Valuation and optimal strategies of convertible bonds

This article presents a contingent claim valuation of a callable convertible bond with the issuer's credit risk. The optimal call, voluntary conversion, and bankruptcy strategies are jointly determined by shareholders and bondholders to maximize the equity value and the bond value, respectively. This model not only incorporates tax benefits, bankruptcy costs, refunding costs, and a call notice period, but also takes account of the issuer's debt size and structure. The numerical results show that the predicted optimal call policies are generally consistent with recent empirical findings; therefore, calling convertible bonds too late or too early can be rational. © 2006 Wiley Periodicals, Inc. Jrl Fut Mark 26:895–922, 2006     

Anatomy of option features in convertible bonds

Several earlier theoretical studies on the optimal issuer's calling policy of a convertible bond suggest that the issuer should call the bond as soon as the conversion value exceeds the call price. However, empirical studies on actual cases of calling by convertible bond issuers reveal that firms “delayed” calling their convertible bonds until the conversion value well exceeded the call price. In this paper, we construct valuation algorithms that price risky convertible bonds with embedded option features. In particular, we examine the impact of the soft call and hard call constraints, notice period requirement and other factors on the optimal issuer's calling policy. Our results show that the critical stock price at which the issuer should optimally call the convertible bond depends quite sensibly on these constraints and requirements. The so‐called “delayed call phenomena” may be largely attributed to the underestimation of the critical call price due to inaccurate modeling of the contractual provisions. © 2004 Wiley Periodicals, Inc. Jrl Fut Mark 24:513–532, 2004     

PRICING CALLABLE BONDS BY MEANS OF GREEN'S FUNCTION1

This paper derives a closed-form solutin for the price of the European and semi-Amirican callable bond for two popular one-factor models of the term structure of interest rates which have been proposed by Vasicek as well as Cox, Ingersoll, and Ross. the price is derived by means of repeated use of Green's function, which, in turn, is derived from a series solution of the partial differential equation to value a discount bond. the boundary conditions which lead to the well-known formulae for the price of a discount bond are also identified. the algorithm to implement the explicit solution relies on numerical quadrature involving Green's function. It offers both higher accuracy and higher speed of computation than finite difference methods, which suffer from numerical instabilites due to discontinuous boundary values. For suitably small time steps, the proposed algorithm can also be applied to American callable bonds or to any American-type option with Green's function being explicitly known.     

The valuation of inflation‐indexed and FX convertible bonds

This paper derives a valuation model of inflation‐indexed convertible bonds that incorporates the firm's stock price, inflation indexing and the firm's credit risk. The pricing of inflation‐indexed convertible bonds traded on the Tel‐Aviv Stock Exchange (TASE) was empirically tested by using a comprehensive database. The study is the first to empirically test the pricing of convertibles in emerging markets. It was found that the theoretical values for the bonds are, on average, 1.94% higher than the observed market prices. Unlike previous studies, it was found that the underpricing increases with the moneyness of the convertible. It was found that as the maturity lengthens, the underpricing increases. © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 28:634–655, 2008     

Pricing risky corporate bonds: An empirical study

This paper empirically studies a model for pricing risky corporate bonds proposed by Baaquie—based on the seminal Merton. The proposed model provides an exact solution for the price of a risky corporate bond with a finite maturity and explains the market price of corporate fixed coupon bonds as being the result of the market risk that is carried by the bond. Baaquie's model is empirically tested using 42 fixed coupon bonds issued by 23 US corporations, between 2011 and 2017. It is found that the proposed model estimates most bond prices quite accurately. Market time (similar to the concept of psychological time), which is distinct from calendar time, is quantified in the paper and is an exogenous behavioral parameter that plays a pivotal role in improving the accuracy of the pricing model for long-maturity risky bonds.     

Electronic Call Market for Commodity Transactions: Design of Computer-Mediated Order Matching System

Commodity exchanges provide potential market structures for electronic trading because commodity products have relatively simple and well-standardized product attributes. Most existing electronic trading systems are introduced for financial exchanges, where qualities of traded products (such as stocks and bonds) are homogeneous, thus taking into account only bid and offer prices for computer-mediated order matching. However, a single commodity market, such as the cotton or grain market, is made up of many heterogeneous goods that are similar to each other but have different product qualities and contract terms. In addition to the price, commodity traders have other pertinent preference ranges over product attributes and delivery conditions. We delineate an electronic call market system for commodity trading, which optimizes the realization of traders' utilities over extended product attributes beyond the price. The electronic call market not only maximizes the total surplus of market participants based on bid and ask prices but also satisfies their qualitative preferences over other attributes, which are difficult to include in the quantitative prices. The trading mechanism of the electronic call market integrates an economic auction model with a social choice model to produce a Pareto-improved transaction. Market simulations are conducted to validate the performance of the proposed electronic call market. The order matching system of the electronic call market is implemented using constraint logic programming.     

