Journal articles: 'STOCHASTIC INTEREST BOND'

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Liu, Daobai. "Bond portfolio's duration and investment term-structure management problem." Journal of Applied Mathematics and Stochastic Analysis 2006 (May 7, 2006): 1–19. http://dx.doi.org/10.1155/jamsa/2006/76920.

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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.

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Brennan, Michael J., and Yihong Xia. "Stochastic Interest Rates and the Bond-Stock Mix." Review of Finance 4, no. 2 (August 1, 2000): 197–210. http://dx.doi.org/10.1023/a:1009890514371.

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Yoon, Ji-Hun, Jeong-Hoon Kim, Sun-Yong Choi, and Youngchul Han. "Stochastic volatility asymptotics of defaultable interest rate derivatives under a quadratic Gaussian model." Stochastics and Dynamics 17, no. 01 (December 15, 2016): 1750003. http://dx.doi.org/10.1142/s0219493717500034.

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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.

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Blenman, Lloyd P., Alberto Bueno-Guerrero, and Steven P. Clark. "Pricing and Hedging Bond Power Exchange Options in a Stochastic String Term-Structure Model." Risks 10, no. 10 (September 27, 2022): 188. http://dx.doi.org/10.3390/risks10100188.

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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.

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Ma, Yong-Ki, and Beom Jin Kim. "Asymptotic Analysis for One-Name Credit Derivatives." Abstract and Applied Analysis 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/567340.

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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.

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Tahani, Nabil, and Xiaofei Li. "Pricing interest rate derivatives under stochastic volatility." Managerial Finance 37, no. 1 (January 31, 2011): 72–91. http://dx.doi.org/10.1108/03074351111092157.

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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.

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Chang, Hao, and Xue-Yan Li. "Optimal Consumption and Portfolio Decision with Convertible Bond in Affine Interest Rate and Heston’s SV Framework." Mathematical Problems in Engineering 2016 (2016): 1–12. http://dx.doi.org/10.1155/2016/4823451.

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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.

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Yang, Xiaofeng, and Zastawniak Tomasz. "Optimal Capital Structure under Stochastic Interest Rates with Endogenous Default Barriers." Advances in Economics and Management Research 1, no. 3 (February 8, 2023): 303. http://dx.doi.org/10.56028/aemr.3.1.303.

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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.

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HUI, C. H., and C. F. LO. "A NOTE ON RISKY BOND VALUATION." International Journal of Theoretical and Applied Finance 03, no. 03 (July 2000): 575–80. http://dx.doi.org/10.1142/s0219024900000656.

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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.

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Yin, Hong-Ming, Jin Liang, and Yuan Wu. "On a New Corporate Bond Pricing Model with Potential Credit Rating Change and Stochastic Interest Rate." Journal of Risk and Financial Management 11, no. 4 (December 6, 2018): 87. http://dx.doi.org/10.3390/jrfm11040087.

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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.

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Tomas, Michael J., and Jun Yu. "An Asymptotic Solution for Call Options on Zero-Coupon Bonds." Mathematics 9, no. 16 (August 14, 2021): 1940. http://dx.doi.org/10.3390/math9161940.

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We present an asymptotic solution for call options on zero-coupon bonds, assuming a stochastic process for the price of the bond, rather than for interest rates in general. The stochastic process for the bond price incorporates dampening of the price return volatility based on the maturity of the bond. We derive the PDE in a similar way to Black and Scholes. Using a perturbation approach, we derive an asymptotic solution for the value of a call option. The result is interesting, as the leading order terms are equivalent to the Black–Scholes model and the additional next order terms provide an adjustment to Black–Scholes that results from the stochastic process for the price of the bond. In addition, based on the asymptotic solution, we derive delta, gamma, vega and theta solutions. We present some comparison values for the solution and the Greeks.

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Wei, Longfei, Lu Liu, and Jialong Hou. "Pricing hybrid-triggered catastrophe bonds based on copula-EVT model." Quantitative Finance and Economics 6, no. 2 (2022): 223–43. http://dx.doi.org/10.3934/qfe.2022010.

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<abstract><p>This paper presents a hybrid-triggered catastrophe bond (CAT bond) pricing model. We take earthquake CAT bonds as an example for model construction and numerical analysis. According to the characteristics of earthquake disasters, we choose direct economic loss and magnitude as trigger indicators. The marginal distributions of the two trigger indicators are depicted using extreme value theory, and the joint distribution is established by using a copula function. Furthermore, we derive a multi-year hybrid-triggered CAT bond pricing formula under stochastic interest rates. The numerical experiments show that the bond price is negatively correlated with maturity, market interest rate and dependence of trigger indicators, and positively correlated with trigger level and coupon rate. This study can be used as a reference for formulating reasonable CAT bond pricing strategies.</p></abstract>

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YE, C., R. H. LIU, and D. REN. "OPTIMAL ASSET ALLOCATION WITH STOCHASTIC INTEREST RATES IN REGIME-SWITCHING MODELS." International Journal of Theoretical and Applied Finance 21, no. 05 (August 2018): 1850032. http://dx.doi.org/10.1142/s0219024918500322.

