On the Upper Bound of a Call Option

Using only a weak set of assumptions, Merton (1973) shows that the upper bound of a European or American call option on a non-dividend paying stock is the underlying stock price: a result which is often extended to options on dividend paying stocks. In this short technical piece we show that the underlying stock price is in fact not the least upper bound of either a European or an American call option on a stock that pays one or more known dividends prior to maturity. Based on Merton's (1973) original framework, new upper bounds are established which depend on the size(s) of the dividend(s) compared to the size of the strike. JEL Classification: G12, G13     

EVIDENCE OF A RELATION BETWEEN STOCK PRICE REACTIONS AROUND CASH DIVIDEND CHANGES AND YIELDS

Here, the relation between stock price reactions to announced dividend changes and the yields of the underlying securities is examined. A significant positive (negative) relationship is detected between announcement date returns and yield for dividend increases (decreases) even after controlling for the magnitude of the dividend change. Price reactions associated with dividend increases vary directly with the change in yield and, on average, low-yielding companies do not experience abnormal returns when they increase their dividends. Implied in these results is that the information conveyed through dividend changes varies with the yield of the underlying security and the market response is a function of factors beyond the pure information effect.     

Lost in translation: Delayed ex-dividend price adjustments of Hong Kong ADRs

Previous research documents that Hong Kong stocks have a full ex-dividend price adjustment consistent with dividends and capital gains being tax free. We examine ex-dividend price behavior of Hong Kong ADRs to assess the impact of differing tax environments in US and Hong Kong. These ADRs typically go ex-dividend before their underlying stock. They experience significant abnormal returns of 1.16% on their ex-day; the average ex-day price drop is only 30% of the dividend. However, ADR prices drop when the underlying stock goes ex-dividend subsequently. The cumulative ADR price drop is equal to the dividend. Thus, the ADR ex-dividend adjustment resembles that of the underlying stock, consistent with home country tax laws governing ADR price behavior. Neither liquidity nor transaction costs can explain the anomalous delayed ex-dividend adjustment of ADRs.     

Pricing via recursive quantization in stochastic volatility models

We provide the first recursive quantization-based approach for pricing options in the presence of stochastic volatility. This method can be applied to any model for which an Euler scheme is available for the underlying price process and it allows one to price vanillas, as well as exotics, thanks to the knowledge of the transition probabilities for the discretized stock process. We apply the methodology to some celebrated stochastic volatility models, including the Stein and Stein [Rev. Financ. Stud. 1991, (4), 727–752] model and the SABR model introduced in Hagan et al. [Wilmott Mag., 2002, 84–108]. A numerical exercise shows that the pricing of vanillas turns out to be accurate; in addition, when applied to some exotics like equity-volatility options, the quantization-based method overperforms by far the Monte Carlo simulation.     

Informed Options Trading Prior to Dividend Change Announcements

This paper investigates the information content of options trading prior to dividend change announcements. I find a positive (negative) relation between pre‐announcement abnormal implied volatility (IV) spread (abnormal IV skew) and cumulative abnormal stock returns around dividend change announcements. The predictive power of informed options trading is stronger for announcements of dividend reduction and when the options market is more liquid relative to the stock market and weaker when information has already been incorporated in the stock market. The predictability of informed options trading is robust to a placebo test and alternative measures of informed options trading. Overall results suggest that informed options trading predicts dividend change announcement returns.     

Stochastic dividend yields and derivatives pricing in complete markets

When an underlying yields a stochastic dividend yield, derivatives with linear payoff at their maturities that are written on this underlying have the following properties: (i) they have a unique price only if markets are complete; (ii) the dynamic strategies that replicate these contingent claims contain hedging components against the state variables in the economy; (iii) the prices of these derivatives will depend upon the dynamics of the market prices of risk even when markets are complete. Within an affine framework, we explicitly price forward and futures contracts with stochastic dividends. We also show that the quantitative impact of assuming that dividends are deterministic when they are actually stochastic is significant. JEL Classification G12 · G13     

Efficient option pricing on stocks paying discrete or path-dependent dividends with the stair tree

Pricing options on a stock that pays discrete dividends has not been satisfactorily settled because of the conflicting demands of computational tractability and realistic modelling of the stock price process. Many papers assume that the stock price minus the present value of future dividends or the stock price plus the forward value of future dividends follows a lognormal diffusion process; however, these assumptions might produce unreasonable prices for some exotic options and American options. It is more realistic to assume that the stock price decreases by the amount of the dividend payout at the ex-dividend date and follows a lognormal diffusion process between adjacent ex-dividend dates, but analytical pricing formulas and efficient numerical methods are hard to develop. This paper introduces a new tree, the stair tree, that faithfully implements the aforementioned dividend model without approximations. The stair tree uses extra nodes only when it needs to simulate the price jumps due to dividend payouts and return to a more economical, simple structure at all other times. Thus it is simple to construct, easy to understand, and efficient. Numerous numerical calculations confirm the stair tree's superior performance to existing methods in terms of accuracy, speed, and/or generality. Besides, the stair tree can be extended to more general cases when future dividends are completely determined by past stock prices and dividends, making the stair tree able to model sophisticated dividend processes.     

