained as special cases of bond power exchange options under a stochastic string term-structure model.

We propose approximate solutions to price defaultable zero-coupon bonds as well as the corresponding credit default swaps and bond options. We consider the intensity-based approach of a two-correlated-factor Hull-White model with stochastic volatility of interest rate process. Perturbations from the stochastic volatility are computed by using an asymptotic analysis. We also study the sensitive properties of the defaultable bond prices and the yield curves.

PurposeThe purpose of this paper is to derive semi‐closed‐form solutions to a wide variety of interest rate derivatives prices under stochastic volatility in affine‐term structure models.Design/methodology/approachThe paper first derives the Frobenius series solution to the cross‐moment generating function, and then inverts the related characteristic function using the Gauss‐Laguerre quadrature rule for the corresponding cumulative probabilities.FindingsThis paper values options on discount bonds, coupon bond options, swaptions, interest rate caps, floors, and collars, etc. The valuation approach suggested in this paper is found to be both accurate and fast and the approach compares favorably with some alternative methods in the literature.Research limitations/implicationsFuture research could extend the approach adopted in this paper to some non‐affine‐term structure models such as quadratic models.Practical implicationsThe valuation approach in this study can be used to price mortgage‐backed securities, asset‐backed securities and credit default swaps. The approach can also be used to value derivatives on other assets such as commodities. Finally, the approach in this paper is useful for the risk management of fixed‐income portfolios.Originality/valueThis paper utilizes a new approach to value many of the most commonly traded interest rate derivatives in a stochastic volatility framework.

We are concerned with an optimal investment-consumption problem with stochastic affine interest rate and stochastic volatility, in which interest rate dynamics are described by the affine interest rate model including the Cox-Ingersoll-Ross model and the Vasicek model as special cases, while stock price is driven by Heston’s stochastic volatility (SV) model. Assume that the financial market consists of a risk-free asset, a zero-coupon bond (or a convertible bond), and a risky asset. By using stochastic dynamic programming principle and the technique of separation of variables, we get the HJB equation of the corresponding value function and the explicit expressions of the optimal investment-consumption strategies under power utility and logarithmic utility. Finally, we analyze the impact of market parameters on the optimal investment-consumption strategies by giving a numerical example.

Based on the principle of maximization of the utility value for shareholders, we establish an optimal capital structure model under stochastic interest rates with improved endogenous default barriers by considering the tax and bankruptcy risk. From the numerical results, we find the drift and volatility of the firm’s log return, the average risk aversion of all the shareholders, the long term mean level of interest rate and the bond maturity are the key variables in determining optimal capital structure. We also find that the utility values behave as a concave function with bond principals. We can conclude that there exists an optimal amount of bond issuance to maximize the utility value of shareholders.

This paper develops a corporate bond valuation model that incorporates a default barrier with dynamics depending on stochastic interest rates and variance of the corporate bond function. Since the volatility of the firm value affects the level of leverage over time through the variance of the corporate bond function, more realistic default scenarios can be put into the valuation model. When the firm value touches the barrier, bondholders receive an exogenously specified number of riskless bonds. We derive a closed-form solution of the corporate bond price as a function of firm value and a short-term interest rate, with time-dependent model parameters governing the dynamics of the firm value and interest rate. The numerical results show that the dynamics of the barrier has material impact on the term structures of credit spreads. This model provides new insight for future research on risky corporate bonds analysis and modelling credit risk.

In this paper, we consider a new corporate bond-pricing model with credit-rating migration risks and a stochastic interest rate. In the new model, the criterion for rating change is based on a predetermined ratio of the corporation’s total asset and debt. Moreover, the rating changes are allowed to happen a finite number of times during the life-span of the bond. The volatility of a corporate bond price may have a jump when a credit rating for the bond is changed. Moreover, the volatility of the bond is also assumed to depend on the interest rate. This new model improves the previous existing bond models in which the rating change is only allowed to occur once with an interest-dependent volatility or multi-ratings with constant interest rate. By using a Feynman-Kac formula, we obtain a free boundary problem. Global existence and uniqueness are established when the interest rate follows a Vasicek’s stochastic process. Calibration of the model parameters and some numerical calculations are shown.

