Power law bond price and yield approximation

PurposeThis paper determines a simple transformation that nearly linearizes the bond price formula. The transformed price can be used to derive a highly accurate approximation of the change in a bond price resulting from a change in interest rates.Design/methodology/approachA logarithmic transformation exactly linearizes the price function for a zero coupon bond and a reciprocal transformation exactly linearizes the price function for a perpetuity. A power law transformation combines aspects of both types of transformations and provides a superior approximation of the bond price sensitivity for both short-term and long-term bonds.FindingsIt is demonstrated that the new formula, based on power-law transformation, is a much better approximation than either the traditional duration-convexity approximation and the more recently developed approximations based on logarithmic transformation of the price function.Originality/valueThe new formula will be used by risk managers to perform stress-testing on bond portfolios. The new formula can easily be inverted, making it possible to relate the distribution of prices (which are observable in the market) to the distribution of yields (which are numerical solutions that are not directly observable).

US financial services will help mainstream cryptos

Significance Yet snowballing interest outpaces crypto's use in any of the three main roles of money: a medium of exchange, unit of account or store of value. Crypto accounts for a sliver of US financial assets and retail sales. It remains overshadowed by its reputation as the currency of cybercriminals. Impacts Safeguards to prevent criminals from exploiting crypto will hinder legitimate crypto innovation. Transaction monitoring and know-your-customer due diligence will become a higher priority for crypto exchanges, reducing anonymity. Crypto's non-correlation with equity and bond price movements, an investor attraction, will lessen with broader use

Corporate Social Responsibility and Bond Price at Issuances: U.S. Evidence

Bondholders are arm’s-length lenders with limited insider information. In this paper, we explore whether corporate social responsibility (CSR) activities could work as an information channel for bondholders to better understand the riskiness of bond-issuing firms. We find a significant negative relation between CSR scores and corporate bond yield spread, especially for firms which invest heavily in diversity and community relations, suggesting that CSR firms are less risky. The result is robust to different model specifications and endogeneity issues. In addition, the negative relation between the CSR score and bond yield spread is significant only if a firm has a strong internal governance mechanism.

Excess volatility pursuit in autoregressive GARCH model based panel data analysis at country level: BRICS context

PurposeThis particular study examined the government bond price variations in order to determine the presence of excess volatility both at country and panel group level of BRICS countries context.Design/methodology/approachThe study applied the autoregressive GARCH panel model approach proposed by Fakhry and Richter (2015) to evaluate the presence of excess volatility and then examined the diversification benefits. Further, the use of discrete wavelet transformation (DWT) has added the advantage to observe volatility across bonds along with potential diversification benefits by retaining information from the time and frequency domain perspective for both the maturities.FindingsThe main finding indicates that the excess volatility is present in BRICS countries at individual level i.e. in the case of Russia, India and China. However, the 10-year bond showing a less volatility compared to 5-year bond with the possibility of reaping out the benefits of diversification with international portfolio of sovereign bonds.Practical implicationsThe main implication of the research is related to the non-perseverance of EMH as far sovereign bonds of BRICS countries are concerned as the results indicate presence of excess volatility in the 5-year and 10-year bond markets. However, the implicit behavior of 5-year bond could benefit the active fund managers and investors by taking an advantage of a reducing systemic risk through short-medium term investments.Originality/valueThis study contributes not only to the existing studies of similar nature by examining the excess volatility in bond markets but also taking account of co-moment of distinct maturities to confirm possible international diversification benefits for BRICS countries context.

An Asymptotic Solution for Call Options on Zero-Coupon Bonds

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.

Improving Quality of Long-Term Bond Price Prediction Using Artificial Neural Networks

Purpose: The aim of this paper is to propose nonlinear autoregressive neural network which can improve quality of bond price forecasting. Methodology/Approach: Due to the complex nature of market information that influence bonds, artificial intelligence could be accurate, robust and fast choice of bond price prediction method. Findings: Our results have reached a coefficient of determination higher than 95% in the training, validation and testing sets. Moreover, we proposed the nonlinear autoregressive network with external inputs using 50 year interest-rate swaps denominated in EUR and volatility index VIX as two external variables. Research Limitation/Implication: Our sample of daily prices between 4th January 2016 and 13th January 2021 (totally 1,270 trading days) suggest that both Levenberg-Marquardt and Scaled conjugate gradient learning algorithms achieved excellent results. Originality/Value of paper: Despite the fact that both learning algorithms achieved satisfying outcomes, implementation of an independent variable into the autoregressive neural network environment had no significant impact on prediction ability of the model.

Comparison of numerical methods to price zero coupon bonds in a two-factor CIR model

In this paper we price a zero coupon bond under a Cox–Ingersoll–Ross (CIR) two-factor model using various numerical schemes. To the best of our knowledge, a closed-form or explicit price functional is not trivial and has been less studied. The use and comparison of several numerical methods to determine the bond price is one contribution of this paper. Ordinary differential equations (ODEs) , finite difference schemes and simulation are the three classes of numerical methods considered. These are compared on the basis of computational efficiency and accuracy, with the second aim of this paper being to identify the most efficient numerical method. The numerical ODE methods used to solve the system of ODEs arising as a result of the affine structure of the CIR model are more accurate and efficient than the other classes of methods considered, with the Runge–Kutta ODE method being the most efficient. The Alternating Direction Implicit (ADI) method is the most efficient of the finite difference scheme methods considered, while the simulation methods are shown to be inefficient. Our choice of considering these methods instead of the other known and apparently new numerical methods (eg Fast Fourier Transform (FFT) method, Cosine (COS) method, etc.) is motivated by their popularity in handling interest rate instruments. Keywords: Cox–Ingersoll–Ross model; numerical methods; Runge–Kutta method; zero-coupon bonds; Alternating Direction Implicit method

Reputation and Sovereign Default

This paper presents a continuous‐time model of sovereign debt. In it, a relatively impatient sovereign government's hidden type switches back and forth between a commitment type, which cannot default, and an opportunistic type, which can, and where we assume outside lenders have particular beliefs regarding how a commitment type should borrow for any given level of debt and bond price. In any Markov equilibrium, the opportunistic type mimics the commitment type when borrowing, revealing its type only by defaulting on its debt at random times. The equilibrium features a “graduation date”: a finite amount of time since the last default, after which time reputation reaches its highest level and is unaffected by not defaulting. Before such date, not defaulting always increases the country's reputation. For countries that have recently defaulted, bond prices and the total amount of debt are increasing functions of the amount of time since the country's last default. For countries that have not recently defaulted (i.e., those that have graduated), bond prices are constant.