CONVERTIBLE BOND VALUATION: AN EMPIRICAL TEST

This research applies the options pricing model to the valuation of convertible bonds. A numeric algorithm is used to obtain theoretical values for a sample of 103 convertible bond issues. When market prices are compared with model valuations, the means are not significantly different, and 90 percent of model predictions are within 10 percent of market values. As a further test, the sample is divided on the basis of whether the model prices are (1) greater or (2) less than market prices. Returns are compared over a subsequent three-year holding period. The results indicate that without risk adjustment, the returns for the subsample identified by the model as “undervalued” (model prices exceed market prices) are significantly greater than returns for the subsample identified by the model as “overvalued” (market prices exceed model prices).     

商业银行内部评级体系构建的模型风险研究

自上个世纪70年代以来,风险管理模型为银行的风险量化管理提供了工具,但也同时引致了模型风险。除少数银行外,大多数商业银行在实施内部评级法时都着力构建自己的风险管理模型体系。不论是直接引入外部模型还是自我构建模型,都必然存在模型风险的问题,其模型风险主要产生于基础模型和构建过程两个方面。由于中国正处于转轨经济阶段,因此中国商业银行在内部评级体系构建中的模型风险除了来源于基础模型、模型数据以外,模型使用环境的特殊性也是一个不可忽视的因素。压力测试和极端值方法是避免模型风险的有效技术手段,而风险文化的建设则是规避模型风险的根本所在。     

Forecasting stock market volatility: Further international evidence

Abstract

This paper evaluates the out-of-sample forecasting accuracy of eleven models for monthly volatility in fifteen stock markets. Volatility is defined as within-month standard deviation of continuously compounded daily returns on the stock market index of each country for the ten-year period 1988 to 1997. The first half of the sample is retained for the estimation of parameters while the second half is for the forecast period. The following models are employed: a random walk model, a historical mean model, moving average models, weighted moving average models, exponentially weighted moving average models, an exponential smoothing model, a regression model, an ARCH model, a GARCH model, a GJR-GARCH model, and an EGARCH model. First, standard (symmetric) loss functions are used to evaluate the performance of the competing models: mean absolute error, root mean squared error, and mean absolute percentage error. According to all of these standard loss functions, the exponential smoothing model provides superior forecasts of volatility. On the other hand, ARCH-based models generally prove to be the worst forecasting models. Asymmetric loss functions are employed to penalize under-/over-prediction. When under-predictions are penalized more heavily, ARCH-type models provide the best forecasts while the random walk is worst. However, when over-predictions of volatility are penalized more heavily, the exponential smoothing model performs best while the ARCH-type models are now universally found to be inferior forecasters.     

The Determinants of the Treasury Security Yield Curve

Investors' security demands and two points on the yield curve are jointly determined using a disaggregated structural model of the U.S. Treasury securities market. The empirical results indicate that the structural model is capable of accurately explaining Treasury yields and that changes in a variety of nonyield variables affect the yield curve. Among these nonyield variables are Treasury security supplies, which are found to have significant but somewhat volatile impacts depending on investors' wealth flows. The within-sample predictions from the structural model are also compared to those of a naive model.     

APT VS. CAPM ESTIMATES OF THE RETURN-GENERATING FUNCTION PARAMETERS FOR REGULATED PUBLIC UTILITIES

In public utility rate hearings, there are extensive arguments concerning the most appropriate model of the return-generating function. Bower, Bower, and Logue (1984) suggest that the APT is superior to the CAPM, but their results have troublesome ranking differences between the two models when applied to returns from electric versus natural gas utilities. The purposes of this paper are to develop forward estimates of the parameters for both of these models applied to five different utility portfolios of electric and natural gas companies at a point in time, and to test whether these estimates are valid during a subsequent or future period. Also, forecasting errors for each model are compared to determine which model is best and to ascertain if there are any ranking conflicts. There are no ranking conflicts with the models as the market model consistently underestimates the actual return. Thus, the analysis suggests that the arbitrage model is a superior representation of the return-generating process of these utilities.     

Stochastic volatility: A tale of co-jumps,non-normality,GMM and high frequency data

In this article we introduce a linear–quadratic volatility model with co-jumps and show how to calibrate this model to a rich dataset. We apply GMM and more specifically match the moments of realized power and multi-power variations, which are obtained from high-frequency stock market data. Our model incorporates two salient features: the setting of simultaneous jumps in both return process and volatility process and the superposition structure of a continuous linear–quadratic volatility process and a Lévy-driven Ornstein–Uhlenbeck process. We compare the quality of fit for several models, and show that our model outperforms the conventional jump diffusion or Bates model. Besides that, we find evidence that the jump sizes are not normally distributed and that our model performs best when the distribution of jump-sizes is only specified through certain (co-) moment conditions. Monte Carlo experiments are employed to confirm this.     