The aim of this work is to use one-factor stochastic term structure models to evaluate stochastic interest bonds, that are bonds bundled together some interest rate derivative, and to compare them with the theoretical value that the issuer indicates in the prospectus for the public offering. Stochastic interest bonds are a sub-set of the big family of structured bonds, the latter being bonds that present specific algorithms driving coupons computation and payment at maturity, mainly due to the presence of one or more derivative components embedded in their financial structure. Structured bonds are mainly issued by banks. Over the last two decades the offering of structured bonds to retail investors has consistently increased, with a contextual rise in the variety of the payoff structures. Chapter 1, after a brief exposure of the evolution of term structure models and their classification, is devoted to analyze several one-factor affine term structure models: the Vasicek model, the Ho-Lee model and the Hull-White model. Chapter 2 shows how to use the above models to price some typical interest rate derivatives (namely caps and floors) that are often embedded in the structure of stochastic interest bonds like those that will be considered in Chapter 5, which in fact, will include either a cap or a floor or both these two types of interest rate derivatives. Chapter 3 is devoted to analyze some key concepts about credit risk in order to take into account the impact of this risk factor on the bond value. To this aim, we will illustrate some key results regarding credit derivatives, and, specifically, credit default swaps whose market quotes allow to infer reliable estimates of the cumulative and intertemporal default probabilities of an issuer at various maturities by using the so-called bootstrapping technique. Once these default probabilities are estimated they can be used to derive a general pricing formula for defaultable bonds which will be used to perform the fair evaluation of the ten stochastic interest bonds analyzed in Chapter 5. Chapter 4 is devoted to study in detail the financial engineering of a specific kind of stochastic interest bonds, namely the so-called collared floaters, which are floating-rate coupon bonds whose coupons are subject to both an upper and a lower bound, hence embedding two interest rate derivatives, either a long cap and a short cap or a long floor and a short cap depending on the specific unbundling choice we make. In particular, the unbundling of a generic collared floater into its various elementary components is examined, as it will be useful to the pricing of many bonds included in the set of securities analyzed in Chapter 5. Chapter 5 is focused on the pricing of ten stochastic interest bonds recently issued by four of the major Italian banks: six of them are pure collared floaters, two of them are mixed fixed-floating coupon bonds, whose floating coupons have the typical structure of collared floaters, one bond is a floating-rate coupon bond embedding a floor, and one bond is a floating-rate coupon bond embedding a floor for the first half of its life and a cap for the second half of its life. After the illustration of their unbundling, these bonds are priced by means of two alternative pricing methodologies. The first methodology is based on the unbundling of their financial structure which reveals how these bonds can be seen as the composition of one or more pure bond components and of one or more interest rate derivatives, namely caps and/or floors, whose closed formulas - in the framework of the one-factor affine term structure models of Chapter 1 developed under the risk neutral probability measure - have been presented in Chapter 2. The second methodology relies instead on Monte Carlo simulations, performed again under the risk neutral probability measure; in this case the fair value of a bond is determined by discounting back at the evaluation date the final value of the security over each simulated trajectory and, then, by averaging these discounted values. The two pricing methodologies are implemented both in the framework of the Vasicek model and in that of the Hull and White model. Their results turn out to be consistent and, compared with the theoretical value indicated in the final terms of the prospectus published by the issuers, are a useful instrument to explore the reliability and the accuracy of the informative set included in this document that investors use to take their financial decisions.

The aim of this thesis is to investigate about the quantitative models used for pricing and managing life insurance risks. It was done analyzing the existing literature about methods and models used in the insurance field in order to developing (1) new stochastic models for longevity and mortality risks and (2) new pricing functions for life insurance policies and options embedded in such contracts. The motivations for this research are to be searched essentially in: (1) a new risk-based solvency framework for the insurance industry, the so-called Solvency II project, that will becomes effective in 2013/2014; (2) a new IAS/IFRS fair value-based accounting for insurance contracts, the so-called IFRS 4 (Phase 2) project (to be approval); (3) more rigorous quantitative analysis required by the industry in pricing and risk management of life insurance risks. The first part of the thesis (first and second chapters) contains a review of the quantitative models used for interest rates and longevity/mortality modeling. The second part (remaining chapters) describes new methods and quantitative models that it thinks could be useful in the context of pricing and insurance risk management.

In the first part of this thesis, we introduce a new methodology for stress-test exercises. Our approach allows to consider richer stress-test exercises, which assess the impact of a modification of the whole distribution of asset prices' factors, rather than focusing as the common practices on a single realization of these factors, and take into account the potential reaction to the shock of the portfolio manager. The second part of the thesis is devoted to the pricing of bonds with very long-term time-to-maturity (more than ten years). Modeling the volatility of very long-term rates is a challenge, due to the constraints put by no-arbitrage assumption. As a consequence, most of the no-arbitrage term structure models assume a constant limiting rate (of infinite maturity). The second chapter investigates the compatibility of the so-called "level" factor, whose variations have a uniform impact on the modeled yield curve, with the no-arbitrage assumptions. We introduce in the third chapter a new class of arbitrage-free term structure factor models, which allows the limiting rate to be stochastic, and present its empirical properties on a dataset of US T-Bonds.

