Coupon Bonds Research Articles

Merton’s equation and the quantum oscillator: Pricing risky corporate coupon bonds

Merton has proposed a model of the contingent claims on a firm as an option on the firms value, and the model is based on a generalization of the Black–Scholes stochastic equation. Merton’s model can be used to price any contingent claim on the firm. A risk-sharing oscillator model for the pricing of corporate coupon bonds is proposed that leads to stochastic coupons, with the dynamics of the contingent claims being determined by the quantum oscillator. The oscillator model allows for the exact derivation of many results using quantum mathematics. The price of the risk-sharing coupon bonds and the stochastic coupons is derived exactly using the Feynman path integral.

The effect of extreme asset prices to the valuation of zero coupon bond with jump diffusion processes

In general, the logarithmic returns of asset prices are not normally distributed. Brownian motion and normal distribution have been widely used in the Black-Scholes-Merton bond framework to model the return of assets. Merton has provided a formula for the valuation of a zero coupon bond where the asset price process contains a continuous Poisson jump component, in addition to a continuous log-normally distributed component. This paper applies jump diffusion processes to derive some bond parameters, these are equity and default probability, when the asset prices have extreme values.

Between the Two Extreme Practices of Rent-Only and Deposit-Only Leases in Korea: Default Risk vs. Cost of Capital

Security deposits in Korea simultaneously serve as zero coupon bonds that maximize the landlord’s return, put options for selling the property, and call options for buying credit loss reimbursement. Given these properties of the deposits, we construct a rent-deposit equilibrium model between landlords and tenants with a stochastic process of the use value of the property. The model predicts that the equilibrium deposit-to-rent ratio increases with the landlord’s return on property investment and decreases with the tenant’s cost of capital. In particular, the theory with the cost of capital explains why both deposit-only and rent-only leases co-exist in Korea. Empirical results from Korean household data support the model’s predictions.

Noncausal Affine Processes with Applications to Derivative Pricing

Linear factor models, where the factors are affine processes, play a key role in Finance, since they allow for quasi-closed form expressions of the term structure of risks. We introduce the class of noncausal affine linear factor models by considering factors that are affine in reverse time. These models are especially relevant for pricing sequences of speculative bubbles. We show that they feature much more complicated non affine dynamics in calendar time, while still providing (quasi) closed form term structures and derivative pricing formulas. The framework is illustrated with zero coupon bond and European call option pricing examples.

BondValuation: An R Package for Fixed Coupon Bond Analysis

The purpose of this paper is to introduce the R package BondValuation for analysis of large datasets of fixed coupon bonds. The conceptual heterogeneity of fixed coupon bonds traded in the global markets imposes a high degree of complexity on their comparative analysis. Contrary to baseline fixed income theory, in practice, the majority of bonds feature coupon period irregularities. In addition, there is a multitude of day count methods, which determine the interest accrual, the cash flows and the discount factors used in bond valuation. Several R packages, e.g., fBonds, RQuantLib, and YieldCurve, provide tools for fixed income analysis. However, none of them is capable of evaluating bonds featuring irregular first and/or final coupon periods, and neither provides adequate coverage of day count conventions currently used in the global bond markets. The R package BondValuation closes this gap.

Zero-coupon interest rates: Evaluating three alternative datasets

The zero-coupon yield curve is a common input for most financial purposes. We consider three popular yield curve datasets and explore the extent to which the decision as to what dataset to use for a particular application may have an impact on the results. Many term structure papers evaluate alternative models for estimating zero coupon bonds based on their ability to replicate bond prices. However, in this paper we take a step forward by analyzing the consequences of using these alternative datasets in estimates of other moments and variables such as interest rate volatilities or the resulting forward rates and their correlations. After finding significant differences, we also explore the existence of volatility spillover effects among these three datasets. Finally, we illustrate the relevance of the choice of one particular dataset by examining the differences that may arise when testing the expectations hypothesis. In the conclusions, we provide guidance to end users in selecting a particular dataset.