Generic pricing of FX,inflation and stock options under stochastic interest rates and stochastic volatility

We consider the pricing of FX, inflation and stock options under stochastic interest rates and stochastic volatility, for which we use a generic multi-currency framework. We allow for a general correlation structure between the drivers of the volatility, the inflation index, the domestic (nominal) and the foreign (real) rates. Having the flexibility to correlate the underlying FX/inflation/stock index with both stochastic volatility and stochastic interest rates yields a realistic model that is of practical importance for the pricing and hedging of options with a long-term exposure. We derive explicit valuation formulas for various securities, such as vanilla call/put options, forward starting options, inflation-indexed swaps and inflation caps/floors. These vanilla derivatives can be valued in closed form under Schöbel and Zhu [Eur. Finance Rev., 1999, 4, 23–46] stochastic volatility, whereas we devise an (Monte Carlo) approximation in the form of a very effective control variate for the general Heston [Rev. Financial Stud., 1993, 6, 327–343] model. Finally, we investigate the quality of this approximation numerically and consider a calibration example to FX and inflation market data.     

Stock returns,dividend yield,and book-to-market ratio

A dividend yield model has been widely used in previous research that relates stock market valuations to cash flow fundamentals. Given controversies about using dividends as a proxy for cash flows, a loglinear book-to-market model has recently been proposed. However, these models rely on the assumption that dividend yield and book-to-market ratio are both stationary, and empirical evidence for this is, at best, mixed. We develop a new model, the loglinear cointegration model, that explains future profitability and excess stock returns in terms of a linear combination of log book-to-market ratio and log dividend yield. The loglinear cointegration model performs better than the log dividend yield model and the log book-to-market model in terms of cross-equation restriction tests and forecasting performance comparisons. The superior performance of the loglinear cointegration model suggests that the linear combination may be a better indicator of intrinsic fundamentals than the dividend yield or the book-to-market ratio separately.     

The ex-dividend day stock price behavior in the Chinese stock market

This paper analyzes the ex-dividend day stock price behavior in the Chinese stock market. This market allows to examine the impact of tax effects while keeping any microstructure factors constant. The findings from non-taxable stocks show that their price, on the ex-dividend day, falls by an amount that is not statistically different from the dividend. For the taxable sample, stock prices of small dividend yield stocks fall proportionally to the dividend paid. For the large dividend yield stocks, the price adjustment depends on the effective tax rate on dividend income. The overall findings are consistent with the tax hypothesis.     

On the Predictability of Japanese Stock Returns Using Dividend Yield

The aim of this paper is to provide a critical and comprehensive reexamination of empirical evidence on the ability of the dividend yield to predict Japanese stock returns. Our empirical results suggest that in general, the predictability is weak. However, (1) if the bubble economy period (1986–1998), during which dividend yields were persistently lower than the historical average, is excluded from the sample, and (2) if positive autocorrelation in monthly aggregate returns is taken into account, there is some evidence that the log dividend yield is indeed useful in forecasting future stock returns. More specifically, the log dividend yield contributes to predicting monthly stock returns in the sample after 1990 and when lagged stock returns are included simultaneously.     

A closed-form solution to American options under general diffusion processes

This paper investigates American option pricing under general diffusion processes. Specifically, the underlying asset price is assumed to follow a diffusion process in which both the dividend yield and volatility are functions of time and the underlying asset price. Using the generalized homotopy analysis method, the determination of the early exercise boundary is separated from the valuation procedure of American options. Then, an exact and explicit solution for American options on a dividend-paying stock is derived as a Maclaurin series. In addition, the corresponding optimal early exercise boundary and the Greeks are obtained in closed-form solutions. A nonlinear sequence transformation, the Padé technique, is used to effectively accelerate the convergence of the partial sums of the infinite series. As the homotopy constructed in this paper is based on a generalized deformation with a shape parameter and kernel function, the error of the homotopic approximation could be reduced further for a fixed order. Numerical examples demonstrate the validity, effectiveness, and flexibility of the proposed approach.     

Over-the-Counter Option Market Dividend Protection and “Biases” in the Black-Scholes Model: A Note

Most options are traded over-the-counter (OTC) and are dividend “protected;” the exercise price decreases on the ex date by an amount equal to the dividend. This protection completely inhibits the early exercise of American call options. Nevertheless, OTC-protected options have market values which differ systematically from Black-Scholes values for European options on non-dividend paying stocks. The pricing difference is related to both the variance of the underlying stock return and to time until expiration of the option, but it is quite small in dollar amount.     