碩士
國立中興大學
財務金融系所
99
Convertible bonds have become the main financing tool of domestic corporate in recent years, so the pricing method improvements become more important. Although there are many convertible pricing methods in the literature, most of them to take advantage of Nelson and Ramaswamy (1990) transform process, but the method not only must make the transformation but also calculate the probability in every node. It is too complex. We use of simple binomial tree algorithm, based on construction of a stochastic interest rate stock price model. Interest rate models us using the Vasicek (1977) model. According to Chen and Yang (2006), we use coercive recombine, fix the probability method, and interest rate binomial tree begin to spread up rapidly; Price model using integral area under the forward curve instead of the drift term of stock Brownian motion. Finally, we set the boundary condition to price convertible bond. We take three companies for example. Empirical results, the theoretical price are lower than the price announced on the prospectus.

碩士
逢甲大學
財務金融學所
92
The objective of this study is to search for an appropriate model for pricing equity-linked bond in a stochastic interest rate framework. A two-step procedure has been adopted to examine the issue. First, six major stochastic interest rate models has been compared to determine the best model in terms of their ability in capturing the dynamics of stochastic interest rate volatility. Second, we adopt the selected interest rate model is utilized to simulate the Equity-linked Bond price utilizing Monte-Carlo technique. Consistent with the finding of Bali (2003), our empirical result suggests that an incorporation of level-GARCH model do improve the pricing performance of stochastic interest rate model. Finally, a numerical example is utilized to verified the argument and further prove that an application of Level-GARCH model is a more appropriate model for pricing the equity-linked bond.

碩士
國立交通大學
財務金融研究所
98
Acharya (2002) analyzes the evaluation of corporate bond with defaultable and callable features when interest rates and firm value are stochastic. This thesis analyzes the sensitivity characteristics of putable bond and convertible bonds. By combining the results of Acharya (2002), we can analyze the corporate bond with multiple features, says callable-convertible bond. We also use a numerical method DFPM–WHT, to verify the analytical properties of corporate bonds proved in this thesis. Besides, we find that the payment rule greatly influence the right of bond holders, and use our numerical model to analyze the bondholder protection problem.

碩士
輔仁大學
金融研究所
82
This paper develops a model of the pricing of convertibles which differs from the previous domain work in allowing for the uncertainty in interest rates. The analysis is to treat convertibles as a contingent claim and to value it using the option-pricing method created by Black- Scholes(1973). We derive the differential equation of the value of convertibles then numerically solve the convertible bond valuation problem. We use Hopscotch finite-difference method which is a hybrid of explicit and implicit methods and could be efficient in a number of two-variable applications in finance. The difference between variable interest rates model values and constant interest rates model values is ambiguous and the resulting estimated theoretical value always overvalues convertibles. We think the main reason for the CCA model always overvalues c nvertibles in the domain security market is because of the two- stage conversion frame. In our study, allowing for the uncertainty in interest rates can not get the theoretical value that is closer to the market price than the earlier work.

碩士
國立政治大學
金融學系
89
With the growth in the area of financial engineering, more and more financial products are designed to meet demands of the market participants. Interest rate derivatives are those instruments whose values depend on interest rate changes. These derivatives form a huge market worth several trillions of dollars. The first step to design or develop a new financial product is pricing. In the real world interest rate is not a constant as in the B-S option instead it changes over time. Stochastic interest rate models are used for capturing the volatile behavior of interest rate and valuing interest rate derivatives. Appropriate models are necessary to value these instruments. Here we want to use stochastic interest rate models to construct the yield curve of Taiwan Government Bond (TGB) market. It is important to construct yield curve for pricing some financial instruments such as interest rate derivatives and fixed income securities. In Taiwan Although most of the research surrounding interest rate models is intended towards studying their usefulness in valuing and hedging complex interest rate derivatives by simulation. But just a few papers focus on empirical study. Maybe this is due to the problems for data collection. In this paper we want to use stochastic interest models to construct the yield curve of Taiwan’s Government Bond market. The estimation method that we use in this paper is GMM (Generalized Method of Moment) followed CKLS (1992). I introduce three different interest rate model, Vasicek model (Vasicek 1977), Vasicek with stochastic mean model (BDFS 1998) and Vasicek with stochastic mean and stochastic volatility model (Chen,Lin 1996). The last two models first appear in Taiwan’s research .In the Chapter 3, I will introduce these models in detail and in the appendix of my thesis I will show how to use PDE approach to derive each model’s zero coupon bond price close-form solution. In this paper we regard Taiwan CP (commercial Paper) rates as a proxy of short rate to estimate the parameters of each model. Finally we use these models to construct the yield curve of Taiwan Government Bonds market and to tell which model has the best fitting bond prices performance. Our metric of performance for these models is RMSE (Root mean squared Price Prediction Error). The main contribution of this study is to construct the yield curve of TGB market and it is useful to price derivatives and fixed income securities and I introduce two stochastic interest rates models, which first appear in Taiwan’s research. I also show how to solve the PDE for a bond price and it is a useful practice for someone who wants to construct his/her own model.

