Date of Degree
Volatility puzzle, Habit Persistence, modified asset pricing model, Double Barrier Knock out European Call Option, Finite Element Method, Crank-Nicolson method
The equity premium puzzle emanates from the inability of the theoretical models to explain the empirically observed high equity premium (when the average stock returns so much higher than the average bond returns). The puzzle is that in order to reconcile the much higher return on stock compared to the return on government bonds in the United States, individuals must have very high (unrealistic) risk aversion according to standard economics models.
Mehra and Prescott (1985)  found that for high values of relative risk aversion coefficients (=RRA), and a given small variance of the growth rate in the per capita consumption, an Equity Premium puzzle exists.
The primary goal of this dissertation is to test different theoretical models, while calibrating their parameters to the data used by Mehra and Prescot (1985) , in order to better understand the equity premium puzzle and to find a plausible explanation to that puzzle. I also compare the performance of the models I test with the performance of the models used by Mehra and Prescott (1985)  and Constantinides (1990) .
The dissertation consists of three essays. In the first essay, I use a model with no time separability of preferences and with habit persistence (= adjacent complementarity in consumption) to try and explain the equity premium puzzle. In addition, and unique to this paper, I represent the stock price movement using a right skewed non-Gaussian model (a skewed Lognormal distribution). I start with defining the model and its assumptions. I then continue with finding the optimal Consumption policy and Investment policy by implementing Ito’s Lemma formulation. Next, I derive the distribution of the subsistence rate of consumption generated by Habit Persistence (z) and use it to calculate the unconditional mean and variance of consumption growth. I then derive the relation between the RRA coefficient and the intertemporal Elasticity of Substitution in Consumption (s). In the final step I examine the Equity Premium puzzle after calibrating the model’s parameter, and then I derive the effect of time separability in utility preferences and Habit persistence on the Equity Premium puzzle.
In the second essay, I examine the ability of a dynamic asset-pricing model to explain both the Equity Premium and the Volatility puzzles. I modify the standard asset pricing model in four aspects. First, I use a time varying price of risk (i.e. time varying excess return per unit risk). Second, I incorporate Duesenberry’s demonstration effect and define the Habit formulation that utilizes quasi- ratio consumption. Third, I include tax rates in my model to control for any extreme valuation, relative to GDP, caused by tax rates and not by stock market factors. Fourth, I represent the stock price movement using a right skewed non-Gaussian model (a skewed Lognormal distribution). I utilize the conjecture and verification method to find the form of the state valuation function. After calibrating the model’s parameters, I derive the conditions that enable the Equity Premium puzzle and / or the Volatility puzzle to exist, and then I find the RRA coefficients that meet these conditions.
In the third essay, I do not investigate the Equity Premium puzzle. I examine the use of the Finite Element numerical method to price a Double Barrier Knock out European Call Option. I first convert the Black-Scholes partial differential equation into the Heat Equation and then solve it using the Finite Element Method. Numerical experiments are presented to compare the performance of the Finite Element Method with the performance of the Finite Difference Method when pricing the Double Barrier Knock out European Call Option.
The dissertation concludes with the role of habit persistence in future economic research paths and in other economics research fields.
Shmuel, Oren, "Essays on the Equity Premium Puzzle" (2019). CUNY Academic Works.