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This paper focuses on optimal asset allocation with stochastic interest rates in regime-switching models. A class of stochastic optimal control problems with Markovian regime-switching is formulated for which a verification theorem is provided. The theory is applied to solve two portfolio optimization problems (a portfolio of stock and savings account and a portfolio of mixed stock, bond and savings account) while a regime-switching Vasicek model is assumed for the interest rate. Closed-form solutions are obtained for a regime-switching power utility function. Numerical results are provided to illustrate the impact of regime-switching on the optimal investment decisions.

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Zhang, Xin, and Xiaoxiao Zheng. "Optimal Investment-Reinsurance Policy with Stochastic Interest and Inflation Rates." Mathematical Problems in Engineering 2019 (December 17, 2019): 1–14. http://dx.doi.org/10.1155/2019/5176172.

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The aim of this paper is to study a classic problem in actuarial mathematics, namely, an optimal reinsurance-investment problem, in the presence of stochastic interest and inflation rates. This is of relevance since insurers make investment and risk management decisions over a relatively long horizon where uncertainty about interest rate and inflation rate may have significant impacts on these decisions. We consider the situation where three investment opportunities, namely, a savings account, a share, and a bond, are available to an insurer in a security market. In the meantime, the insurer transfers part of its insurance risk through acquiring a proportional reinsurance. The investment and reinsurance decisions are made so as to maximize an expected power utility on terminal wealth. An explicit solution to the problem is derived for each of the two well-known stochastic interest rate models, namely, the Ho–Lee model and the Vasicek model, using standard techniques in stochastic optimal control theory. Numerical examples are presented to illustrate the impacts of the two different stochastic interest rate modeling assumptions on optimal decision making of the insurer.

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Ballotta, Laura, and Ioannis Kyriakou. "Convertible bond valuation in a jump diffusion setting with stochastic interest rates." Quantitative Finance 15, no. 1 (August 4, 2014): 115–29. http://dx.doi.org/10.1080/14697688.2014.935464.

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Vetzal, Kenneth R. "Stochastic volatility, movements in short term interest rates, and bond option values." Journal of Banking & Finance 21, no. 2 (February 1997): 169–96. http://dx.doi.org/10.1016/s0378-4266(96)00035-0.

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Shen, Yang, and Tak Kuen Siu. "Longevity bond pricing under stochastic interest rate and mortality with regime-switching." Insurance: Mathematics and Economics 52, no. 1 (January 2013): 114–23. http://dx.doi.org/10.1016/j.insmatheco.2012.11.006.

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Acharya, Viral V., and Jennifer N. Carpenter. "Corporate Bond Valuation and Hedging with Stochastic Interest Rates and Endogenous Bankruptcy." Review of Financial Studies 15, no. 5 (October 2002): 1355–83. http://dx.doi.org/10.1093/rfs/15.5.1355.

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Anggraini, Dian, and Yasir Wijaya. "Obligasi Bencana Alam Dengan Suku Bunga Stokastik Dan Pendekatan Campuran." Al-Jabar : Jurnal Pendidikan Matematika 7, no. 1 (June 16, 2016): 49–62. http://dx.doi.org/10.24042/ajpm.v7i1.130.

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This study contains the group claims model as discussed by (Lee, 2007) for the pricing of natural disaster bonds. This research was conducted with several stages. First make the formula of bond price with stochastic interest rate and disaster event following non homogeneous poisson process. It further estimates the parameters of disaster loss data from the Insurance Information Institute (III) from 1989 to 2012 and interest rates from the Federal Reserve Bank. Because the determination of aggregate distribution is difficult to be exact, numerical calculation is done by mixed approach method (Gamma and Inverse Gaussian) to determine the solution of natural disaster bond price. Finally, shows how the impact of financial risk and disaster risk on the price of natural disaster bonds.

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Zhang, Chubing, and Ximing Rong. "Optimal Investment Strategies for DC Pension with Stochastic Salary under the Affine Interest Rate Model." Discrete Dynamics in Nature and Society 2013 (2013): 1–11. http://dx.doi.org/10.1155/2013/297875.

