Stochastic Dividend Research Articles

Stochastic DDM with regime–switching process

This paper introduces a stochastic dividend discount model with regime–switching and conditional heteroscedasticity. We obtain formulas, corresponding to a default probability and $ \ell $-th moment of a random stock price of a company. Next, we connect option pricing, hedging, and equity–linked life insurance products to the stochastic dividend discount model. Also, the paper provides maximum likelihood estimators of parameters of the stochastic dividend discount model. Finally, we present numerical results for the equity–linked life insurance products in the case of Walmart.

PARAMETER ESTIMATION METHODS OF REQUIRED RATE OF RETURN ON STOCK

In this study, we introduce new estimation methods for the required rate of returns on equity of private and public companies using the stochastic dividend discount model (DDM). To estimate the required rate of return on equity, we use the maximum likelihood method, the Bayesian method, and the Kalman filtering. We apply the model to a set of firms from the S&P 500 index using historical dividend and price data over a 32-year period. Overall, the suggested methods can be used to estimate the required rate of returns.

Pricing Equity-Indexed Annuities under a Stochastic Dividend Model

In this paper, we examine the valuations of equity-indexed annuities (EIAs) when their reference stocks distribute stochastic dividends. Due to the fact that stocks typically pay dividends at discrete times after the payment dates are announced, pricing EIAs with dividends is deemed to be practically significant. We directly model the discrete dividend payments using the jump diffusion process with regime switching, and then determine the dynamics of the stock price. The equivalent martingale measure of fair valuation in incomplete markets is determined by employing the Esscher transform. Finally, the pricing formulas of several of the most common EIAs in the market under the stochastic dividend model are obtained. Our model incorporates and extends the present literature on EIAs with accurate and effective valuation methods.

Pricing Variance Swaps Under Heston Stochastic Volatility Model with Stochastic Interest Rate and Stochastic Dividend Yield

Pricing Variance Swaps Under Heston Stochastic Volatility Model with Stochastic Interest Rate and Stochastic Dividend Yield

OPTIMAL DIVIDEND POLICY AND STOCK PRICES

We model a corporation dividend as an exchange option on stochastic cash flow and capital budge. Then we solve optimal dividend policy problem completely based on the dividend model under the assumption that the cash reservoir of a corporation follows a mean reverting process from empirical evidence and economic arguments. Our optimal dividend controls depend on explicitly with the cash flow and the capital budget of the corporation, and maximizes the HARA utility performance. We specify the unique optimal dividend control for the cash flow and the capital budge. Multiplicity or absence of optimal dividend policies are given. The stock price of the corporation is studied in terms of our stochastic dividend model. We find an explicit relation among the volatility of the stock price, the volatility of the cash flow and the volatility of the capital budget. The ex-dividend stock price is positively proportional to the stochastic cash flow and the probability of the dividend delta with respect to the cash flow, and negatively proportional to the capital budget and the probability of the dividend delta with respect to the capital budget. Hence, our approach provides another passage through which countercyclical volatility of the stock price can arise from the countercyclical cash flow and capital budget directly.

The valuation of options on index futures with stochastic dividend yields

This paper develops a valuation model for European options on index futures considering the stochastic nature of dividend yields. In addition, this research examines two subjects: first, whether the assumption of stochastic dividend yields is relevant; and second, the model's performance regarding the futures volatility curve. The model is calibrated using maximum likelihood estimation. The results suggest that the assumption of stochastic dividend yields has a significant influence in the valuation of options on index futures, even after considering commission costs. In addition, the model performs well in explaining the observed futures volatility curve. In this sense, the findings suggest that investment strategies based on mathematical models must consider the stochastic nature of dividend yields.

The valuation of options on index futures with stochastic dividend yields

This paper develops a valuation model for European options on index futures considering the stochastic nature of dividend yields. In addition, this research examines two subjects: first, whether the assumption of stochastic dividend yields is relevant; and second, the model's performance regarding the futures volatility curve. The model is calibrated using maximum likelihood estimation. The results suggest that the assumption of stochastic dividend yields has a significant influence in the valuation of options on index futures, even after considering commission costs. In addition, the model performs well in explaining the observed futures volatility curve. In this sense, the findings suggest that investment strategies based on mathematical models must consider the stochastic nature of dividend yields.

Extensions of Dupire Formula: Stochastic Interest Rates and Stochastic Local Volatility

We derive generalizations of Dupire formula to the cases of general stochastic drift and/or stochastic local volatility. First, we handle a case in which the drift is given as difference of two stochastic short rates. Such a setting is natural in foreign exchange context where the short rates correspond to the short rates of the two currencies, equity single-currency context with stochastic dividend yield, or commodity context with stochastic convenience yield. We present the formula both in a call surface formulation as well as total implied variance formulation where the latter avoids calendar spread arbitrage by construction. We provide derivations for the case where both short rates are given as single factor processes and present the limits for a single stochastic rate or all deterministic short rates. The limits agree with published results. Then we derive a formulation that allows a more general stochastic drift and diffusion including one or more stochastic local volatility terms. In the general setting, our derivation allows the computation and calibration of the leverage function for stochastic local volatility models.

