arXiv subjects
Publications and source records attributed to Robert A. Jarrow.
We develop a unified modeling framework that connects two distinct types of bubbles defined in the literature: the rational bubbles (aka P-bubbles), and the local martingale bubbles (aka Q-bubbles). We show that the local martingale bubble model includes the classical rational bubble as a special case. We relate both types of bubbles to an equity's risk premium via a novel decomposition.
In this paper we provide an exhaustive survey of the current state of the mathematics of filtration enlargement and an interpretation of the key results of the literature from the viewpoint of mathematical finance. The emphasis is on providing a well-structured compendium of known mathematical results that can be used by researchers in mathematical finance. We mainly state the results and discuss their role and significance, with references provided for the omitted proofs. The discussion of mathematical results is accompanied by numerous examples from mathematical finance.
The paper proposes a new algorithm for the high-dimensional financial data -- the Groupwise Interpretable Basis Selection (GIBS) algorithm, to estimate a new Adaptive Multi-Factor (AMF) asset pricing model, implied by the recently developed Generalized Arbitrage Pricing Theory, which relaxes the convention that the number of risk-factors is small. We first obtain an adaptive collection of basis assets and then simultaneously test which basis assets correspond to which securities, using high-dimensional methods. The AMF model, along with the GIBS algorithm, is shown to have a significantly better fitting and prediction power than the Fama-French 5-factor model.
The purpose of this paper is to test the time-invariance of the beta coefficients estimated by the Adaptive Multi-Factor (AMF) model. The AMF model is implied by the generalized arbitrage pricing theory (GAPT), which implies constant beta coefficients. The AMF model utilizes a Groupwise Interpretable Basis Selection (GIBS) algorithm to identify the relevant factors from among all traded ETFs. We compare the AMF model with the Fama-French 5-factor (FF5) model. We show that for nearly all time periods with length less than 6 years, the beta coefficients are time-invariant for the AMF model, but not for the FF5 model. This implies that the AMF model with a rolling window (such as 5 years) is more consistent with realized asset returns than is the FF5 model.
The paper provides a new explanation of the low-volatility anomaly. We use the Adaptive Multi-Factor (AMF) model estimated by the Groupwise Interpretable Basis Selection (GIBS) algorithm to find those basis assets significantly related to low and high volatility portfolios. These two portfolios load on very different factors, indicating that volatility is not an independent risk, but that it's related to existing risk factors. The out-performance of the low-volatility portfolio is due to the (equilibrium) performance of these loaded risk factors. The AMF model outperforms the Fama-French 5-factor model both in-sample and out-of-sample.
A constrained informationally efficient market is defined to be one whose price process arises as the outcome of some equilibrium where agents face restrictions on trade. This paper investigates the case of short sale constraints, a setting which despite its simplicity, generates new insights. In particular, it is shown that short sale constrained informationally efficient markets always admit equivalent supermartingale measures and local martingale deflators, but not necessarily local martingale measures. And if in addition some local martingale deflator turns the price process into a true martingale, then the market is constrained informationally efficient. Examples are given to illustrate the subtle phenomena that can arise in the presence of short sale constraints, with particular attention to representative agent equilibria and the different notions of no arbitrage.
We show that with suitable restrictions on allowable trading strategies, one has no arbitrage in settings where the traditional theory would admit arbitrage possibilities. In particular, price processes that are not semimartingales are possible in our setting, for example, fractional Brownian motion.