CONVERTIBLE BOND PRICING MODELS

Convertible bonds are an important segment of the corporate bond market, with worldwide outstandings approaching US$235 billion. Simple pricing models value a convertible bond as being equivalent to a straight bond with an embedded option that enables the bond holder to convert to a specific amount of common stock. The straight bond is subject to both interest rate and credit risk, whereas the option to convert is dependent on the underlying stock price, which exposes the convertible bond holder to equity risk. The complexity of these features means that convertible bonds tend to be treated casually in major derivatives and corporate finance textbooks. This paper presents a survey of the theoretical and empirical aspects of convertible bond pricing. The limitations of these studies are highlighted to identify those areas of research that may improve the valuation process and facilitate the application of these securities for corporate financing.     

Option pricing: a yet simpler approach

Decisions in Economics and Finance - We provide a lean, non-technical exposition on the pricing of path-dependent and European-style derivatives in the Cox–Ross–Rubinstein (CRR) pricing...     

审计失败对公司债券发行定价的传染效应——基于共同审计师的视角

审计失败会对客户公司产生负面影响,并且可能波及拥有共同审计师的公司。基于共同审计师视角,选取2007—2022年公司债数据,实证检验审计失败在债券发行定价中的传染效应。研究发现,当发生审计失败后,拥有共同审计师的关联公司债券发行定价显著提高,即审计失败对债券发行定价具有传染效应,经过多种稳健性检验后结论依旧成立。机制检验表明,风险信息传递、低质量会计信息是审计失败产生传染效应的作用机制。进一步研究发现,当聘用学历较高或具有行业专长的审计师、投资者面临风险更小、投资者保护更好时,传染效应有所减弱。     

A closed-form exact solution for pricing fixed-income variance swaps with affine-jump model

Fixed-income variance swaps became popular for investors to trade and hedge the fluctuation of interest rates after the recent global financial crisis over the past few decades, however, their valuations and risk management have not been studied sufficiently. This paper presents an analytic approach for pricing some discretely sampled fixed-income variance swaps under an affine-jump model with stochastic mean, stochastic volatility, and jumps. We employ a generalized characteristic function to derive the closed-form pricing formulas of these swaps, including two kinds of zero-coupon bond variance swap, Libor variance swap, and bond yield variance swap, to be precise. We also perform some numerical studies based on these models, which suggest that the fair strike values of these variance swaps are within a reasonable range regardless of estimation risk with data dependence and near-zero short rate regime. Our numerics show that the influences of varying sampling frequency and time-to-maturity on the values of these swaps are significant, and highlight the risks of specifying short rate model. Furthermore, the sensitivity analysis on the key parameters finds that the risks of stochastic volatility and jumps play prominent roles in pricing these variance swaps under the near-zero short rate regime.     

Electricity derivatives pricing with forward-looking information

In order to increase overall transparency on key operational information, power transmission system operators publish an increasing amount of fundamental data, including forecasts of electricity demand and available capacity. We employ a fundamental model for electricity prices which lends itself well to integrating such forecasts, while retaining ease of implementation and tractability to allow for analytic derivatives pricing formulae. In an extensive futures pricing study, the pricing performance of our model is shown to further improve based on the inclusion of electricity demand and capacity forecasts, thus confirming the general importance of forward-looking information for electricity derivatives pricing. However, we also find that the usefulness of integrating forecast data into the pricing approach is primarily limited to those periods during which electricity prices are highly sensitive to demand or available capacity, whereas the impact is less visible when fuel prices are the primary underlying driver to prices instead.     

考虑违约风险的可转换债券定价新模型

随着近几年我国证券市场可转换债券的发展,对其进行定价成为学界的一个热门课题。利用期权定价方法对可转换债券进行定价,并得到了一个考虑违约风险的可转换债券定价新模型。     

The stock–bond comovements and cross-market trading

We propose an asset pricing model with heterogeneous agents allocating capital to the stock and bond markets to optimize their portfolios, utilizing the dynamic interaction between the two markets. While some agents focus on the stock market and have more expertise in it, the others specialize in the bond market. Based on their comparative advantages in a particular market, heterogeneous agents constantly revise their investment portfolios by taking into account the time-varying stock–bond return comovements and the changing market conditions. Agents׳ collective investment behavior shapes the stock–bond interlinkage, which feedbacks on their subsequent capital allocations. Using monthly US stock and bond data from January 1990 to June 2014, we estimate the vector autoregression model with threshold and Markov switching mechanisms. We find evidence in support of flight-to-quality and show that it is mainly driven by the technical traders who actively sell stocks and buy bonds during periods of high market uncertainty.     