Callable bull/bear contracts,call auction sessions,and price manipulations: Evidence from Hong Kong

Call auction sessions are widely adopted to improve the price discovery process. The suspension of the closing call auction session (CAS) of the Hong Kong Stock Exchange (HKEx) in 2009 and the reintroduction of an enhanced CAS in 2016 provide us a unique experimental environment to assess the effectiveness of the two different CAS models in reducing market manipulation. In examining the probability of mandatory call events (MCEs) of callable bull/bear contracts (CBBCs), we find the enhanced CAS model being more effective in price manipulation reduction. We also find the enhanced CAS reducing price manipulation in the preopening auction session.     

Term Structure Models Driven by General Lévy Processes

As a generalization of the Gaussian Heath–Jarrow–Morton term structure model, we present a new class of bond price models that can be driven by a wide range of Lévy processes. We deduce the forward and short rate processes implied by this model and prove that, under certain assumptions, the short rate is Markovian if and only if the volatility structure has either the Vasicek or the Ho–Lee form. Finally, we compare numerically forward rates and European call option prices in a model driven by a hyperbolic Lévy motion with those in the Gaussian model.     

MODELING THE RECOVERY RATE IN A REDUCED FORM MODEL

This paper provides a model for the recovery rate process in a reduced form model. After default, a firm continues to operate, and the recovery rate is determined by the value of the firm's assets relative to its liabilities. The debt recovers a different magnitude depending upon whether or not the firm enters insolvency and bankruptcy. Although this recovery rate process is similar to that used in a structural model, the reduced form approach is maintained by utilizing information reduction in the sense of Guo, Jarrow, and Zeng. Our model is able to provide analytic expressions for a firm's default intensity, bankruptcy intensity, and zero-coupon bond prices both before and after default.     

The Chinese equity index options market

Using Bakshi et al. (2000), and Bakshi and Kapadia's (2003) methodology, this paper studies the Chinese equity index options market that has been developing since 2015. Empirical evidence shows that the market price of call (put) option is generally lower (higher) than their Black-Scholes prices with historical volatility. The prices of the options do not support the one-dimensional diffusion model properties. We find 61.79% (63.25%) of delta-hedged gains in call (put) options to be negative. The analysis of the non-zero delta-hedged gain suggests that the investors are mainly trading on additional volatility risk in the options market in China.     

ASSET PRICE BUBBLES IN INCOMPLETE MARKETS*

This paper studies asset price bubbles in a continuous time model using the local martingale framework. Providing careful definitions of the asset's market and fundamental price, we characterize all possible price bubbles in an incomplete market satisfying the “no free lunch with vanishing risk (NFLVR)” and “no dominance” assumptions. We show that the two leading models for bubbles as either charges or as strict local martingales, respectively, are equivalent. We propose a new theory for bubble birth that involves a nontrivial modification of the classical martingale pricing framework. This modification involves the market exhibiting different local martingale measures across time—a possibility not previously explored within the classical theory. Finally, we investigate the pricing of derivative securities in the presence of asset price bubbles, and we show that: (i) European put options can have no bubbles; (ii) European call options and discounted forward prices have bubbles whose magnitudes are related to the asset's price bubble; (iii) with no dividends, American call options are not exercised early; (iv) European put‐call parity in market prices must always hold, regardless of bubbles; and (v) futures price bubbles can exist and they are independent of the underlying asset's price bubble. Many of these results stand in contrast to those of the classical theory. We propose, but do not implement, some new tests for the existence of asset price bubbles using derivative securities.     

我国可转债转股价调整条款设计存在的问题与修正建议

可转债转股价格调整条款设计的基本原则是要使可转债是红利保护的，要实现这一目标，必须将转股价格和股票价格进行同比例调整。我国可转债发行过程中转股价格调整条款对现金红利、增发和配股的处理办法在一般情况下基本符合红利保护的原则，但在现金红利数额较大，增发和配股比例比较高的情况下，必须根据更科学的方法来调整转股价格。     

Why Doesn't the Black‐‐Scholes Model Fit Japanese Warrants and Convertible Bonds?

In this paper, we investigate the systematic departures of traded prices of Japanese equity warrants and convertible bonds from their theoretical Black–Scholes values. We briefly consider transactions costs and the dilution adjustment as potential explanations of the discrepancy. However, our major focus is on shifts in volatility of the prices of the underlying stocks as a function of the stock price changes; such shifts are not taken into account in the Black–Scholes values. We assume that the pseudo‐probability distributions of prices of stocks of cross‐sections of companies which are roughly similar in size are identical. This simple assumption, which can be generalized, enables us to infer the implied probability distribution and binomial tree for stock price changes using the Derman and Kani (1994), Rubinstein (1994) and Shimko (1993) approach. The cross‐section of warrant prices implies an inverse volatility smile and a positively skewed probability density for stock prices. Rubinstein's identifying assumptions generate an implied binomial tree in which the relative size of up‐steps and down‐steps, and thus volatility, changes systematically as stock prices change. We briefly consider potential explanations for the implied behaviour, and for the difference in the smile pattern between index options and the warrants and convertibles.     