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We study the optimal investment strategies of DC pension, with the stochastic interest rate (including the CIR model and the Vasicek model) and stochastic salary. In our model, the plan member is allowed to invest in a risk-free asset, a zero-coupon bond, and a single risky asset. By applying the Hamilton-Jacobi-Bellman equation, Legendre transform, and dual theory, we find the explicit solutions for the CRRA and CARA utility functions, respectively.

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Park, Sang-Hyeon, Min-Ku Lee, and Jeong-Hoon Kim. "The Term Structure of Interest Rates Under Heath–Jarrow–Morton Models with Fast Mean-Reverting Stochastic Volatility." Fluctuation and Noise Letters 15, no. 02 (June 2016): 1650014. http://dx.doi.org/10.1142/s0219477516500140.

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This paper is a study of the term structure of interest rates based on the Heath–Jarrow–Morton (HJM) models with Hull–White volatility function. Under fast mean-reverting stochastic volatility, we obtain an analytic formula for an approximate bond price with estimated error using a Markovian transform method combined with a singular perturbation method. The stochastic volatility correction effect against time-to-maturity is revealed so that it can capture more of the complexities of the interest rate term structure.

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CHIARELLA, CARL, SAMUEL CHEGE MAINA, and CHRISTINA NIKITOPOULOS SKLIBOSIOS. "CREDIT DERIVATIVES PRICING WITH STOCHASTIC VOLATILITY MODELS." International Journal of Theoretical and Applied Finance 16, no. 04 (June 2013): 1350019. http://dx.doi.org/10.1142/s0219024913500192.

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This paper proposes a model for pricing credit derivatives in a defaultable HJM framework. The model features hump-shaped, level dependent, and unspanned stochastic volatility, and accommodates a correlation structure between the stochastic volatility, the default-free interest rates, and the credit spreads. The model is finite-dimensional, and leads (a) to exponentially affine default-free and defaultable bond prices, and (b) to an approximation for pricing credit default swaps and swaptions in terms of defaultable bond prices with varying maturities. A numerical study demonstrates that the model captures stylized various features of credit default swaps and swaptions.

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RUSSO, EMILIO, and ALESSANDRO STAINO. "A LATTICE-BASED MODEL FOR EVALUATING BONDS AND INTEREST-SENSITIVE CLAIMS UNDER STOCHASTIC VOLATILITY." International Journal of Theoretical and Applied Finance 21, no. 04 (June 2018): 1850023. http://dx.doi.org/10.1142/s0219024918500231.

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We propose a flexible lattice model for pricing bonds and interest-sensitive claims under stochastic volatility, which is able to accommodate different dynamics specifications, and permits correlation between the interest rate and volatility diffusion. The model is based on the forward shooting grid method where the volatility process, as the primary state variable, is discretized by means of a recombining binomial tree. Then, the interest rate, as the auxiliary state variable, is discretized by attaching a subset of representative realizations to each node of the volatility lattice to cover the range of possible interest rates at each time slice. Finally, we develop a bivariate lattice presenting four branches for each node, where the joint probabilities for the possible jumps embed the correlation. Since the model works on representative interest rate values, a linear interpolation technique is used when solving backward through the lattice to compute the bond present value or the interest-sensitive claim price.

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Paseka, Alex, and Aerambamoorthy Thavaneswaran. "Bond valuation for generalized Langevin processes with integrated Lévy noise." Journal of Risk Finance 18, no. 5 (November 20, 2017): 541–63. http://dx.doi.org/10.1108/jrf-09-2016-0125.

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Purpose Recently, Stein et al. (2016) studied theoretical properties and parameter estimation of continuous time processes derived as solutions of a generalized Langevin equation (GLE). In this paper, the authors extend the model to a wider class of memory kernels and then propose a bond and bond option valuation model based on the extension of the generalized Langevin process of Stein et al. (2016). Design/methodology/approach Bond and bond option pricing based on the proposed interest rate models presents new difficulties as the standard partial differential equation method of stochastic calculus for bond pricing cannot be used directly. The authors obtain bond and bond option prices by finding the closed form expression of the conditional characteristic function of the integrated short rate process driven by a general Lévy noise. Findings The authors obtain zero-coupon default-free bond and bond option prices for short rate models driven by a variety of Lévy processes, which include Vasicek model and the short rate model obtained by solving a second-order Langevin stochastic differential equation (SDE) as special cases. Originality/value Bond and bond option pricing plays an important role in capital markets and risk management. In this paper, the authors derive closed form expressions for bond and bond option prices for a wider class of interest rate models including second-order SDE models. Closed form expressions may be especially instrumental in facilitating parameter estimation in these models.

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Zhu, Jiaqi, and Shenghong Li. "Time-Consistent Investment and Reinsurance Strategies for Mean-Variance Insurers under Stochastic Interest Rate and Stochastic Volatility." Mathematics 8, no. 12 (December 7, 2020): 2183. http://dx.doi.org/10.3390/math8122183.