On the Development of the Innovation and Investment Market of Moscow Exchange and Provision of Tax Benefits in this Segment

The paper outlines the importance of the securities market for the financing of innovative companies. It summarizes works of foreign and Russian economists, including selected publications on the development of the innovation and investment market of the Moscow Exchange (IIM–MOEX). Both positive and negative implications of the access of innovative companies to public capital markets are identified. The purpose of the research was to investigate the innovation and investment market of the Moscow Exchange and opportunities for individual and institutional investors to obtain tax benefits in this segment. Based on the open data of the Moscow Exchange, the current state of the innovation and investment market has been analyzed. A number of problems have been identified including a limited number of issuers, lack of bonds and investment units, high entry barriers, low liquidity in this segment as well as likely market manipulation and fraud. The prospects for the IIM–MOEX development are outlined. The specifics of the long-term ownership of securities in the innovation sector are analyzed. It is noted that the benefit for long-term ownership of securities of the innovation sector is not popular and faces potential application difficulties. There are few securities eligible for its application (seven shares). The possibility of combining benefits for long-term ownership of the innovation sector securities with individual investment accounts as well as the new corporate bond coupon benefit was substantiated. Arguments are given in favor of the need to consider the benefit for long-term ownership of the innovation sector securities in interrelation with investment tax deductions in general and the benefit for long-term ownership of securities in particular. The areas of further research related to the IIM–MOEX studies and tax benefits for investors in this segment are determined.

BondValuation: An R Package for Fixed Coupon Bond Analysis

The purpose of this paper is to introduce the R package BondValuation for analysis of large datasets of fixed coupon bonds. The conceptual heterogeneity of fixed coupon bonds traded in the global markets imposes a high degree of complexity on their comparative analysis. Contrary to baseline fixed income theory, in practice, the majority of bonds feature coupon period irregularities. In addition, there is a multitude of day count methods, which determine the interest accrual, the cash flows and the discount factors used in bond valuation. Several R packages, e.g., fBonds, RQuantLib, and YieldCurve, provide tools for fixed income analysis. However, none of them is capable of evaluating bonds featuring irregular first and/or final coupon periods, and neither provides adequate coverage of day count conventions currently used in the global bond markets. The R package BondValuation closes this gap.

The Valuation of Corporate Coupon Bonds

This paper proposes and estimates a tractable, arbitrage-free valuation model for corporate coupon bonds that includes a more realistic recovery rate process. The existing empirical literature uses a recovery rate process that is misspecified because it includes recovery rates for coupons due after default. Misspecification errors resulting from assuming recovery on all coupons can be substantial in size. They are larger if recovery rates, coupons, maturity and default probabilities are larger. We present evidence that coupon bond market transaction prices reflect the different recovery rates that our model predicts and that our model provides a good fit to market prices.

BEHAVIOUR OF BOND’S EMBEDDED OPTION WITH REGARD TO CREDIT RATING

In this financial engineering research, we study the behaviour of an option premium of a call/put option which is embedded in a typical fixed coupon bond with finite maturity. The contribution of the research is the conclusion about the dynamics of premium changes; represented by direction and sensitivity; with respect to the changes in credit rating and also risk-free interest rate development. The aim of the research is also to clearly demonstrate this theoretically complicated topic to the financial practitioners using a practical example. We are about to consider a 3-dimensional process where the dimensions are: time, rating development process and risk-free interest rate development. We use Standard & Poor’s rating transition matrix to create rating tree and Hull-White model for modelling of risk-free interest rate development. We add embedded call/put option to the bond structure and assume the call/put option to be exercised in case of interest rates decline/rise or rating worsening/improvement. For valuation, we use the risk-neutral concept. Using a numerical solution on the 3-dimensional tree (implemented in MATLAB), we avoid problems that appear while analytical solving of partial differential equations.

Analytic Option Prices for the Black-Karasinski Short Rate Model

We consider a one-parameter family of short rate models which encompasses both Hull-White (normal) and Black-Karasinski (lognormal) models. We deduce a general form for the relevant Green's function as an asymptotic series, assuming only that the deviations of the short rate from the forward curve are on average small in absolute terms, and show how this solution can be parametrised in such a way as to fit the model to a term structure of zero coupon bond prices. We use the derived Green's function to calculate conditional bond prices and pricing formulae for caps and floors to second order accuracy. The results are seen to take a form which is straightforward to compute using quadrature and even the first order expressions achieve highly favourable comparison with benchmark Monte Carlo computations for a wide range of market conditions with both long and short cap/floor maturities.