Volatility of the short rate in the rational lognormal model

A recent article of Flesaker and Hughston introduces a one factor interest rate model called the rational lognormal model. This model has a lot to recommend it including guaranteed finite positive interest rates and analytic tractability. Consequently, it has received a lot of attention among practioners and academics alike. However, it turns out to have the undesirable feature of predicting that the asymptotic value of the short rate volatility is zero. This theoretical result is proved rigorously in this article. The outcome of an empirical study complementing the theoretical result is discussed at the end of the article. European call options are valued with the rational lognormal model and a comparably calibrated mean reverting Gaussian model. unsurprisingly, rational lognormal option values are considerably lower than the analogous mean reverting Gaussian option values. In other words, the volatility in the rational lognormal model declines so quickly that options are severely undervalued.     

A Regime-Switching Model of Long-Term Stock Returns

Abstract

In this paper I first define the regime-switching lognormal model. Monthly data from the Standard and Poor’s 500 and the Toronto Stock Exchange 300 indices are used to fit the model parameters, using maximum likelihood estimation. The fit of the regime-switching model to the data is compared with other common econometric models, including the generalized autoregressive conditionally heteroskedastic model. The distribution function of the regime-switching model is derived. Prices of European options using the regime-switching model are derived and implied volatilities explored. Finally, an example of the application of the model to maturity guarantees under equity-linked insurance is presented. Equations for quantile and conditional tail expectation (Tail-VaR) risk measures are derived, and a numerical example compares the regime-switching lognormal model results with those using the more traditional lognormal stock return model.     

A Hidden Markov Approach to Disability Insurance

Point and interval estimation of future disability inception and recovery rates is predominantly carried out by combining generalized linear models with time series forecasting techniques into a two-step method involving parameter estimation from historical data and subsequent calibration of a time series model. This approach may lead to both conceptual and numerical problems since any time trend components of the model are incoherently treated as both model parameters and realizations of a stochastic process. We suggest that this general two-step approach can be improved in the following way: First, we assume a stochastic process form for the time trend component. The corresponding transition densities are then incorporated into the likelihood, and the model parameters are estimated using the Expectation-Maximization algorithm. We illustrate the modeling procedure by fitting the model to Swedish disability claims data.     

An International Analysis of Historical and Forecast Earnings in Accounting-Based Valuation Models

Abstract:  In this paper we examine whether the valuation properties of historical accounting amounts, namely earnings and equity book value, differ from those of forecasted earnings for firms in 17 developed countries classified into six accounting regimes. We compare the performance of a historical model and a residual-income forecast model for explaining security prices. The historical model uses the book value of equities and actual historical earnings and the forecast model uses the book value of equities and analysts' forecasts of earnings in the residual income for estimating the intrinsic value of the firm. The results suggest that book values, historical earnings or forecasted earnings are value relevant in most regimes and countries examined. The forecast model offers significantly greater explanatory power for security prices than the historical model in the Anglo-Saxon and North American countries, Japan, Germany, and three Nordic countries. The explanatory power of the historical model is similar to that of the forecast model in the Latin countries, two Nordic countries, and Switzerland. We find that the forecast model performs similarly to the historical model where financial analysts' forecasts are noisy and analysts are less active. Further results indicate that the forecasted earnings are more value-relevant than the historical earnings in countries with stronger investor protection laws, less conservative GAAP, greater income conservatism, and more transparent accounting systems.     

How to choose the return model for market risk? Getting towards a right magnitude of stressed VaR

Value at Risk (VaR) and stressed value at Risk (SVaR) or expected shortfall are important risk measures widely used in the financial services industry for risk management and market risk capital computation. Fundamental to any (S)VaR model is the choice of the return type model for each risk factor. Because the resulting SVaR numbers are highly sensitive to the chosen return type model it is important to make a prudent choice on the return type modelling. We propose to estimate the return type model from historic data without making an a priori model assumption on the return model. We explain the fundamentals of return type modelling and how it impacts the magnitude of SVaR. We further show how to obtain a global return type model from a set of similar return type models by using geometric calculus. Numerical simulations and illustrations are provided. In this paper, we consider interest rate data, but the proposed methodology is general and can be applied to any other asset class such as inflation, credit spread, equity or fx.     

An Empirical Comparison of Convertible Bond Valuation Models

This paper empirically compares three convertible bond valuation models. We use an innovative approach where all model parameters are estimated by the Marquardt algorithm using a subsample of convertible bond prices. The model parameters are then used for out-of-sample forecasts of convertible bond prices. The mean absolute deviation is 1.86% for the Ayache-Forsyth-Vetzal model, 1.94% for the Tsiveriotis-Fernandes model, and 3.73% for the Brennan-Schwartz model. For this and other measures of fit, the Ayache-Forsyth-Vetzal and Tsiveriotis-Fernandes models outperform the Brennan-Schwartz model.     

Predicting issuer credit ratings using a semiparametric method

This paper proposes a prediction method based on an ordered semiparametric probit model for credit risk forecast. The proposed prediction model is constructed by replacing the linear regression function in the usual ordered probit model with a semiparametric function, thus it allows for more flexible choice of regression function. The unknown parameters in the proposed prediction model are estimated by maximizing a local (weighted) log-likelihood function, and the resulting estimators are analyzed through their asymptotic biases and variances. A real data example for predicting issuer credit ratings is used to illustrate the proposed prediction method. The empirical result confirms that the new model compares favorably with the usual ordered probit model.     