Stock and bond returns with Moody Investors

We present a tractable, linear model for the simultaneous pricing of stock and bond returns that incorporates stochastic risk aversion. In this model, analytic solutions for endogenous stock and bond prices and returns are readily calculated. After estimating the parameters of the model by the general method of moments, we investigate a series of classic puzzles of the empirical asset pricing literature. In particular, our model is shown to jointly accommodate the mean and volatility of equity and long term bond risk premia as well as salient features of the nominal short rate, the dividend yield, and the term spread. Also, the model matches the evidence for predictability of excess stock and bond returns. However, the stock–bond return correlation implied by the model is somewhat higher than that in the data.     

The effects of dividend yield and dividend policy on common stock prices and returns

This paper suggests that it is not possible to demonstrate, using the best available empirical methods, that the expected returns on high yield common stocks differ from the expected returns on low yield common stocks either before or after taxes. A taxable investor who concentrates his portfolio in low yield securities cannot tell from the data whether he is increasing or decreasing his expected after-tax return by so doing. A tax exempt investor who concentrates his portfolio in high yield securities cannot tell from the data whether he is increasing or decreasing his expected return. We argue that the best method for testing the effects of dividend policy on stock prices is to test the effects of dividend yield on stock returns. Thus the fact that we cannot tell, using the best available methods, what effects dividend yield has on stock returns implies that we cannot tell what effect, if any, a change in dividend policy will have on a corporation's stock price.     

A multivariate Markov chain stock model

ABSTRACT

We propose a dividend stock valuation model where multiple dividend growth series and their dependencies are modelled using a multivariate Markov chain. Our model advances existing Markov chain stock models. First, we determine assumptions that guarantee the finiteness of the price and risk as well as the fulfilment of transversality conditions. Then, we compute the first- and second-order price-dividend ratios by solving corresponding linear systems of equations and show that a different price-dividend ratio is attached to each combination of states of the dividend growth process of each stock. Subsequently, we provide a formula for the computation of the variances and covariances between stocks in a portfolio. Finally, we apply the theoretical model to the dividend series of three US stocks and perform comparisons with existing models. The results could also be applied for actuarial purposes as a general stochastic investment model and for calculating the initial endowment to fund a portfolio of dependent perpetuities.     

Mean-reversion properties of implied volatilities

In this paper, we present a new stylized fact for options whose underlying asset is a stock index. Extracting implied volatility time series from call and put options on the Deutscher Aktien index (DAX) and financial times stock exchange index (FTSE), we show that the persistence of these volatilities depends on the moneyness of the options used for its computation. Using a functional autoregressive model, we show that this effect is statistically significant. Surprisingly, we show that the diffusion-based stochastic volatility models are not consistent with this stylized fact. Finally, we argue that adding jumps to a diffusion-based volatility model help recovering this volatility pattern. This suggests that the persistence of implied volatilities can be related to the tails of the underlying volatility process: this corroborates the intuition that the liquidity of the options across moneynesses introduces an additional risk factor to the one usually considered.     

On the reversal of return and dividend growth predictability: A tale of two periods

A disconcerting, albeit generally accepted, finding is that aggregate stock returns are predictable by dividend yield but dividend growth is unpredictable. I show that part of this lack of dividend growth predictability stems from how dividend growth is constructed. I then show a dramatic reversal of predictability in the 134 years during 1872–2005: stock returns are largely unpredictable in the first seven decades, but become predictable in the postwar period; dividend growth is strongly predictable in the prewar years but this predictability disappears in the postwar years. New evidence on the predictability of long-run returns and dividend growth is also shown.     

USING DIVIDEND POLICY AND MANAGERIAL OWNERSHIP TO REDUCE AGENCY COSTS

In this study we examine dividends and chief executive officer (CEO) stock ownership as interrelated mechanisms that may be used to reduce agency costs. We find a significant nonmonotonic relation between dividend yield and CEO stock ownership. Our evidence shows that until the CEO becomes entrenched, increased executive stock ownership reduces agency costs and decreases dividend yield. Beyond that point, increased stock ownership increases dividend yield. Whether additional stock ownership can reduce agency costs depends upon the CEO's degree of control in the firm.     

Valuation of American call options on dividend-paying stocks: Empirical tests

This paper examines the pricing performance of the valuation equation for American call options on stocks with known dividends and compares it with two suggested approximation methods. The approximation obtained by substituting the stock price net of the present value of the escrowed dividends into the Black-Scholes model is shown to induce spurious correlation between prediction error and (1) the standard deviation of stock return, (2) the degree to which the option is in-the-money or out-of-the-money, (3) the probability of early exercise, (4) the time to expiration of the option, and (5) the dividend yield of the stock. A new method of examining option market efficiency is developed and tested.