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This paper studies the time-consistent optimal investment and reinsurance problem for mean-variance insurers when considering both stochastic interest rate and stochastic volatility in the financial market. The insurers are allowed to transfer insurance risk by proportional reinsurance or acquiring new business, and the jump-diffusion process models the surplus process. The financial market consists of a risk-free asset, a bond, and a stock modelled by Heston’s stochastic volatility model. Interest rate in the market is modelled by the Vasicek model. By using extended dynamic programming approach, we explicitly derive equilibrium reinsurance-investment strategies and value functions. In addition, we provide and prove a verification theorem and then prove the solution we get satisfies it. Moreover, sensitive analysis is given to show the impact of several model parameters on equilibrium strategy and the efficient frontier.

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Stehlíková, Beáta. "On the bond pricing partial differential equation in a convergence model of interest rates with stochastic correlation." Mathematica Slovaca 70, no. 4 (August 26, 2020): 995–1002. http://dx.doi.org/10.1515/ms-2017-0408.

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AbstractConvergence models of interest rates are used to model a situation, where a country is going to enter a monetary union and its short rate is affected by the short rate in the monetary union. In addition, Wiener processes which model random shocks in the behaviour of the short rates can be correlated. In this paper we consider a stochastic correlation in a selected convergence model. A stochastic correlation has been already studied in different contexts in financial mathematics, therefore we distinguish differences which come from modelling interest rates by a convergence model. We provide meaningful properties which a correlation model should satisfy and afterwards we study the problem of solving the partial differential equation for the bond prices. We find its solution in a separable form, where the term coming from the stochastic correlation is given in its series expansion for a high value of the correlation.

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Sorwar, Ghulam, and Sharif Mozumder. "Implied Bond and Derivative Prices Based on Non-Linear Stochastic Interest Rate Models." Applied Mathematics 01, no. 01 (2010): 37–43. http://dx.doi.org/10.4236/am.2010.11006.

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Wang, Xiaoyu, Dejun Xie, Jingjing Jiang, Xiaoxia Wu, and Jia He. "Value-at-Risk estimation with stochastic interest rate models for option-bond portfolios." Finance Research Letters 21 (May 2017): 10–20. http://dx.doi.org/10.1016/j.frl.2016.11.013.

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Di Girolamo, Francesca Erica, Francesca Campolongo, Jan De Spiegeleer, and Wim Schoutens. "Contingent conversion convertible bond: New avenue to raise bank capital." International Journal of Financial Engineering 04, no. 01 (March 2017): 1750001. http://dx.doi.org/10.1142/s2424786317500013.

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This paper provides an in-depth analysis of the structuring and the pricing of an innovative financial market product. This instrument is called a contingent conversion convertible bond or “CoCoCo”. This hybrid bond is itself a combination of two other hybrid instruments: a contingent convertible (“CoCo”) and a convertible bond. This combination introduces more complexity in the structure but it also allows investors to profit from strong share price performances. This upside potential is added on top of the normal contingent convertible mechanics of CoCos, which expose the investors to mainly downside risk. First, we explain how the features of the contingent convertible bonds on one side and the features of the standard convertible bonds on the other side are combined. Thereafter, we propose a pricing approach which moves away from the standard Black[Formula: see text]Scholes setting. The CoCoCos are evaluated using the Heston process to which a Hull-White interest rate process has been added. We demonstrate the importance of using a stochastic interest rate when modeling this instrument. Finally we quantify the loss absorbing capacity of this instrument.

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Zhang, Shuhua, and Zhuo Yang. "The Valuation of Carbon Bonds Linked with Carbon Price." Computational Methods in Applied Mathematics 16, no. 2 (April 1, 2016): 345–59. http://dx.doi.org/10.1515/cmam-2016-0001.

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AbstractThe carbon bonds issued by countries or enterprises can solve the problem of funds in low carbon economy growth. Now most of carbon bonds pay fixed interest rates, and a few pay floating rates. The diversity of carbon bonds can attract more investors to participate green energy projects. The London Accord project group proposed the index linked carbon bonds in the World Band Government Borrowers' Forum in May 2009, and pointed out that the interest paid regularly may be linked to carbon price, governments' carbon emission targets, in-country fossil fuel prices or tariff feed-in prices. In this paper, the interests are considered to be linked with carbon prices in the condition of stochastic risk-free interest rate, and a partial differential equation is established for carbon bond interests. Also, a fitted finite volume method is employed to solve the resulting partial differential equation numerically, and on the basis of the valuation for zero-coupon bonds, the price of carbon bonds is obtained. Finally, some data are utilized for the calibration of the parameters in the established pricing models, and some numerical examples are presented and the effects of parameters on solutions are also demonstrated, which can provide references for the issuers of carbon bonds.

