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We address the problem of asset pricing in a market where there is no risky asset. Previous work developed a theoretical model for a shadow riskless rate (SRR) for such a market in terms of the drift component of the state-price deflator for that asset universe. Assuming asset prices are modeled by correlated geometric Brownian motion, in this work we develop a computational approach to estimate the SRR from empirical datasets. The approach employs: principal component analysis to model the effects of the individual Brownian motions; singular value decomposition to capture the abrupt changes in condition number of the linear system whose solution provides the SRR values; and a regularization to control the rate of change of the condition number. Among other uses (e.g., for option pricing, developing a term structure of interest rate), the SRR can be employed as an investment discriminator between asset classes. We apply the computational procedure to markets consisting of groups of stocks, varying asset type and number. The theoretical and computational analysis provides not only the drift, but also the total volatility of the state-price deflator. We investigate the time trajectory of these two descriptive components of the state-price deflator for the empirical datasets., Comment: 23 pages, 14 figures

We propose a discrete-time econometric model that combines autoregressive filters with factor regressions to predict stock returns for portfolio optimisation purposes. In particular, we test both robust linear regressions and general additive models on two different investment universes composed of the Dow Jones Industrial Average and the Standard & Poor's 500 indexes, and we compare the out-of-sample performances of mean-CVaR optimal portfolios over a horizon of six years. The results show a substantial improvement in portfolio performances when the factor model is estimated with general additive models.

We introduce a discrete binary tree for pricing contingent claims with the underlying security prices exhibiting history dependence characteristic of that induced by market microstructure phenomena. Example dependencies considered include moving average or autoregressive behavior. Our model is market-complete, arbitrage-free, and preserves all of the parameters governing the historical (natural world) price dynamics when passing to an equivalent martingale (risk-neutral) measure. Specifically, this includes the instantaneous mean and variance of the asset return and the instantaneous probabilities for the direction of asset price movement. We believe this is the first paper to demonstrate the ability to include market microstructure effects in dynamic asset/option pricing in a market-complete, no-arbitrage, format.

We consider the use of P-spline generalized additive hedonic models for real estate prices in large U.S. cities, contrasting their predictive efficiency against linear and polynomial based generalized linear models. Using intrinsic and extrinsic factors available from Redfin, we show that GAM models are capable of describing 84% to 92% of the variance in the expected ln(sales price), based upon 2021 data. As climate change is becoming increasingly important, we utilized the GAM model to examine the significance of environmental factors in two urban centers on the northwest coast. The results indicate city dependent differences in the significance of environmental factors. We find that inclusion of the environmental factors increases the adjusted R-squared of the GAM model by less than one percent., Comment: 12 pages, 3 figures, 4 tables

ESG ratings provide a quantitative measure for socially responsible investment. We present a unified framework for incorporating numeric ESG ratings into dynamic pricing theory. Specifically, we introduce an ESG-valued return that is a linearly constrained transformation of financial return and ESG score. This leads to a more complex portfolio optimization problem in a space governed by reward, risk and ESG score. The framework preserves the traditional risk aversion parameter and introduces an ESG affinity parameter. We apply this framework to develop ESG-valued: portfolio optimization; capital market line; risk measures; option pricing; and the computation of shadow riskless rates., Comment: Main article: 51 pages, 11 figures, 5 tables. Supplementary appendix: 17 pages, 11 figures, 6 tables

Measures of tail dependence between random variables aim to numerically quantify the degree of association between their extreme realizations. Existing tail dependence coefficients (TDCs) are based on an asymptotic analysis of relevant conditional probabilities, and do not provide a complete framework in which to compare extreme dependence between two random variables. In fact, for many important classes of bivariate distributions, these coefficients take on non-informative boundary values. We propose a new approach by first considering global measures based on the surface area of the conditional cumulative probability in copula space, normalized with respect to departures from independence and scaled by the difference between the two boundary copulas of co-monotonicity and counter-monotonicity. The measures could be approached by cumulating probability on either the lower left or upper right domain of the copula space, and offer the novel perspective of being able to differentiate asymmetric dependence with respect to direction of conditioning. The resulting TDCs produce a smoother and more refined taxonomy of tail dependence. The empirical performance of the measures is examined in a simulated data context, and illustrated through a case study examining tail dependence between stock indices.