The financial markets use stochastic models to represent the seemingly random behavior of assets such as stocks, commodities, relative currency prices such as the price of one currency compared to that of another, such as the price of US Dollar compared to that of the Euro, and interest rates. These models are then used by quantitative analysts to value options on stock prices, bond prices, and on interest rates. This chapter gives an overview of the stochastic models and methods used in financial risk management. Given the random nature of future events on financial markets, the field of stochastic processes obviously plays an important role in quantitative risk management. Random walk, Brownian motion and geometric Brownian motion processes in risk management are explained. Simulations of these processes are provided with some software codes.

The financial markets use stochastic models to represent the seemingly random behavior of assets such as stocks, commodities, relative currency prices such as the price of one currency compared to that of another, such as the price of US Dollar compared to that of the Euro, and interest rates. These models are then used by quantitative analysts to value options on stock prices, bond prices, and on interest rates. This chapter gives an overview of the stochastic models and methods used in financial risk management. Given the random nature of future events on financial markets, the field of stochastic processes obviously plays an important role in quantitative risk management. Random walk, Brownian motion and geometric Brownian motion processes in risk management are explained. Simulations of these processes are provided with some software codes.

The paper examines simplified backward and forward transmission mechanism of monetary policy instrument to perturbation in un-employment rate. We apply three variables time-varying VAR model, with stochastic volatility, to determine the dynamic relationship among unemployment rate, interest rate and supply of money in the context of Euro Area. We concluded that, there is a possible stabilization potential through the increase in the money supply has dramatically risen before (and after) the COVID-19 pandemic; the reaction function of ECB to negative unemployment shock has been tied-up by the zero low bound and space for intense interest rate decrease has been empirically reduced in the pandemic times.

