scholarly journals Bond portfolio's duration and investment term-structure management problem

2006 ◽  
Vol 2006 ◽  
pp. 1-19
Author(s):  
Daobai Liu
Keyword(s):  
Interest Rate ◽  
Term Structure ◽  
Interest Rate Risk ◽  
Management Problem ◽  
Short Term ◽  
Bond Portfolio ◽  
Stochastic Interest ◽  
Bond Portfolios ◽  
Interest Rate Model ◽  
The Interest Rate

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.

scholarly journals Total Return Swap Valuation with Counterparty Risk and Interest Rate Risk

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Anjiao Wang ◽  
Zhongxing Ye
Keyword(s):  
Interest Rate ◽  
Closed Form ◽  
Interest Rate Risk ◽  
Counterparty Risk ◽  
Rate Model ◽  
Change Of Measure ◽  
Market Interest Rate ◽  
Rate Risk ◽  
Interest Rate Model ◽  
The Interest Rate

We study the pricing of total return swap (TRS) under the contagion models with counterparty risk and the interest rate risk. We assume that interest rate follows Heath-Jarrow-Morton (HJM) forward interest rate model and obtain the Libor market interest rate. The cases where default is related to the interest rate and independent of interest rate are considered. Using the methods of change of measure and the “total hazard construction,” the joint default probabilities are obtained. Furthermore, we obtain the closed-form formulas of TRS under different contagion models, respectively.

A Bayesian Pricing of Longevity Derivatives with Interest Rate Risks

2017 ◽  
Vol 0 (0) ◽  
Author(s):  
Atsuyuki Kogure ◽  
Takahiro Fushimi
Keyword(s):  
Interest Rate ◽  
Interest Rates ◽  
Mortality Risk ◽  
Interest Rate Risk ◽  
Stochastic Interest Rates ◽  
Rate Risk ◽  
Stochastic Interest ◽  
The Interest Rate ◽  
Longevity Bonds ◽  
Carter Model

AbstractMortality-linked securities such as longevity bonds or longevity swaps usually depend on not only mortality risk but also interest rate risk. However, in the existing pricing methodologies, it is often the case that only the mortality risk is modeled to change in a stochastic manner and the interest rate is kept fixed at a pre-specified level. In order to develop large and liquid longevity markets, it is essential to incorporate the interest rate risk into pricing mortality-linked securities. In this paper we tackle the issue by considering the pricing of longevity derivatives under stochastic interest rates following the CIR model. As for the mortality modeling, we use a two-factor extension of the Lee-Carter model by noting the recent studies which point out the inconsistencies of the original Lee-Carter model with observed mortality rates due to its single factor structure. To address the issue of parameter uncertainty, we propose using a Bayesian methodology both to estimate the models and to price longevity derivatives in line with (Kogure, A., and Y. Kurachi. 2010. “A Bayesian Approach to Pricing Longevity Risk Based on Risk Neutral Predictive Distributions.”

scholarly journals Valuing strategic investments under stochastic interest rates: A real option approach

2019 ◽  
Vol 16 (3) ◽  
pp. 89-97
Author(s):  
Luca Vincenzo Ballestra ◽  
Graziella Pacelli ◽  
Davide Radi
Keyword(s):  
Interest Rate ◽  
Option Pricing ◽  
Interest Rates ◽  
Real Option ◽  
Interest Rate Risk ◽  
Stochastic Interest Rates ◽  
Investment Projects ◽  
Rate Risk ◽  
Stochastic Interest ◽  
The Interest Rate

One of the most challenging issues in management is the valuation of strategic investments. In particular, when undertaking projects such as an expansion or the launch of a new brand, or an investment in R&D and intellectual capital, which are characterized by a long-term horizon, a firm has also to face the risk due to the interest rate. In this work, we propose to value investments subject to interest rate risk using a real options approach (Schulmerich, 2010). This task requires the typical technicalities of option pricing, which often rely on complex and time-consuming techniques to value investment projects. For instance, Schulmerich (2010) is, to the best of our knowledge, the first work where the interest rate risk is considered for real option analysis. Nevertheless, the valuation of investment projects is done by employing binomial trees, which are computationally very expensive. In the current paper, a different modeling framework (in continuous-time) for real option pricing is proposed which allows one to account for interest rate risk and, at the same time, to reduce computational complexity. In particular, the net present value of the cash inflows is specified by a geometric Brownian motion and the interest rate is modeled by using a process of Vasicek type, which is calibrated to real market data. Such an approach yields an explicit formula for valuing various kinds of investment strategies, such as the option to defer and the option to expand. Therefore, the one proposed is the first model in the field of real options that accounts for the interest rate risk and, at the same time, offers an easy to implement formula which makes the model itself very suitable for practitioners. An empirical analysis is presented which illustrates the proposed approach from the practical point-of-view and highlights the impact of stochastic interest rates in investment valuation.