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Kim, Sang Su. "A Priching Model for Inflation-indexed Bonds." Journal of Derivatives and Quantitative Studies 19, no. 2 (May 31, 2011): 175–206. http://dx.doi.org/10.1108/jdqs-02-2011-b0003.

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This paper derives the theoretical price of nominal bonds and inflation-indexed bonds through extracting the factors, which are assumed that their stochastic property follows the standard O-U process, in the term structure of nominal interest rates and yields of inflation-indexed bonds by the Principal Component Analysis (PCA). In particular, through reflecting the complex structure of inflation-indexed bonds by accurately applying theoretical price, it brought differentiation from other literatures, and applied this pricing model to Japanese Government Inflation-indexed Bond (JGB) data. The empirical results of above model show that explanation of time series and cross section of Janpan's real and nominal interest rates were outstanding and was found that Fisher hypothesis was rejected in further

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Liang, Jin, Xinfu Chen, Yuan Wu, and Hong-Ming Yin. "On a Corporate Bond Pricing Model with Credit Rating Migration Risksand Stochastic Interest Rate." Quantitative Finance and Economics 1, no. 3 (2017): 300–319. http://dx.doi.org/10.3934/qfe.2017.3.300.

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Hautsch, Nikolaus, and Yangguoyi Ou. "Analyzing interest rate risk: Stochastic volatility in the term structure of government bond yields." Journal of Banking & Finance 36, no. 11 (November 2012): 2988–3007. http://dx.doi.org/10.1016/j.jbankfin.2012.06.020.

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Song, Lina, and Kele Li. "Pricing Option with Stochastic Interest Rates and Transaction Costs in Fractional Brownian Markets." Discrete Dynamics in Nature and Society 2018 (August 1, 2018): 1–8. http://dx.doi.org/10.1155/2018/7056734.

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This work deals with European option pricing problem in fractional Brownian markets. Two factors, stochastic interest rates and transaction costs, are taken into account. By the means of the hedging and replicating techniques, the new equations satisfied by zero-coupon bond and the nonlinear equation obeyed by European option are established in succession. Pricing formulas are derived by the variable substitution and the classical solution of the heat conduction equation. By the mathematical software and the parameter estimation methods, the results are reported and compared with the data from the financial market.

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Mordecki, Ernesto, and Andrés Sosa Rodríguez. "Country risk for emerging economies: a dynamical index proposal with a case study." Brazilian Review of Econometrics 40, no. 2 (April 30, 2021): 285–302. http://dx.doi.org/10.12660/bre.v40n22020.80944.

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We introduce a dynamical country risk index for emerging economies. The proposal is based on the intensity approach of credit risk, i.e. the default is the first jump of a point process with stochastic intensity. Two different models are used to estimate the yield spread. They differ in the relationship between the default-free instantaneous interest rate process and the intensity process. The dynamics of the interest rates is modeled through a multidimensional affine model, and the Kalman filter with an Expectation-Maximization algorithm is used to calibrate it. The USD interest rates constitute part of the input of the model, while prices of relevant domestic bonds in the emerging market complete the input. For an application, we select the Uruguayan bond market as the emerging economy.

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Feldman, K. S., B. Bergman, A. J. G. Cairns, G. B. Chaplin, G. D. Gwilt, P. R. Lockyer, and F. B. Turley. "Report of the Fixed-Interest Working Group." British Actuarial Journal 4, no. 2 (June 1, 1998): 213–63. http://dx.doi.org/10.1017/s1357321700000039.

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ABSTRACTActuarial models of the market in conventional British Government Stocks, also known as the Gilt-Edged market, are reviewed and contrasted with the methods which have been developed, during the last twenty years, by financial economists.Following the Treasury's announcement in May 1995 (regarding the taxation of institutional bond holdings), the so-called ‘coupon effect’ has largely disappeared and gilt prices can now be fitted very closely by using the same simple discounting functions for both income and capital flows. A new model suitable for the calculation of yield indices is proposed and is contrasted with the model currently underlying the FTSE Actuaries Government Securities (FTSEAGS) Yield Indices. A number of new possible applications of the reformulated yield indices, such as forward pricing, asset/liability matching and stochastic simulation, are discussed. An analogous model for index-linked gilts leads to applications involving the forward market in the retail prices index.A survey of professional users of the FTSEAGS Indices is described, and a revised presentation for the published yield indices is suggested. A summary of current statutory references to the indices is presented.