Abstract CO2 has some critical technical and economic reasons for its use as an injection gas for oil recovery. CO2 is very soluble in crude oil at reservoir pressures; it contributes to sweep efficiency enhancement as it swells the oil and significantly reduces its viscosity. Although the mechanism of CO2 flooding is the same as that for other gases, CO2 is easier to handle, it is cheaper, and it is an environmentally better candidate than other gases. Formation evaluation and reservoir engineering have been major areas in the oil and gas industry that are heavily influenced by technology advances, to increase efficiency, improve hydrocarbon recovery and allow real-time reservoir monitoring. Water flooding for increasing oil recovery has been amongst the oldest production mechanisms widely utilized since the end of the 19th century to maintain pressure levels in the reservoir and push hydrocarbons accumulations towards the producing wellbore locations (Satter, Iqbal, & Buchwalter, 2008). Produced water from the reservoir formation was reinjected in order to maintain pressure levels, as well as seawater and aquifer water injection have also taken a strong mandate. With the advent of technology and processing plants this injection process was further refined, allowing salinity control of the injected water as well as monitor the injection and distribution of the water levels in near real time (Boussa, Bencherif, Hamza, & Khodja, 2005). Formation evaluation has seen an even greater penetration of technology in its area with the quest to achieve real-time formation evaluation during the drilling process. Conventional formation evaluation is conducted utilizing wireline logging technology, which is deployed after the drilling of the well and allows to analyze the reservoir formation. Given the significant advancement of logging technologies, acquiring the measurements during the drilling process (LWD) has been at the forefront of interest, allowing improved well placement and geosteering as well as real-time formation evaluation to optimize well completion strategies (Hill, 2017). Amongst the technologies recently deployed, surfaced logging and advanced mud and logging allow to determine on cuttings in real time mostly any of the properties previously possible only on direct measurements on cores (Santarelli, Marsala, Brignoli, Rossi, & Bona, 1998; Katterbauer & Marsala, A Novel Sparsity Deploying Reinforcement Deep Learning Algorithm for Saturation Mapping of Oil and Gas Reservoirs, 2021; Katterbauer, Marsala, Schoepf, & Donzier, 2021). With advances in AI, reservoir characterization is now moving towards real-time or near real-time analysis at the rig site. For near real-time analysis, the main physical source of data is drill cuttings as it guides the drilling operation by determining important depth point such as formation tops, coring intervals. Traditionally, the description of these cuttings is done manually by geologists at the well site. The accuracy of these descriptions can be variable depending on the geologist's experience and indeed their mental state and tiredness level. Cores is another source of data. New techniques and older techniques imbued with AI components new allow for greater automation, efficiency, and consistency. The use of AI on traditional images are of great interest in the oil and gas community as they are: 1) fast to acquire, and 2) do not typically require expensive hardware. For example, Arnesen and Wade used convolutional neural networks; specifically, an inception-v3 inspired architecture, to predict lithological variations in cuttings (Arnesen & Wade, 2018). In their study, each sample is related to one lithology. Buscombe used a customized convolutional neural network to predict the granulometry of sediments, specifically the grain size distribution (Buscombe, 2019). Similarly, automated core description systems (e.g., (Kanagandran; de Lima, Bonar, Coronado, Marfurt, & Nicholson, 2019; de Lima, Marfurt, Coronado, & Bonar, 2019) and microfossil identification systems (e.g., (de Lima, Bonar, Coronado, Marfurt, & Nicholson, 2019)) are also being explored using neural networks with varying degree of success. A comprehensive review on the state of usage of rock images for reservoir characterization presented by de Lima et al. (de Lima, Marfurt, Coronado, & Bonar, 2019). In addition, the community is also recognizing the potential of improving older techniques by integrating artificial intelligence into their workflow. In reservoir characterization, chemostratigraphic analysis X-ray fluorescence is a prime example for this especially with the difficulties encountered when analyzing mudrocks in shale plays using traditional methods. The rise of XRF measurement was also fueled by the introduction of highly portable XRF devices that take 10s of seconds to measure one sample. The use of artificial intelligence techniques is being studied. For example, fully connected neural networks are applied on XRF data to predict total organic carbon (Lawal, Mahmoud, Alade, & Abdulraheem, 2019; Alnahwi & Loucks, 2019). In addition to the traditional elemental to mineralogical inversion methods such as constrained optimization, neural networks are being utilized (Alnahwi & Loucks, 2019). The integration between XRF, X-ray diffraction (XRD) measurements (Marsala, Loermans, Shen, Scheibe, & Zereik, 2012), and well logs using traditional statistical methods and neural network methods is also being explored (Al Ibrahim, Mukerji, & Hosford Scheirer, 2019). The integration between artificial intelligence systems and automated robotic scanning systems (e.g., (Croudace, Rindby, & Rothwell, 2006)) is key in introducing these technologies into the daily rig operations. The low density of CO2 relative to the reservoir fluid (oil and water) results in gravity override whereby the injected CO2 gravitates towards the top of the reservoir, leaving the bulk of the reservoir uncontacted. This may lead to poor sweep efficiency and poor oil recovery; this criticality can be minimized by alternating CO2 injection with water or similar chase fluids. This process is known as Water Alternating Gas (WAG). A major challenge in the optimization of the WAG process is to determine the cycle periods and the injection levels to optimize recovery and production ranges. In this work we present a data-driven approach to optimizing the WAG process for CO2 Enhanced Oil Recovery (EOR). The framework integrates a deep learning technique for estimating the producer wells’ output levels from the injection parameters set at the injector wells. The deep learning technique is incorporated into a stochastic nonlinear optimization framework for optimizing the overall oil production over various WAG cycle patterns and injection levels. The framework was examined on a realistic synthetic field test case with several producer and injection wells. The results were promising, allowing to efficiently optimize various injection scenarios. The results outline a process to optimize CO2-EOR from the reservoir formation via the utilization of CO2 as compared to sole water injection. The novel framework presents a data-driven approach to the WAG injection cycle optimization for CO2-EOR. The framework can be easily implemented and assists in the pre-selection of various injection scenarios to validate their impact with a full feature reservoir simulation. A similar process may be tailored for other Improved Oil Recovery (IOR) mechanisms.