Bond Yield Curve Convexity Trading

Bond Yield curve is an important indicator of the borrowing costs and lending returns, is also one of the most observed indicator by traders in fixed income trading desk among investment banks. The shape of the yield curve can be normal, flat or inverted. In most cases, bond yield curve is concavely shaped. There are theories to explain the economical meaning for a normal, flat or inverted yield curve. However, there is a lack of explanation for the concave shape of the yield curve. We in this article try to provide an explanation by constructing arbitrage portfolio under the assumption that the yield curve moves in parallel. We can show that under this assumption, zero coupon bond yield curve should be concavely shaped. We will also reach the same conclusion for swap curves. In this process, we also discover some interesting properties which were never discussed in the literature.

Calibration of one-factor and two-factor Hull–White models using swaptions

In this paper, we analize a novel approach for calibrating the one-factor and the two-factor Hull–White models using swaptions under a market-consistent framework. The technique is based on the pricing formulas for coupon bond options and swaptions proposed by Russo and Fabozzi (J Fixed Income 25:76–82, 2016b; J Fixed Income 27:30–36, 2017b). Under this approach, the volatility of the coupon bond is derived as a function of the stochastic durations. Consequently, the price of coupon bond options and swaptions can be calculated by simply applying standard no-arbitrage pricing theory given the equivalence between the price of a coupon bond option and the price of the corresponding swaption. This approach can be adopted to calibrate parameters of the one-factor and the two-factor Hull–White models using swaptions quoted in the market. It represents an alternative with respect to the existing approaches proposed in the literature and currently used by practitioners. Numerical analyses are provided in order to highlight the quality of the calibration results in comparison with existing models, addressing some computational issues related to the optimization model. In particular, calibration results and sensitivities are provided for the one- and the two-factor models using market data from 2011 to 2016. Finally, an out-of-sample analysis is performed in order to test the ability of the model in fitting swaption prices different from those used in the calibration process.

Explosion in the quasi-Gaussian HJM model

We study the explosion of the solutions of the SDE in the quasi-Gaussian HJM model with a CEV-type volatility. The quasi-Gaussian HJM models are a popular approach for modeling the dynamics of the yield curve. This is due to their low-dimensional Markovian representation which simplifies their numerical implementation and simulation. We show rigorously that the short rate in these models explodes in finite time with positive probability, under certain assumptions for the model parameters, and that the explosion occurs in finite time with probability one under some stronger assumptions. We discuss the implications of these results for the pricing of the zero coupon bonds and Eurodollar futures under this model.

Contingent capital with repeated interconversion between debt‐ and equity‐like instruments

AbstractThis paper introduces a new form of contingent capital, contingent convertible securities (CCSs), which might repeatedly convert between debt‐ and equity‐like instruments depending on financial conditions. We derive explicit prices of corporate securities, assuming the cash flow is modeled as a geometric Brownian motion. We present an explicit value of the increased tax shields due to CCSs. We provide an explicit optimal capital structure when CCSs are issued and interestingly, the ratio of the optimal straight bond coupon to CCS coupon is constant and independent of the firm's financial conditions. All the conclusions hold true also for contingent convertibles.

The Bond Coupon’s Impact on Liquidity

Corporate bond investors are compensated for liquidity and counterparty risk in the yield received in excess of the credit premium and risk-free rate. This article shows that the liquidity premium as a hedge against uncertain future states is determined by the ratio of excess coupon payments after paying for credit protection to the capital gain realized after hedging interest rate risk. The liquidity premium increases with the time that investors must wait for compensation. The results suggest that the way in which investors receive compensation for liquidity risk is a more significant determinant of the liquidity premium than turnover.

