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In this paper, we consider a dynamic asset pricing model in an approximate fractional economy to address empirical regularities related to both investor protection and past information. Our newly developed model features not only in terms with a controlling shareholder who diverts a fraction of the output, but also good (or bad) memory in his budget dynamics which can be well-calibrated by a pathwise way from the historical data. We find that poorer investor protection leads to higher stock holdings of controlling holders, lower gross stock returns, lower interest rates, and lower modified stock volatilities if the ownership concentration is sufficiently high. More importantly, by establishing an approximation scheme for good (bad) memory of investors on the historical market information, we conclude that good (bad) memory would increase (decrease) aforementioned dynamics and reveal that good (bad) memory strengthens (weakens) investor protection for minority shareholder when the ownership concentration is sufficiently high, while good (bad) memory inversely weakens (strengthens) investor protection for minority shareholder when the ownership concentration is sufficiently low. Our models implications are consistent with a number of interesting facts documented in the recent literature.
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A new framework for asset price dynamics is introduced in which the concept of noisy information about future cash flows is used to derive the price processes. In this framework an asset is defined by its cash-flow structure. Each cash flow is modelled by a random variable that can be expressed as a function of a collection of independent random variables called market factors. With each such X-factor we associate a market information process, the values of which are accessible to market agents. Each information process is a sum of two terms; one contains true information about the value of the market factor; the other represents noise. The noise term is modelled by an independent Brownian bridge. The market filtration is assumed to be that generated by the aggregate of the independent information processes. The price of an asset is given by the expectation of the discounted cash flows in the risk-neutral measure, conditional on the information provided by the market filtration. When the cash flows are the dividend payments associated with equities, an explicit model is obtained for the share-price, and the prices of options on dividend-paying assets are derived. Remarkably, the resulting formula for the price of a European call option is of the Black-Scholes-Merton type. The information-based framework also generates a natural explanation for the origin of stochastic volatility.
This paper investigates whether security markets price the effect of social distancing on firms operations. We document that firms that are more resilient to social distancing significantly outperformed those with lower resilience during the COVID-19 outbreak, even after controlling for the standard risk factors. Similar cross-sectional return differentials already emerged before the COVID-19 crisis: the 2014-19 cumulative return differential between more and less resilient firms is of similar size as during the outbreak, suggesting growing awareness of pandemic risk well in advance of its materialization. Finally, we use stock option prices to infer the markets return expectations after the onset of the pandemic: even at a two-year horizon, stocks of more pandemic-resilient firms are expected to yield significantly lower returns than less resilient ones, reflecting their lower exposure to disaster risk. Hence, going forward, markets appear to price exposure to a new risk factor, namely, pandemic risk.
Option price data are used as inputs for model calibration, risk-neutral density estimation and many other financial applications. The presence of arbitrage in option price data can lead to poor performance or even failure of these tasks, making pre-processing of the data to eliminate arbitrage necessary. Most attention in the relevant literature has been devoted to arbitrage-free smoothing and filtering (i.e. removing) of data. In contrast to smoothing, which typically changes nearly all data, or filtering, which truncates data, we propose to repair data by only necessary and minimal changes. We formulate the data repair as a linear programming (LP) problem, where the no-arbitrage relations are constraints, and the objective is to minimise prices changes within their bid and ask price bounds. Through empirical studies, we show that the proposed arbitrage repair method gives sparse perturbations on data, and is fast when applied to real world large-scale problems due to the LP formulation. In addition, we show that removing arbitrage from prices data by our repair method can improve model calibration with enhanced robustness and reduced calibration error.
We give an exposition and numerical studies of upper hedging prices in multinomial models from the viewpoint of linear programming and the game-theoretic probability of Shafer and Vovk. We also show that, as the number of rounds goes to infinity, the upper hedging price of a European option converges to the solution of the Black-Scholes-Barenblatt equation.
We consider a stochastic volatility model with Levy jumps for a log-return process $Z=(Z_{t})_{tgeq 0}$ of the form $Z=U+X$, where $U=(U_{t})_{tgeq 0}$ is a classical stochastic volatility process and $X=(X_{t})_{tgeq 0}$ is an independent Levy process with absolutely continuous Levy measure $ u$. Small-time expansions, of arbitrary polynomial order, in time-$t$, are obtained for the tails $bbp(Z_{t}geq z)$, $z>0$, and for the call-option prices $bbe(e^{z+Z_{t}}-1)_{+}$, $z eq 0$, assuming smoothness conditions on the {PaleGrey density of $ u$} away from the origin and a small-time large deviation principle on $U$. Our approach allows for a unified treatment of general payoff functions of the form $phi(x){bf 1}_{xgeq{}z}$ for smooth functions $phi$ and $z>0$. As a consequence of our tail expansions, the polynomial expansions in $t$ of the transition densities $f_{t}$ are also {Green obtained} under mild conditions.
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