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FUTAMI, HIDENORI. "REGIME SWITCHING TERM STRUCTURE MODEL UNDER PARTIAL INFORMATION." International Journal of Theoretical and Applied Finance 14, no. 02 (March 2011): 265–94. http://dx.doi.org/10.1142/s0219024911006358.

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In this study, we attempt to calculate the term structure of the interest rate under partial information using a model in which the mean reversion level of the short rate changes in accordance with a regime shift in the economy. Under partial information, an investor observes the history of only the short rate and not a regime shift; hence, calculating the term structure of the interest rate is reduced to the problem of filtering the current regime from observable short rates. Therefore, we calculate it using the filtering theory that estimates a stochastic process from noisy observations, and investigate the effects of the regime shift under partial information on the market price of risk and the volatility of a bond price compared with those under full information, in which the regime is assumed to be observable. We find that, under partial information, the regime-shift risk converts into the diffusion risk. As a result, we find that both the market price of diffusion risk and the volatility of a bond price under partial information become stochastic, even though these under full information are constant.

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Melichercik, Igor, and Daniel Sevcovic. "Dynamic stochastic accumulation model with application to pension savings management." Yugoslav Journal of Operations Research 20, no. 1 (2010): 1–24. http://dx.doi.org/10.2298/yjor1001001m.

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We propose a dynamic stochastic accumulation model for determining optimal decision between stock and bond investments during accumulation of pension savings. Stock prices are assumed to be driven by the geometric Brownian motion. Interest rates are modeled by means of the Cox-Ingersoll-Ross model. The optimal decision as a solution to the corresponding dynamic stochastic program is a function of the duration of saving, the level of savings and the short rate. Qualitative and quantitative properties of the optimal solution are analyzed. The model is tested on the funded pillar of the Slovak pension system. The results are calculated for various risk preferences of a saver.

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Vayanos, Dimitri, and Jean-Luc Vila. "A Preferred‐Habitat Model of the Term Structure of Interest Rates." Econometrica 89, no. 1 (2021): 77–112. http://dx.doi.org/10.3982/ecta17440.

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We model the term structure of interest rates that results from the interaction between investors with preferences for specific maturities and risk‐averse arbitrageurs. Shocks to the short rate are transmitted to long rates through arbitrageurs' carry trades. Arbitrageurs earn rents from transmitting the shocks through bond risk premia that relate positively to the slope of the term structure. When the short rate is the only risk factor, changes in investor demand have the same relative effect on interest rates across maturities regardless of the maturities where they originate. When investor demand is also stochastic, demand effects become more localized. A calibration indicates that long rates underreact to forward‐guidance announcements about short rates. Large‐scale asset purchases can be more effective in moving long rates, especially if they are concentrated at long maturities.

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SIU, TAK KUEN, and ROBERT J. ELLIOTT. "HEDGING OPTIONS IN A DOUBLY MARKOV-MODULATED FINANCIAL MARKET VIA STOCHASTIC FLOWS." International Journal of Theoretical and Applied Finance 22, no. 08 (December 2019): 1950047. http://dx.doi.org/10.1142/s021902491950047x.

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The hedging of a European-style contingent claim is studied in a continuous-time doubly Markov-modulated financial market, where the interest rate of a bond is modulated by an observable, continuous-time, finite-state, Markov chain and the appreciation rate of a risky share is modulated by a continuous-time, finite-state, hidden Markov chain. The first chain describes the evolution of credit ratings of the bond over time while the second chain models the evolution of the hidden state of an underlying economy over time. Stochastic flows of diffeomorphisms are used to derive some hedge quantities, or Greeks, for the claim. A mixed filter-based and regime-switching Black–Scholes partial differential equation is obtained governing the price of the claim. It will be shown that the delta hedge ratio process obtained from stochastic flows is a risk-minimizing, admissible mean-self-financing portfolio process. Both the first-order and second-order Greeks will be considered.

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Jaffal, H., Y. Rakotondratsimba, and A. Yassine. "Sensitivities under G2++ model of the yield curve." International Journal of Financial Engineering 04, no. 01 (March 2017): 1750008. http://dx.doi.org/10.1142/s2424786317500086.

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The two-additive-factor Gaussian model G2[Formula: see text] is a famous stochastic model for the instantaneous short rate. It has functional qualities required in various practical purposes, as in Asset Liability Management and in Trading of interest rate derivatives. Though closed formulas for the prices of various main interest-rate instruments are known and used under the G2[Formula: see text] model, it seems that references for the corresponding sensitivities are not clearly presented over the financial literature. To fill this gap is one of our purposes in the present work. We derive here analytic expressions for the sensitivities of zero-coupon bond, coupon-bearing bonds, portfolio of coupon bearing bonds. The sensitivities under consideration here are those with respect to the shocks linked to the unobservable two-uncertainty shock risk/opportunity factors underlying the G2[Formula: see text] model. As a such, the hedging of a position sensitive to the interest rate by means of a portfolio (in accordance with the market participants practice) becomes easily transparent as just resulting from the balance between the various involved sensitivities.