中国企业债券特征与风险补偿

利率风险、信用风险、流动性风险是债券市场上常见的风险类型,而债券的特征可以直接或间接地反映这些风险。本文通过分析中国企业债券市场上的债券发行量、已发行时间、债券期限、息票利率、收益率波动性、久期、凸性、到期收益率等债券特征对债券定价的影响,实证检验这些债券特征与债券风险及风险补偿的关系。本文的分析结论认为,这些债券特征显著地影响企业债券的定价,它们与利率风险、信用风险和流动性风险有显著关系,其中对企业债券信用风险的影响最大。流动性风险未被合理定价,低流动性债券未能获得显著的风险补偿。     

Nonparametric state price density estimation using constrained least squares and the bootstrap

The economic theory of option pricing imposes constraints on the structure of call functions and state price densities. Except in a few polar cases, it does not prescribe functional forms. This paper proposes a nonparametric estimator of option pricing models which incorporates various restrictions (such as monotonicity and convexity) within a single least squares procedure. The bootstrap is used to produce confidence intervals for the call function and its first two derivatives and to calibrate a residual regression test of shape constraints. We apply the techniques to option pricing data on the DAX.     

公司债券参考定价模型

本文基于我国公司债券现状,对公司债券的价值进行分析,提出了新的公司债券参考模型,为公司债券的发行和交易提供参考,以利于繁荣公司债券市场。     

Measure preserving derivatives and the pricing kernel puzzle

Recent empirical studies have found evidence of nonmonotonicity in the pricing kernels for a variety of market indices. This phenomenon is known as the pricing kernel puzzle. The payoff distribution pricing model of Dybvig predicts that the payoff distribution of a direct investment of $1 in a market index may be replicated by investing less than $1 in some derivative written on that market index whenever the associated pricing kernel is nondecreasing. Using the Hardy–Littlewood rearrangement inequality, we obtain an explicit solution for the cheapest replicating derivative, which we refer to as the optimal measure preserving derivative. The optimal measure preserving derivative is the permutation appearing in Ryff’s decomposition of the pricing kernel with respect to the market payoff measure. We compute optimal measure preserving derivatives corresponding to the estimated physical and risk neutral distributions in the paper by Jackwerth (2000) that first brought attention to the pricing kernel puzzle.     

Hedging gas bills with weather derivatives

Natural gas company managers concerned with customer satisfaction attempt to minimize the occurrence of extreme bills. Previously, only price fluctuations were addressed with derivative instruments; exchange-traded weather derivatives present a means of hedging exposure to increases in quantity of gas demanded during colder than expected winter months. We model a natural gas company’s ability to adjust for consumer sensitivity and exposure to extreme bills with the use of an optimal mix of weather derivatives and gas pricing derivatives. We find consumer exposure to extreme bills is minimized when the utility uses pricing and weather derivatives.(JEL G11, L51)     

Financial innovation and bank behavior: Evidence from credit markets

This paper investigates whether, and through which channel, the active use of credit derivatives changes bank behavior in the credit market, and how this channel was affected by the crisis of 2007–2009. Our principal finding is that banks with larger gross positions in credit derivatives charge significantly lower corporate loan spreads, while banks׳ net positions are not consistently related to loan pricing. We argue that this is consistent with banks passing on risk management benefits to corporate borrowers but not with alternative channels through which credit derivative use may affect loan pricing. We also find that the magnitude of the risk management effect remained unchanged during the crisis period of 2007–2009. In addition, banks with larger gross positions in credit derivatives cut their lending by less than other banks during the crisis and have consistently lower loan charge-offs. In sum, our study is suggestive of significant risk management benefits from financial innovations that persist under adverse conditions – that is, when they matter most.     

Computationally simple lattice methods for option and bond pricing

We propose new lattice-based algorithms for option and bond pricing, which rely on computationally simple trees, i.e., trees with the number of nodes that grows at most linearly in the number of time intervals. Contrary to commonly used methods, the target diffusion is approximated directly, without having to transform the original process into a constant volatility process. The discrete approximating process converges to the target continuous process, and the proposed algorithms are shown to be efficient and accurate for pricing purposes.     

A pricing‐error rule on share distribution in equity joint ventures: The Bayesian approach

Equity joint ventures (EJVs) are a popular governance mode of inter‐firm cooperation that has attracted substantial research attention. The literature, however, still lacks a precise rule for the parents to follow in splitting the equity shares of an EJV, although share distribution is critical to almost all aspects of the co‐ownership relationship. In this study, we fill this literature gap by taking the Bayesian approach to draw a pricing‐error rule on share distribution in EJVs. More specifically, we contend that equity participation by two firms in an EJV allows profit sharing to correct for the errors that they might commit in pricing their inputs to the EJV. For profit sharing to fully nullify such pricing errors, the shares of an EJV must be split between the parent firms in a percentage combination that matches the relative sizes of their pricing errors. Because pricing errors are observable only afterward, share distribution in EJVs resembles a Bayesian process, in which the partners keep updating their estimates on pricing errors to adjust share distribution to a percentage combination that could best nullify their pricing errors. Thus, the eventual outcome of share adjustment is EJV buyout, in that the partner whose pricing errors remain substantial buys out the shares of the other whose pricing errors have become tolerable.     