The Role of Inflation-Indexed Bond in Optimal Management of Defined Contribution Pension Plan During the Decumulation Phase

This paper investigates the optimal investment strategy for a defined contribution (DC) pension plan during the decumulation phase which is risk-averse and pays close attention to inflation risk. The plan aims to maximize the expected constant relative risk aversion (CRRA) utility from the terminal real wealth by investing the fund in a financial market consisting of an inflation-indexed bond, an ordinary zero coupon bond and a risk-free asset. We derive the optimal investment strategy in closed-form using the dynamic programming approach by solving the related Hamilton-Jacobi-Bellman (HJB) equation. The results reveal that, with any level of the parameters, an inflation-indexed bond has significant advantage to hedge inflation risk.

Rush for Duration

Fixed income indices are designed to include a large number of rebalancing driven changes that are responsible for creating price pressure events, through inclusion and exclusion effects, and coupon reinvestment that occurs based on the index rules. These events are highly predictable and results in a source of alpha for unconstrained active managers capable of absorbing tracking-error risk. The anomaly depends on issuance, and the aversion against duration risk for passive managers. The primary drivers of these flows relates to bond issuance and coupon payments. As long as the issuance schedule is busy, and index managers are unwilling to take duration risk, these price pressures will continue to persist.

Bonds with index-linked stochastic coupons in quantum finance

An index-linked coupon bond is defined that pays coupons whose values are stochastic, depending on a market defined index. This is an asset class distinct from the existing coupon bonds. The index-linked coupon bond is an example of a sukuk, which is an instrument that implements one of the cornerstones of Islamic finance (Askari et al., 2012): that an investor must share in the risk of the issuer in order to earn profits from the investment. The index-linked coupon bond is defined using the mathematical framework of quantum finance (Baaquie, 2004, 2010). The coupons are stochastic, with the quantum of coupon payments depending on a publicly traded index that is chosen to reflect the primary drivers of the revenues of the issuer of the bond. The index ensures there is information symmetry – regarding the quantum of coupon being paid – between issuer and investor. The dependence of the coupon on the index is designed so that the variation of the index mirrors the changing fortunes of the issuer, with the coupon’s quantum increasing for increasing values of the index and conversely, decreasing with a fall of the index.

Stochastic Differential Equation for Approval Ratings and Scoring Systems

Feedback and rating/scoring systems are used almost everywhere nowadays. Generally customers are being asked to rate a product on a scale of 1 to 10, or 1 to 5 or on any other positive real number scale. The average score then would provide for the qualitative assessment of the product. For example Movies would be rated by their viewers and critics alike. The mean or some king of weighted mean of there feedback scores would then become their APPROVAL or AR for short. Approval ratings thus are measures of central tendency for approval/disapproval for a product. But these approval ratings keep changing as new feedback data is punched into the system. Hence they are dynamic (stochastic in nature) with their value changing as and when more feedback data keep flowing in. The most simple feedback system is where a customer is just asked whether they liked/disliked a product. The sequence of responses then would look like the output of a coin toss experiment (with heads/approval would be scored as 1 and tails/disapproval would be 0). At any point of time the overall mean would then be reported as the Approval Rating Score. The sequence of all running means, updated with the latest feedback data from customers, would form the APPROVAL RATING VECTOR or ARV for short. If we take a look at a sequence of evolution of the approval rating score with newer feedbacks, we would realise that even though we are using the last available data as the latest rating the whole path and the data hidden behind that path is never actually used. In Finance for example a measure called IRR (Internal Rate of Return) would describe the whole yield curve. While IRR is a single number, it is derived by using the information from the whole path followed by the yield curve. Similar mechanism is also present in the field of quantitative finance where the zero coupon bond prices would be calculated from the expected value of the continuous compounding of the rates which could be described by any popular short rate model. The short rate model parameters are calculated by taking in information of whole path of evolution of the interest rate. While the future is predicted by calculating the expectation over all possible future paths that the interest rate could take. The point is that the expectation is taken over the whole path. The prevailing interest rate today is not the only component used for pricing the zero coupon bond. Approval ratings however are just described by the present mean/weighted mean, and do not use the information provided by the path it took to reach to the present value, devoiding us the power to predict its future.