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Huang, Fei, Adam Butt, and Kin-Yip Ho. "Stochastic economic models for actuarial use: an example from China." Annals of Actuarial Science 8, no. 2 (May 15, 2014): 374–403. http://dx.doi.org/10.1017/s1748499514000104.

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AbstractIn this paper, the first study of stochastic economic modelling with Chinese data is conducted for actuarial use. Univariate models, vector autoregression and two cascade systems (equity-driving cascade system and price-inflation-driving cascade system) are described and compared. We focus on six major economic assumptions for modelling purposes, which are price inflation rate, wage inflation rate, long-term interest rate, short-term interest rate, equity total return and bond total return. Granger causality tests are used to identify the driving force of a cascade system. Robust standard errors are estimated for each model. Diagnostic checking of residuals, goodness-of-fit measures and out-of-sample validations are applied for model selection. By comparing different models for each variable, we find that the equity-driving cascade system is the best structure for actuarial use in China. The forecasts of the variables could be applied as economic inputs to stochastic projection models of insurance portfolios or pension funds for short-term asset and liability cash flow forecasting.

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AKAHORI, JIRÔ, and ANDREA MACRINA. "HEAT KERNEL INTEREST RATE MODELS WITH TIME-INHOMOGENEOUS MARKOV PROCESSES." International Journal of Theoretical and Applied Finance 15, no. 01 (February 2012): 1250007. http://dx.doi.org/10.1142/s0219024911006553.

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We consider a heat kernel approach for the development of stochastic pricing kernels. The kernels are constructed by positive propagators, which are driven by time-inhomogeneous Markov processes. We multiply such a propagator with a positive, time-dependent and decreasing weight function, and integrate the product over time. The result is a so-called weighted heat kernel that by construction is a supermartingale with respect to the filtration generated by the time-inhomogeneous Markov processes. As an application, we show how this framework naturally fits the information-based asset pricing framework where time-inhomogeneous Markov processes are utilized to model partial information about random economic factors. We present examples of pricing kernel models which lead to analytical formulae for bond prices along with explicit expressions for the associated interest rate and market price of risk. Furthermore, we also address the pricing of fixed-income derivatives within this framework.

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Izgi, Burhaneddin, and Ahmet Bakkaloglu. "Fundamental solution of bond pricing in the Ho-Lee stochastic interest rate model under the invariant criteria." New Trends in Mathematical Science 1, no. 5 (March 19, 2017): 196–203. http://dx.doi.org/10.20852/ntmsci.2017.138.

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CHU, CHI CHIU, and YUE KUEN KWOK. "VALUATION OF GUARANTEED ANNUITY OPTIONS IN AFFINE TERM STRUCTURE MODELS." International Journal of Theoretical and Applied Finance 10, no. 02 (March 2007): 363–87. http://dx.doi.org/10.1142/s0219024907004160.

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We propose three analytic approximation methods for numerical valuation of the guaranteed annuity options in deferred annuity pension policies. The approximation methods include the stochastic duration approach, Edgeworth expansion, and analytic approximation in affine diffusions. The payoff structure in the annuity policies is similar to a quanto call option written on a coupon-bearing bond. To circumvent the limitations of the one-factor interest rate model, we model the interest rate dynamics by a two-factor affine interest rate term structure model. The numerical accuracy and the computational efficiency of these approximation methods are analyzed. We also investigate the value sensitivity of the guaranteed annuity option with respect to different parameters in the pricing model.

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Hao, Ruili, and Zhongxing Ye. "The Intensity Model for Pricing Credit Securities with Jump Diffusion and Counterparty Risk." Mathematical Problems in Engineering 2011 (2011): 1–16. http://dx.doi.org/10.1155/2011/412565.

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We present an intensity-based model with counterparty risk. We assume the default intensity of firm depends on the stochastic interest rate driven by the jump-diffusion process and the default states of counterparty firms. Furthermore, we make use of the techniques in Park (2008) to compute the conditional distribution of default times and derive the explicit prices of bond and CDS. These are extensions of the models in Jarrow and Yu (2001).

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Sukono, Riza Andrian Ibrahim, Moch Panji Agung Saputra, Yuyun Hidayat, Hafizan Juahir, Igif Gimin Prihanto, and Nurfadhlina Binti Abdul Halim. "Modeling Multiple-Event Catastrophe Bond Prices Involving the Trigger Event Correlation, Interest, and Inflation Rates." Mathematics 10, no. 24 (December 10, 2022): 4685. http://dx.doi.org/10.3390/math10244685.

