Springer Science and Business Media LLC

In models of financial bubbles, the price of a stock is typically unbounded, and this plays a fundamental role in the analysis of finite horizon local martingale bubbles. It would seem that price bubbles do not apply to a priori bounded risky asset prices, such as bond prices. To avoid this limitation, to characterize, and to identify bond price mispricings consistent with an absence of arbitrage, we develop the concept of a relative asset price bubble. This notion uses a risky asset’s price as the numéraire instead of the money market account’s value. This change of numéraire generates some interesting mathematical complexities because many important numéraires, including risky bonds, can vanish with positive probability over the model’s horizon.

In stochastic portfolio theory, a relative arbitrage is an equity portfolio which is guaranteed to outperform a benchmark portfolio over a finite horizon. When the market is diverse and sufficiently volatile, and the benchmark is the market or a buy-and-hold portfolio, functionally generated portfolios introduced by Fernholz provide a systematic way of constructing relative arbitrages. In this paper we show that if the market portfolio is replaced by the equal or entropy weighted portfolio among many others, no relative arbitrages can be constructed under the same conditions using functionally generated portfolios. We also introduce and study a shaped-constrained optimization problem for functionally generated portfolios in the spirit of maximum likelihood estimation of a log-concave density.

Investors can generate excess returns by implementing trading strategies based on publicly available equity analyst forecasts. This paper captures the information provided by analysts by the implied cost of capital (ICC), the internal rate of return that equates a firm’s share price to the present value of analysts’ earnings forecasts. We find that U.S. stocks with a high ICC outperform low ICC stocks on average by 6.0 % per year. This spread is significant when controlling the investment returns for their risk exposure as proxied by standard pricing models. Further analysis across the world’s largest equity markets validates these results.

This paper analyses the accuracy of replicating portfolio methods in predicting asset prices. In a two-period, general equilibrium model with incomplete financial markets and heterogeneous agents, a computational study is conducted under various distributional assumptions. The focus is on the price of a call option on an underlying risky asset. There is evidence that the value of the (approximate) replicating portfolio is a good approximation for the general equilibrium price for CRRA preferences, but not for CARA preferences. Furthermore, there is strong evidence that the introduction of the call option reduces market incompleteness, but that the price of the underlying asset is unchanged. There is, however, inconclusive evidence on the welfare effects of the option.

Heterogeneity and evolutionary behaviour of investors are two of the most important characteristics of financial markets. This paper incorporates the adaptive behaviour of agents with heterogeneous beliefs and establishes an evolutionary capital asset pricing model (ECAPM) within the mean-variance framework. We show that the rational behaviour of agents switching to better-performing trading strategies can cause large deviations of the market price from the fundamental value of one asset to spill over to other assets. Also, this spill-over effect is associated with high trading volumes and persistent volatility characterized by significantly decaying autocorrelations of, and positive correlation between, price volatility and trading volume.

Recent empirical evidences indicate that default rates are influenced not only by the observable or latent risk factors, but also depend on the history of past defaults. Motivated by this empirical finding, we consider in this paper a reduced-form, intensity-based credit risk model, which allows for both frailty and default contagion, using a so-called “self-exciting” intensity, in the sense that the default intensity varies not only with the risk factors, but also depends on the previous default history of all the firms. With “self-exciting” default intensity, we are able to obtain closed-form expressions for the pricing of credit derivative securities in our model. The estimation of parameters using the EM algorithm is considered as well.

We consider the option pricing problem when the risky underlying assets are driven by Markov-modulated Geometric Brownian Motion (GBM). That is, the market parameters, for instance, the market interest rate, the appreciation rate and the volatility of the underlying risky asset, depend on unobservable states of the economy which are modelled by a continuous-time Hidden Markov process. The market described by the Markov-modulated GBM model is incomplete in general and, hence, the martingale measure is not unique. We adopt a regime switching random Esscher transform to determine an equivalent martingale pricing measure. As in Miyahara [33], we can justify our pricing result by the minimal entropy martingale measure (MEMM).