Office Rent Determinants Utilising Factor Analysis—A Case Study for İstanbul

In recent studies, a wide range of variables has been suggested for modelling the variation in office rent. However, only a few of them are found to influence the explanatory power of the model significantly. Moreover, the significance of these variables varies from model to model, depending on the characteristics of the region or/and the model. It is well established that the regression model of complex phenomena do not perform well, unless the effects of all major determinants are adequately represented. It is also known that complex phenomena may involve a large number of variables, and linear regression models often becomes cumbersome as the number of variables increases. A practical solution to the problem may be to pre-select the significant variables, and leave the less influential ones out. An even better solution could be to include all or most variables, while incorporating the group effect of some variables into a reasonable number factor variables. This way, both the accuracy and practicality of the model can be sustained. Serving this purpose, ‘Factor Analysis’ has been employed in establishing the office rent model for the metropolitan area of ?stanbul. The results of four different versions of the model, using linear and non-linear regressions are discussed.     

Rational expectations and monetary models of exchange rate determination: An empirical examination

One asset model of exchange rate determination that has received substantial attention in the literature is the monetary model. As with other asset models, expectations of future exchange rates play a key role. Usually these expectations are assumed to be formed rationally. However, to date there has been no attempt to empirically estimate a complete monetary model with rational expectations. In this paper, such a model is estimated and the restrictions implicity imposed by the rational expectation hypothesis tested. The results suggest that both the parameter constraints associated with the monetary model and those implied by the REH are consistent with recent exchange rate behavior.     

A Prepayment Model for the Japanese Mortgage Loan Market: Prepayment-Type-Specific Parametric Model Approach

This paper proposes a framework for construction of a prepayment model suitedto the Japanese mortgage loan market and assesses the validity of thisframework based on an empirical analysis using data from Japan. In thisframework, a model is constructed for each of three prepayment types, namely,`full prepayment', `partial prepayment', and `subrogation', using a parametricproportional hazards model, which was also employed by Schwartz and Torous(1989). Combining these three types of models allows one to take into accountthe effects of partial prepayments, which are frequently used in the Japanesemortgage market, and to simultaneously construct a model for both prepaymentand default. Time-dependent (path-dependent) covariates are introduced intothe model, which are estimated by the maximum likelihood method based on thefull likelihood that takes into account the time-dependence of the covariates.Results of the empirical analysis indicate that the hazard functions differsubstantially depending on the prepayment type. In addition, results indicatethat the fit of the model can be improved by the distinction of prepaymenttypes and the introduction of the market interest rates as path-dependentcovariates.     

An application of a three-factor performance index to measure stockholder gains from merger

This article re-examines the magnitude of stockholder gains from merger. To measure stockholder gains we employ four alternative two-factor market-industry models in combination with a matched non-merging control group. The four two-factor models are based on either the capital asset pricing model or Black's (1972) zero-beta model combined with two alternative industry factors. The four models are shown to produce generally consistent results. However, the results from a two-factor model are sometimes different from the results of a simpler one-factor model. Also, the introduction of a third factor, the non-merging control group, is shown to have a substantial impact on performance measurement.     

Robust policymaking in the face of sudden stops

This paper considers tax policies to deal with Sudden Stops – declines in aggregate activity that are magnified by a binding collateral constraint – that occasionally occur in emerging market economies. Households and/or the government are assumed to face model uncertainty and desire robustness against alternative models. Welfare gains from optimal taxation are small if the government trusts its model of household expectations, whether those expectations are altered by model uncertainty or not; in contrast, welfare losses are large if the government is uncertain about the household's probability model.     

A censored stochastic volatility approach to the estimation of price limit moves

A censored stochastic volatility model is developed to reconstruct a return series censored by price limits, one popular form of market stabilization mechanisms. When price limits are reached, the observed prices are truncated and the equilibrium prices are unobservable, which makes further financial analyses difficult. The model offers theoretically sound estimates of censored returns and is demonstrated via simulations to outperform existing approaches with respect to the estimates of model parameters, unconditional means, and standard deviations. The algorithm is applied to model stock and futures returns and results are consistent with the simulation outcomes.     

An empirical test of the variance gamma option pricing model

In this paper, we test the three-parameter symmetric variance gamma (SVG) option pricing model and the four-parameter asymmetric variance gamma (AVG) option pricing model empirically. Prices of the Hang Seng Index call options, which are of European style, are used as the data for the empirical test. Since the variance gamma option pricing model is developed for the pricing of European options, the empirical test gives a more conclusive answer than previous papers, which used American option data to the applicability of the VG models. The present study uses a large number of intraday option data, which span over a period of 3 years. Synchronous option and futures data are used throughout the study. Pairwise comparisons between the accuracy of model prices are carried out using both parametric and nonparametric methods.The conclusion is that the VG option pricing model performs marginally better than the Black–Scholes (BS) model. Under the historical approach, the VG models can moderately iron out some of the systematic biases inherent in the BS model. However, under the implied approach, the VG models continue to exhibit predictable biases and its overall performance in pricing and hedging is still far less than desirable.