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

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Enlin Tang ◽  
Song Xu
Keyword(s):  
Interest Rate ◽  
Commercial Banks ◽  
Jump Diffusion ◽  
Interest Rate Risk ◽  
Rate Model ◽  
Interest Rate Marketization ◽  
Interest Rate Model ◽  
Embedded Options ◽  
The Interest Rate ◽  
Interest Margin

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

Convexity Analysis of Option Embedded Bonds

2004 ◽  
Vol 12 (1) ◽  
pp. 23-49
Author(s):  
Seung Hyeon O
Keyword(s):  
Interest Rate ◽  
Interest Rates ◽  
Term Structure ◽  
Factor Model ◽  
Real Term ◽  
Interest Rate Risk ◽  
Vector Model ◽  
Convexity Property ◽  
Rate Risk ◽  
Bond Portfolio

Interest rate risk hedge strategies usually assume that term structure of interest rates in moving under a specific way. If a real term structure is moving differently from the assumed term structure movement, the interest rate risk hedge strategies assuming the special term structure movement may incur unexpected large loss for a bond portfolio manager. Hence an interest rate risk hedge strategy which could be effective under various types of term structure movements has been strongly needed by bond portfolio managers. Duration vector strategies have been developed to satisfy this practical need. To allow various types of term structure movements, duration vector strategies assume multi-factor models for the term structure movement. When a duration vector strategy is considered as a generalization of a duration strategy which is a single factor model for the term structure movement, there will be a generalized concept which measures convexity of a bond under the duration vector model. This study identifies the convexity property of an option embedded bond portfolio under ‘key rate duration model‘ which is a kind of duration vector model suggested by Ho (1992).

scholarly journals Risk Management for Bonds with Embedded Options

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 790
Author(s):  
Antonio Díaz ◽  
Marta Tolentino
Keyword(s):  
Risk Management ◽  
Interest Rate ◽  
Interest Rates ◽  
Interest Rate Risk ◽  
Interest Rate Models ◽  
Management Measures ◽  
Interest Rate Risk Management ◽  
Embedded Options ◽  
The Interest Rate ◽  
Interest Rate Change

This paper examines the behavior of the interest rate risk management measures for bonds with embedded options and studies factors it depends on. The contingent option exercise implies that both the pricing and the risk management of bonds requires modelling future interest rates. We use the Ho and Lee (HL) and Black, Derman, and Toy (BDT) consistent interest rate models. In addition, specific interest rate measures that consider the contingent cash-flow structure of these coupon-bearing bonds must be computed. In our empirical analysis, we obtained evidence that effective duration and effective convexity depend primarily on the level of the forward interest rate and volatility. In addition, the higher the interest rate change and the lower the volatility, the greater the differences in pricing of these bonds when using the HL or BDT models.

scholarly journals CANDIDE et la monnaie

2009 ◽  
Vol 52 (1) ◽  
pp. 75-103
Author(s):  
Jean-Pierre Aubry ◽  
Pierre Duguay
Keyword(s):  
Interest Rate ◽  
Interest Rates ◽  
Term Structure ◽  
Structural Equations ◽  
Reduced Form ◽  
Real Sector ◽  
Short Term ◽  
The Real ◽  
Structure Equations

Abstract In this paper we deal with the financial sector of CANDIDE 1.1. We are concerned with the determination of the short-term interest rate, the term structure equations, and the channels through which monetary policy influences the real sector. The short-term rate is determined by a straightforward application of Keynesian liquidity preference theory. A serious problem arises from the directly estimated reduced form equation, which implies that the demand for high powered money, but not the demand for actual deposits, is a stable function of income and interest rates. The structural equations imply the opposite. In the term structure equations, allowance is made for the smaller variance of the long-term rates, but insufficient explanation is given for their sharper upward trend. This leads to an overstatement of the significance of the U.S. long-term rate that must perform the explanatory role. Moreover a strong structural hierarchy, by which the long Canada rate wags the industrial rate, is imposed without prior testing. In CANDIDE two channels of monetary influence are recognized: the costs of capital and the availability of credit. They affect the business fixed investment and housing sectors. The potential of the personal consumption sector is not recognized, the wealth and real balance effects are bypassed, the credit availability proxy is incorrect, the interest rate used in the real sector is nominal rather than real, and the specification of the housing sector is dubious.

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