European option pricing model with generalized Ornstein\u2013Uhlenbeck process under stochastic earning yield and stochastic dividend yield

This paper aims to examine and establish the models for European option pricing which include parameters of stochastic dividend yield and stochastic earning yield. We generalize the Ornstein–Uhlenbeck process and define it as generalized Ornstein–Uhlenbeck process. We have learned that the firm stocks, according to Black–Scholes–Merton structure, obey the geometric Brownian motion process. Under a stochastic earning yield, the dividend yield complies with the generalized Ornstein–Uhlenbeck process. The firm dividend randomly deviates from the earning yield flow because of the presence of stochastic components of dynamic Wiener process of generalized Ornstein–Uhlenbeck. In this study, we model the stock price with stochastic earning yield, and stochastic dividend yield to be taking account stochastic market price of risk parameter which is mean-reverting as well. We developed explicit formulae for European call option pricing calculations. From numerical simulation, we could evaluate the performance of our new model that could be compared with other notable option pricing models by using actual option price data. The outcomes prove that our new model performance is best when compared with others.

Stochastic dividend discount model: covariance of random stock prices

The price of common stocks, defined as the sum of all future discounted dividends, is at the heart of both the dividend discount models (DDM) and the stochastic DDM (SDDM). Gordon and Shapiro (Manag Sci 3:102–110 1956) assume a deterministic and constant dividends’ growth rate, whereas Hurley and Johnson (Financ Anal J 4:50–54 1994, J Portf Manag 25(1)27–31 1998) and Yao (J Portf Manag 23(4)99–103 1997) introduce randomness by letting the growth rate be a finite-state random variable and random dividends behave in a Markovian fashion. In this second case expected stock price is determined, but what if higher-order moments are needed? In order to address a number of financial topics, the present contribution presents an explicit formula for the covariance between (possibly) correlated stock prices.

Equity Modeling with Stochastic Dividends

In this paper, we show how to incorporate exactly discrete stochastic dividends in (hybrid) local stochastic volatility models. Our algorithm is illustrated by various numerical examples. We also specify a dividend model which is easy simulable and consistent with the market dividend smile.

The Optimal Dividend Payout Model with Terminal Values and Its Application

For some firms with large nonliquid assets, preferred shareholders can still get back a little bit of money when the firms finish disbursement of loans at the status of bankruptcy. For such a situation, to investigate the optimal dividend policy, a stochastic dynamic dividend model with nonzero terminal bankruptcy values is put forward in this paper. Moreover, an analytic solution for the optimal objective function of the discounted dividends is provided and verified. An important application of this result is that it can be employed to construct the solution for the optimal value function on the dividend problem with bailouts at bankruptcy. Further, the relationship for the solutions of these two different problems is demonstrated. In the end, some numerical examples are provided to support our theoretical results and the corresponding economic interpretations are illustrated.

Calibration of local correlation models to basket smiles

Allowing correlation to be local, i.e., state-dependent, in multi-asset models allows better hedging by incorporating correlation moves in the Delta. When options on a basket - be it a stock index, a cross-foreign exchange rate or an interest rate spread - are liquidly traded, one may want to calibrate a local correlation to these option prices. Only two particular solutions have been suggested so far in the literature. Both impose a particular dependency of the correlation matrix on the asset values that one has no reason to undergo. They may also fail to be admissible, i.e., positive semi-definite. We explain how, by combining the particle method presented in smile calibration problem solved by Guyon and Henry-Labordere (2011) with a simple affine transform, we can build all the calibrated local correlation models. The two existing models appear as special cases (if admissible). For the first time, one can now choose a calibrated local correlation in order to fit a view on the correlation skew, or reproduce historical correlation, or match some exotic option prices, thus improving the pricing, hedging and risk-management of multi-asset derivatives. This technique is generalized to calibrate models that combine stochastic interest rates, stochastic dividend yield, local stochastic volatility and local correlation. Numerical results show the wide variety of calibrated local correlations and give insight into a difficult (still unsolved) problem: finding lower bounds/upper bounds on general multi-asset option prices given the whole surfaces of implied volatilities of a basket and its constituents.

On a Connection between Froot-Stein and the De Finetti Optimal Dividends Models

Costly external capital is one of the frictions that violates the premises of the Modigliani and Miller irrelevance theorems. Froot et. al. developed a three-stage model to explain how costly external capital, along with other frictions, provides an opportunity for risk management to create value. This paper extends their model to analyze risk management (in particular, reinsurance) in the context of a going concern. It relates the extended Froot model to a fifty-year-old stochastic dividend optimization problem, introduced by Bruno de Finetti, which has received growing interest in the recent decade.

