AN EQUILIBRIUM GUIDE TO DESIGNING AFFINE PRICING MODELS

We provide new empirical evidence on volatility forecasting in relation to asymmetries present in the dynamics of both return and volatility processes. Leverage and volatility feedback effects of the S&P 500 price and volatility dynamics are examined using recently developed methodologies to detect jumps and to disentangle their size from continuous return and continuous volatility. Granted that jumps in both return and volatility are important components for generating the two effects, we find jumps in return can improve forecasts of volatility, while jumps in volatility improve volatility forecasts to a lesser extent. Moreover, disentangling jump and continuous variations into signed semivariances further improve the out-of-sample performance of volatility forecasting models, with negative jump semivariance being highly more informative then positive jump semivariance. The model proposed is able to capture many empirical stylized facts while still remaining parsimonious in terms of number of parameters to be estimated.

This study aims to understand the contagion effect of the major equity market sentiment events, defined as jumps in the VIX index, on cryptocurrency price jumps and the corresponding feedback effect on investors' sentiment. Using recent high frequency intraday data with multivariate Hawkes processes, we find that several noteworthy contagion effects exist between Bitcoin and the market sentiment proxied by the VIX index. First of all, we find that positive market sentiment jumps tend to trigger a moderate level of cross-contagion on both positive and negative jumps in the Bitcoin market, whereas negative market sentiment jumps have no contagion effect on the Bitcoin prices. We also find that the Bitcoin market shows stronger positive self-contagion and cross-contagion effects than the equity market, in general. We also observe a lasting fear of missing out (FOMO) phenomenon in Bitcoin. It is supported by the evidence that the effect of positive jumps in the Bitcoin market lasts three times as long as that in both the equity market and the negative Bitcoin price jumps, and these positive jumps in Bitcoin may serve as a harbinger of equity market movement. These findings provide a better understanding of risk control and policy guidance for the cryptocurrency market.

This paper presents a theory of equilibrium asset pricing that generalizes the recent work of Connor. The model extends Connor's results to more general sets of asset returns and consumer preferences, introduces production, and provides a framework for analyzing exact and approximate equilibrium asset pricing. The other major contribution of the paper is the introduction of geometric arguments that exploit the properties of induced prefer- ences over assets. This method of analyzing asset pricing provides an intuitively appealing way of analyzing equilibrium asset pricing theories. unifies several well-known asset-pricing models. This paper extends Connor's finite-asset model in a number of directions. These extensions are nontrivial, because they allow the theory to encompass asset-pricing models that were excluded by Connor's assumptions. The second major contribution of the paper is to introduce a method of argument that exploits the geometric properties of induced preferences over assets, and characterizes asset prices using these proper- ties. This technique provides an intuitively appealing way of analyzing asset pricing theories. (For a simple geometric exposition of the main ideas in this paper, see Milne (1987).) 0.2. To place this paper in the context of the literature, it is important to appreciate the development of asset-pricing models over the last two decades. The first-and perhaps the most famous-asset-pricing model is the Capital Asset Pricing Model (CAPM) developed by Sharpe (1964) and Lintner (1965). The model demonstrated a striking result: assuming (i) consumers characterize portfolios in terms of the means and variance of rates of return, (ii) there exists a risk-free asset, and (iii) asset equilibrium; then any asset's expected rate of return could be written as a linear function of the riskless interest rate, and the expected rate of return on the endowment of risky assets (the so-called market portfolio). The original CAPM result was derived from a one period model, but Merton (1973) showed that in a continuous time model where returns could be char- acterized by a diffusion process, the same mean-variance argument could be applied to obtain the CAPM formula. It was well-known that if consumers had von Neumann-Morgenstern prefer- ences, then either quadratic utility and/or multivariate normality of returns were