Volatility swaps and volatility options on discretely sampled realized variance

Volatility swaps and volatility options are financial products written on discretely sampled realized variance. Actively traded in over-the-counter markets, these products are often priced by continuously sampled approximations to simplify the computations. This paper presents an analytical approach to efficiently and accurately price discretely sampled volatility derivatives, under a general stochastic volatility model. We first obtain an accurate approximation for the characteristic function of the discretely sampled realized variance. This characteristic function is then applied to price discrete volatility derivatives through either semi-analytical pricing formulae (up to an inverse Fourier transform) or an efficient Fourier-cosine series method. Numerical experiments show that our approximation is more accurate in comparison to the approximations in the literature. We remark that although discretely sampled variance swaps and options are usually more expensive than their continuously sampled counterparts, discretely sampled volatility swaps are more prone to be cheaper than the continuously sampled counterparts. An analysis is then provided to explain why this is the case in general for realistic contract specifications and reasonable model parameters.     

Quantitative evaluation of contingent capital and its applications

A new type of bank regulatory capital, known as contingent capital, has emerged in tandem with discussions on the BASEL III regulatory framework but there is a lack of consensus on a standard valuation approach among those proposed so far. We think that the practical solution is to be able to price these instruments seamlessly and consistently with other existing derivatives. We propose a novel and practical ⿿convertible bond approach⿿ which is theoretically consistent with existing frameworks such as Black⿿Scholes and is conceptually and technically similar to the pricing models already being used in practice for convertible bonds and hybrid securities. Such a model is reasonable as all of these asset classes are hybrid equity-credit instruments and share many characteristics. Also, contingent capital through its unique mechanisms such as principal loss absorption, presents interesting risk scenarios which may not be readily apparent or may appear counterintuitive. Contingent capital may thus, at first sight, appear to carry obscure risks but, we show that by taking a careful quantitative approach, we can understand the characteristics of such instruments in a concise manner. Further, for discussing the pricing in terms of characteristics of the issuer, one in turn, needs a concise framework to describe those characteristics in terms of Common Equity Tier 1 (CET1) ratio risk. Our framework describes CET1 ratio risk via three intuitive issuer parameters: target, volatility, and resilience. In spite of the exotic risks, an investment decision in contingent capital can be justified if a sufficient return is expected in compensation. In this paper, we present a valuation method based on hurdle Sharpe ratios that has direct implications for investment decision making in the context of expansion of investor's efficient frontier. We also demonstrate the usefulness of our framework as a daily pricing tool for market participants using empirical market data.We appreciate helpful comments from an anonymous referee and the editors of North American Journal of Economics and Finance. The view expressed are those of the authors and do not necessarily reflect views and policies of Nomura Securities.     

The association of default risk factors with the systematic risk of corporate bonds

This study examines the association between bond betas and default risk factors. We find that both long-term debt and the relative ratio of long-term debt to short-term debt increase the bond beta; two measures of profitability, net income/total assets and EBIT/total assets and a cash flow measure of cash flow from operations/total assets decrease the bond beta. A proxy measure of standard deviation of returns is also significantly negatively related to bond betas, confirming the prediction from the option pricing model. In addition, by using new cash flow measures in the discriminant analysis, we improve on the successful prediction rate of bond ratings.     

Generalized affine transform on pricing quanto range accrual note

This paper was to price and hedge a quanto floating range accrual note (QFRAN) by an affine term structure model with affine-jump processes. We first generalized the affine transform proposed by Duffie et al. (2000) under both the domestic and foreign risk-neutral measures with a change of measure, which provides a flexible structure to value quanto derivatives. Then, we provided semi-analytic pricing and hedging solutions for QFRAN under a four-factor affine-jump model with the stochastic mean, stochastic volatility, and jumps. The numerical results demonstrated that both the common and local factors significantly affect the value and hedging strategy of QFRAN. Notably,  the factor of stochastic mean plays the most important role in either valuation or hedging. This study suggested that ignorance of these factors in a term-structure model will result in significant pricing and hedging errors in QFRAN. In summary, this study provided flexible and easily implementable solutions in valuing quanto derivatives.     

浅析期权定价理论及其组合投资策略

本文从期权的发展历史开始追溯,简述了期权在发展过程中的变化趋势,对期权定价理论Black-Scholes模型的意义及缺陷做了深入分析,最后介绍了标的资产与期权组合,总结了它们的特点和盈亏图,为金融衍生产品的期权投资组合策略发展提供一些借鉴。