Variance matters (in stochastic dividend discount models)

Stochastic dividend discount models (Hurley and Johnson in Financ Anal J 50–54. http://www.jstor.org/stable/4479761 , 1994, J Portf Manag 27–31. doi: 10.3905/jpm.1998.409658 , 1998; Yao in J Portf Manag 99–103. doi: 10.3905/jpm.1997.409618 , 1997) present expressions for the expected value of stock prices when future dividends, periodically received by shareholders as a reward for their risky investment, evolve through time in a Markovian setting by the means of a discretely distributed random rate of growth. Such result extends and makes more flexible the classical textbook formula for stock prices known as Gordon model. This paper introduces a closed-form expression for the variance of random stock prices, determines how their variance is affected by the variance of the dividend rate of growth, establishes that, in this framework, the dividend process is non-stationary, and perform a simple econometric analysis applying real market data.

Effects of Executive Compensation Complexity on Investor Behaviour in an Experimental Stock Market

This study experimentally investigates whether shareholders correctly anticipate the incentive effects of increasingly complex compensation packages given to managers, and whether potential biases in individual shareholder beliefs carry over to price and volume effects in a stock market. In the experiment, a manager makes a decision about the stochastic dividend process generating the firm's fundamental value, and shareholders make estimations about fundamental value and trade shares in a stock market. The manager's action is either known or hidden and, nested in the hidden-action condition, compensation is either simple or complex. We hypothesise that hidden action gives rise to perceived behavioural uncertainty, and that this uncertainty has valuation relevance in that it affects both individual estimations of fundamental firm value and stock prices. Furthermore, we hypothesise that perceived behavioural uncertainty increases with the complexity of compensation, and that compensation complexity also affects trading volume. We find supporting evidence for our conjectures. Both estimations and market prices are biased when the manager's action is hidden, and biases are stronger when compensation is complex. We further find that trading volume decreases when compensation is complex, even though the heterogeneity of investors' individual beliefs increases.

Asset Market Dynamics in Equilibrium Models with Heterogeneous Agents: Analytical Results

We examine market dynamics in a discrete- time, Lucas-style asset-pricing model with heteroge- neous, utility-optimizing agents. Finitely many agents trade a single asset paying a stochastic dividend. All agents know the probability distribution of the dividend but not the private information such as wealth and asset holdings of other agents. The market clearing price is determined endogenously in each period such that sup- ply always equals demand. Our aim is to determine whether and how the pricing function evolves toward equilibrium. In the special case where all agents have logarithmic utility, but possibly different holdings and discount factors, we completely describe the market dynamics, including the evolution of the pricing and demand functions, and asset holdings of the agents. The market converges to a stable equilibrium state where only the most patient agents remain, and the equilibrium pricing function is the same as the one arising in the simple homogeneous setting.

A New Class of Local Correlation Models

Allowing correlation to be local, i.e., state-dependent, in multi-asset models allows better hedging by incorporating correlation moves in the delta. When options on a basket, be it a stock index, a cross FX rate, or an interest rate spread, are liquidly traded, one may calibrate a local correlation to these option prices. In this article we introduce a new family of local correlation models from which one can pick a model that not only calibrates to the basket smile but also has extra desirable properties, like fitting a view on correlation skew, mimicking historical correlation, or matching prices of exotic options. The family is built using the particle method and the procedure is easily adapted to calibrate path-dependent volatility models, path-dependent correlation models, and to include stochastic rates, stochastic dividend yield, and stochastic volatility.

A Joint Stock and Bond Market based on the Hyperbolic Gaussian Model

In this paper, we introduce a joint bond and stock market model based on the state price density approach as a mean to discount future payments—whether these are stochastic dividend payments or secure repayments of government zerobonds. Based upon a recipe of Rogers [20], we define a state price density model, the so-called Hyperbolic Gaussian model which allows for closed form zerobond prices and stock prices in an arbitrage-free way. It is particularly useful for insurance applications where large time horizons are considered. We estimate the joint factor model using the extended Kalman filter. The model we propose here is computationally much simpler than other models which have been considered in the literature.

Calculating First Moments and Confidence Intervals for Generalized Stochastic Dividend Discount Models

This paper presents models of equity valuation where future dividends are assumed to follow a generalized Bernoulli process consistent with the actual dividend payout behavior of many firms. This uncertain dividend stream induces a probability distribution of present value. We show how to calculate the first moment of this distribution using functional equations. As well, we demonstrate how to calculate a confidence interval using Monte Carlosimulation. This first moment and interval allows an analyst to determine whether a stock is overor under-valued.