Economic research of the last decade linking macroeconomic fundamentals to asset prices has revealed evidence that standard intertemporal asset pricing theory is not successful in explaining (unconditional) first moments of asset market characteristics such as the risk-free interest rate, equity premium and the Sharpe-ratio. Subsequent empirical research has pursued the question whether those characteristics of asset markets are time varying and, in particular, varying over the business cycle. Recently intertemporal asset pricing models have been employed to replicate those time varying characteristics. The aim of our contribution is (1) to relax some of the assumptions that previous work has imposed on underlying economic and financial variables, (2) to extend the solution technique of Marcet and Den Haan (1990) for those models by nonparametric expectations and (3) to propose a new estimation procedure based on the above solution technique. To allow fornnonparametric expectations in the expectations approach for numerically solving the intertemporal economic model we employ the Local Linear Mapsn(LLMs) of Ritter, Martinetz and Schulten (1992) to approximate conditional expectations in the Euler equation. In our estimation approach based on non-parametric expectations we are able to use full structural information and,nconsequently, Monte Carlo simulations show that our estimations are less biased than the widely applied GMM procedure. Based on quarterly U.S. data we also empirically estimate structural parameters of the model and explore its time varying asset price characteristics for two types of preferences, power utility and habit persistence. We in particular focus on the Sharpe-ratio and find indication that the model is able to capture the time variation of thenSharpe-ratio.

Asset Pricing in a Production Economy with Heterogeneous Investors

Under heterogeneous expectations, the mean–variance model of capital market equilibrium is employed to determine the effect restricting short sales has on equilibrium asset prices. Two equivalent markets differing only with respect to short sale restrictions are compared. It is shown that, in general, risky asset prices can either rise or fall due to short sale constraints. However, under a homogeneity of beliefs for the covariance matrix of future prices, short sale constraints will only increase risky asset prices.

This paper presents a new discrete time approach to pricing contingent claims on a risky asset and stochastic interest rates. The term structure of interest rates is modeled so that arbitrage‐free bond prices depend on an observable initial forward rate curve rather than an exogenously specified market price of risk. A restricted binomial process is employed to model both interest rates and an asset price. As a result, a complete market valuation formula obtains. By choosing the parameters of the discrete joint distribution such that, in the limit, the discrete model converges to the continuous one, a model is obtained that requires the estimation of only three parameters. The approach is parsimonious with respect to alternative models in the literature and can be used to price contingent claims on any two state variables. The procedure is used to numerically analyze the effects of the volatility of interest rates on the determination of mortgage contract rates.

Asset Pricing with Idiosyncratic Risk and Overlapping Generations

This thesis consists of three essays in financial economics, more precisely in the field of asset pricing and optimal portfolio choice. The first essay studies the asset pricing implications of heterogeneity in preferences coupled with long run risk in a dynamic general equilibrium pure exchange economy. It is concerned with the understanding of how risk sharing among different types of agents affects the assets returns moments in equilibrium and moreover, how these agents reacts dynamically to the long run risk that they perceive. The second and third essay approach the question of optimal portfolio with stochastic opportunity sets. The second essay proposes an approximation methodology for deriving approximate closed form solutions of dynamic optimal portfolio allocation problems. The third essay examines the optimal consumption, portfolio rule and life insurance purchase problem of a wage earner having uncertain lifetime when the market price of risk follows a mean-reverting stochastic process.

Estimation of Jump-Diffusion Processes via Empirical Characteristic Functions

Major events often trigger abrupt changes in stock prices and volatility. We study the implications of jumps in prices and volatility on investment strategies. Using the event‐risk framework of Duffie, Pan, and Singleton (2000), we provide analytical solutions to the optimal portfolio problem. Event risk dramatically affects the optimal strategy. An investor facing event risk is less willing to take leveraged or short positions. The investor acts as if some portion of his wealth may become illiquid and the optimal strategy blends both dynamic and buy‐and‐hold strategies. Jumps in prices and volatility both have important effects.

Responsible investing: The ESG-efficient frontier

Asset Pricing with Return Extrapolation

The asset pricing behavior is studied in an overlapping generations model that is dynamically inefficient because of inefficient aggregate risk sharing. The inefficiency is linked with the stochastic distribution of income over agents within a period. The introduction of a clearing house may eliminate the dynamic inefficiency, but depending on how the clearing house operates, households may only have partial insurance against income risk. Hence, the clearing house affects the marginal rate of substitution (MRS) across generations within a period and also the intertemporal marginal rate of substitution faced by a household, which is the stochastic discount factor (SDF) applied to income streams over time. The opportunity to insure against income risk is related to different concepts of Pareto optimality. The implications for asset prices and the market price of risk are derived. In particular, the matrix of contingent claim prices supporting a Pareto optimal allocation must have a dominant root no greater than unity. This is equivalent to restricting the matrix of within-period MRS to have a dominant root no greater than unity. The sequence of powers of the pricing matrix determines the time series properties of the SDF, asset prices and asset returns.

Why do electricity prices jump? Empirical evidence from the Nordic electricity market