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The issuance of multiple-event catastrophe bonds (MECBs) has the potential to increase in the next few years. This is due to the increasing trend in the frequency of global catastrophes, which makes single-event catastrophe bonds (SECBs) less relevant. However, there are obstacles to issuing MECBs since the pricing framework is still little studied. Therefore, this study aims to develop such a new pricing framework. The model uniquely involves three new variables: the trigger event correlation, interest, and inflation rates. The trigger event correlation rate was accommodated by the involvement of the copula while the interest and inflation rates were simultaneously considered using an integrated autoregressive vector stochastic model. After the model was obtained, the model was simulated on storm catastrophe data in the United States. Finally, the effect of the three variables on MECB prices was also analyzed. The analysis results show that the three variables make MECB prices more fairly than other models. This research is expected to guide special purpose vehicles to set fairer MECB prices and can also be used as a reference for investors in choosing MECBs based on the rates of trigger event correlation and the real interest they can expect.

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Tai, Chu-Sheng. "On the Pricing of Credit Risk in Eurocurrency Market." Journal of Finance Issues 6, no. 2 (December 31, 2008): 54–63. http://dx.doi.org/10.58886/jfi.v6i2.2410.

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Most of previous studies on credit risk have been focused on corporate bond markets. This paper focuses on whether the credit risk is priced in the Eurocurrency market. The empirical test relies on a multivariate GARCH (1,1)-in-mean version of the ICAPM model to describe the joint stochastic process of three state variables: world market risk, interest rate risk, and credit risk, during the period January 1986 to December 2002. The paper documents a negative, significant, and time-varying systematic credit risk premium.

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Siregar, Muhammad Akhir, Mustafid Mustafid, and Rukun Santoso. "PENGUKURAN PROBABILITAS KEBANGKRUTAN OBLIGASI KORPORASI DENGAN SUKU BUNGA COX INGERSOLL ROSS MODEL MERTON (Studi Kasus Obligasi PT Indosat, Tbk)." Jurnal Gaussian 7, no. 2 (May 30, 2018): 175–86. http://dx.doi.org/10.14710/j.gauss.v7i2.26652.

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Nowadays bonds become one of the many securities products that are being prefered by investors. Observing the level of the company's rating which good enough or in the criteria of investment grade can’t be a handle of investors. Investing in long-term period investors should understand the risks to be faced, one of investment credit risk on bonds is default risk, this risk is related to the possibility that the issuer fails to fulfill its obligations to the investor in due date. The measurement of the probability of default failure by the structural method approach introduced first by Black-Scholes (1973) than developed by Merton (1974). In Bankruptcy model, merton’s model assumed the company get default (bankrupt) when the company can’t pay the coupon or face value in the due date. Interest rates on the Merton model assumed to be constant values replaced by Cox Ingersoll Ross (CIR) rates. The CIR rate is the fluctuating interest rate in each period and the change is a stochastic process. The empirical study was conducted on PT Indosat, Tbk's bonds issued in 2017 with a face value of 511 Billion in payment of obligations by the issuer for 10 years. Based on simulation results done with R software obtained probability of default value equal to 7,416132E-215 Indicates that PT Indosat Tbk is deemed to be able to fulfill its obligation payment at the end of the bond maturity in 2027. Keywords: Bond, CIR Rate, Merton Model, Ekuity, Probability of default

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HORSKY, ROMAN, and TILMAN SAYER. "JOINING THE HESTON AND A THREE-FACTOR SHORT RATE MODEL: A CLOSED-FORM APPROACH." International Journal of Theoretical and Applied Finance 18, no. 08 (December 2015): 1550056. http://dx.doi.org/10.1142/s0219024915500569.

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In this paper, we present an innovative hybrid model for the valuation of equity options. Our approach includes stochastic volatility according to Heston (1993) [Review of Financial Studies 6 (2), 327–343] and features a stochastic interest rate that follows a three-factor short rate model based on Hull and White (1994) [Journal of Derivatives 2 (2), 37–48]. Our model is of affine structure, allows for correlations between the stock, the short rate and the volatility processes and can be fitted perfectly to the initial term structure. We determine the zero bond price formula and derive the analytic solution for European type options in terms of characteristic functions needed for fast calibration. We highlight the flexibility of our approach, by comparing the price and implied volatility surfaces of our model with the Heston model, where we in particular focus on the correlation structure. Our approach forms a comprehensive market model with an intuitive correlation structure that connects both the equity and interest market to the market volatility.

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Journal articles on the topic 'STOCHASTIC INTEREST BOND'

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