Time‐varying market price of risk in the crude oil futures market

In this study, a three‐factor model of crude oil prices is estimated, which incorporates a time‐varying market price of risk. The model is able to accurately capture the term structure of futures prices with evidence suggesting that risk premiums in the crude oil market are time‐varying. Using the cross‐section of futures prices, we estimate a time‐series of the market price of risk in the crude oil market implied by the model. We find that the risk premiums in the crude oil market are driven by the same risk factors as equity and bond markets. © 2010 Wiley Periodicals, Inc. Jrl Fut Mark 31:779–807, 2011     

中国可转债发行的股权价值效应

本文运用Merton(1990)的或有索取权分析方法,对中国上市公司发行可转债行为对非流通股东和流通股东股权价值的不同影响作了深入的分析,得出如下结论:(1)在中国目前股权分割的情况下,无论可转债是否按照合理价格发行,原有流通股的价值都会减少;(2)在非流通股东占控股地位的情况下,它会选择折价发行并向全体股东配售这一对其最为有利而对流通股东最为不利的可转债发行方案。并在此基础上提出政策建议:修改可转债发行法规,规定可转债只能向原有流通股股东配售,不能向社会公众和非流通股股东配售。     

PRICING AND SEMIMARTINGALE REPRESENTATIONS OF VULNERABLE CONTINGENT CLAIMS IN REGIME‐SWITCHING MARKETS

Using a suitable change of probability measure, we obtain a Poisson series representation for the arbitrage‐free price process of vulnerable contingent claims in a regime‐switching market driven by an underlying continuous‐time Markov process. As a result of this representation, along with a short‐time asymptotic expansion of the claim's price process, we develop an efficient novel method for pricing claims whose payoffs may depend on the full path of the underlying Markov chain. The proposed approach is applied to price not only simple European claims such as defaultable bonds, but also a new type of path‐dependent claims that we term self‐decomposable, as well as the important class of vulnerable call and put options on a stock. We provide a detailed error analysis and illustrate the accuracy and computational complexity of our method on several market traded instruments, such as defaultable bond prices, barrier options, and vulnerable call options. Using again our Poisson series representation, we show differentiability in time of the predefault price function of European vulnerable claims, which enables us to rigorously deduce Feynman‐Ka? representations for the predefault pricing function and new semimartingale representations for the price process of the vulnerable claim under both risk‐neutral and objective probability measures.     

可转换债券融资对我国上市公司价值的影响研究

可转换债券兼有股权融资和债权融资的两种效用,通常会促使投资者对转股时机与转股数量有不同的决策,这些决策对发行可转换债券的公司价值有不同影响。文章通过建立影响公司价值的分析模型,探讨我国上市公司发行可转换债券对公司价值所产生的影响,并利用我国上市公司1998年至2014年期间发行可转换债券的样本数据进行实证分析。研究发现：上市公司进行可转换债券融资后,公司价值会因其偿债能力变化而下降;国有股权比例之于公司价值的影响,是通过影响公司经理人经营行为来实现的;成长性不同的公司在债券存续期内的公司价值变化,并不存在显著差异。文章基于委托代理角度对可转换债券影响我国上市公司价值展开研究,在一定程度和范围内拓宽了公司治理问题的分析空间。     

Black‐Scholes‐Merton revisited under stochastic dividend yields

European options are priced in a framework à la Black‐Scholes‐Merton, which is extended to incorporate stochastic dividend yield under a stochastic mean–reverting market price of risk. Explicit formulas are obtained for call and put prices and their Greek parameters. Some well‐known properties of the Black‐Scholes‐Merton formula fail to hold in this setting. For example, the delta of the call can be negative and even greater than one in absolute terms. Moreover, call prices can be a decreasing function of the underlying volatility although the latter is constant. Finally, and most importantly, option prices highly depend on the features of the market price of risk, which does not need to be specified at all in the standard Black‐Scholes‐Merton setting. The results are simulated in order to assess the economic impact of assuming that the dividend yield is deterministic when it is actually stochastic, as well as to assess the economic importance of the features of the market price of risk. © 2006 Wiley Periodicals, Inc. Jrl Fut Mark 26:703–732, 2006     

Renegotiation, collective action clauses and sovereign debt markets

Collective action clauses (CACs) are provisions specifying that a supermajority of bondholders can change the terms of a bond. We study how CACs determine governments' fiscal incentives, sovereign bond prices, and default probabilities in environments with and without contingent debt and IMF presence. We claim that CACs are likely to be an irrelevant dimension of debt contracts in current sovereign debt markets because of the variety of instruments utilized by sovereigns and the implicit IMF guarantee. Nonetheless, under a new international bankruptcy regime like that recently proposed by the IMF, CACs can increase significantly the cost of borrowing for sovereigns, contrary to what is suggested in previous empirical literature.     

Convertible Debt: Financing Decisions and Voluntary Conversion under Ambiguity

This paper integrates ambiguity into a contingent claim model for convertible debt. We study how convertible debt valuation is affected by the ambiguity biases of equity holders and debt holders and provide sensitivity analysis of the bond value to changes in attitude toward ambiguity, firm and bond parameters. Our results, which are summarized into five main predictions, are consistent with recent empirical evidence and offer a possible interpretation of some corporate finance puzzles.