Signal processing with Levy information

Levy processes, which have stationary independent increments, are ideal for modelling the various types of noise that can arise in communication channels. If a Levy process admits exponential moments, then there exists a parametric family of measure changes called Esscher transformations. If the parameter is replaced with an independent random variable, the true value of which represents a "message", then under the transformed measure the original Levy process takes on the character of an "information process". In this paper we develop a theory of such Levy information processes. The underlying Levy process, which we call the fiducial process, represents the "noise type". Each such noise type is capable of carrying a message of a certain specification. A number of examples are worked out in detail, including information processes of the Brownian, Poisson, gamma, variance gamma, negative binomial, inverse Gaussian, and normal inverse Gaussian type. Although in general there is no additive decomposition of information into signal and noise, one is led nevertheless for each noise type to a well-defined scheme for signal detection and enhancement relevant to a variety of practical situations.Comment: 27 pages. Version to appear in: Proc. R. Soc. London

Leisure and Housing Consumption after Retirement: New Evidence on the Life-Cycle Hypothesis

We revisit the alleged retirement consumption puzzle. According to the life-cycle theory, foreseeable income reductions such as those around retirement should not affect consumption. However, we first recall that given higher leisure endowments after retirement, the theory does predict a fall of total market consumption expenditures. In order not to mistake this predicted drop for a puzzle we focus on housing consumption which can be plausibly regarded as complementary to leisure, and we control for the leisure change in our empirical specifications, using micro data for Germany (SOEP), where housing expenditures are observable as rents for the majority (60%), as well as dwelling relocations. We still find significant negative impacts of the retirement status on housing consumption, which is hard to reconcile with the life-cycle theory. For retirees we also find significant effects of the income reduction at retirement on housing. However, the effects are small in quantitative terms, given the lock-in nature of past housing decisions

Closing a mental account: the realization effect for gains and losses

How do risk attitudes change after experiencing gains or losses? For the case of losses, Imas (Am Econ Rev 106:2086–2109, 2016) shows that subsequent risk-taking behavior depends on whether these losses have been realized or not. After a realized loss, individuals’ risk-taking decreases, whereas it increases after an unrealized (paper) loss. He refers to this asymmetry as the realization effect. In this study, we derive theoretical predictions for risk-taking after paper and realized gains, and for investment opportunities with different skewness. We experimentally test these predictions and, at the same time, replicate Imas’ original study. Independent of a prior gain or loss, we show that subsequent risk-taking is higher when outcomes remain unrealized. However, we find no evidence of a realization effect for non-positively skewed lotteries. While the first result suggests that the effect is more general, the second result reveals its boundary conditions

A study of data-driven momentum and disposition effects in the Chinese stock market by functional data analysis

We apply a functional data analysis approach to decompose the cross-sectional Fama–French three-factor model residuals in the Chinese stock market. Our results indicate that other than Fama–French three factors, there are two orthonormal asset pricing factors describing the behavioral biases in their historical performances: between winner and loser stocks, and extreme and mediocre-performing stocks, respectively. We explain these two factors through investors’ overreaction, overconfidence and the lead-lag effect. These findings empirically show the existence of momentum and disposition effects in the Chinese stock market. A buy-and-hold mean-variance optimized portfolio incorporating these two market anomalies boosts the Sharpe ratio to 1.27

European option pricing with constant relative sensitivity probability weighting function

We evaluate European financial options under continuous cumulative prospect theory. Within this framework, it is possible to model investors’ attitude toward risk, which may be one of the possible causes of mispricing. We focus on probability risk attitudes and consider alternative probability weighting functions. In particular, curvature of the weighting function models optimism and pessimism when one moves from extreme probabilities, whereas elevation can be interpreted as a measure of relative optimism. The constant relative sensitivity weighting function is the only one, amongst those in the literature, which is able to model separately curvature and elevation. We are interested in studying the effects of both these features on options prices

Analogy making and the structure of implied volatility skew

An analogy based option pricing model is put forward. If option prices are determined in accordance with the analogy model, and the Black Scholes model is used to back-out implied volatility, then the implied volatility skew arises, which flattens as time to expiry increases. The analogy based stochastic volatility and the analogy based jump diffusion models are also put forward. The analogy based stochastic volatility model generates the skew even when there is no correlation between the stock price and volatility processes, whereas, the analogy based jump diffusion model does not require asymmetric jumps for generating the skew