# Research articles for the 2021-02-23

Classical Option Pricing and Some Steps Further
Victor Olkhov
arXiv

This paper considers the asset price p as relations C=pV between the value C and the volume V of the executed transactions and studies the consequences of this definition for the option pricing equations. We show that the classical BSM model implicitly assumes that value C and volume V of transactions follow identical Brownian processes. Violation of this identity leads to 2-dimensional BSM-like equation with two constant volatilities. We show that agents expectations those approve execution of transactions can further increase the dimension of the BSM model. We study the case when agents expectations may depend on the option price data and show that such assumption can lead to the nonlinear BSM-like equations. We reconsider the Heston stochastic volatility model for the price determined by the value and the volume and derive 3-dimensional BSM-like model with stochastic value volatility and constant volume volatility. Variety of the BSM-like equations states the problem of reasonable balance between the accuracy and the complexity of the option pricing equations.

Data-driven analysis of central bank digital currency (CBDC) projects drivers
Toshiko Matsui,Daniel Perez
arXiv

In this paper, we use a variety of machine learning methods to quantify the extent to which economic and technological factors are predictive of the progression of Central Bank Digital Currencies (CBDC) within a country, using as our measure of this progression the CBDC project index (CBDCPI). We find that a financial development index is the most important feature for our model, followed by the GDP per capita and an index of the voice and accountability of the country's population. Our results are consistent with previous qualitative research which finds that countries with a high degree of financial development or digital infrastructure have more developed CBDC projects. Further, we obtain robust results when predicting the CBDCPI at different points in time.

Eigenportfolios of US Equities for the Exponential Correlation Model
Akansu, Ali,Xiong, Anqi
SSRN
In this paper, the eigendecomposition of a Toeplitz matrix populated by an exponential function in order to model empirical correlations of US equity returns is investigated. The closed-form expressions for eigenvalues and eigenvectors of such a matrix are available. These eigenvectors are used to design the eigenportfolios of the model, and we derive their performance for the two metrics. The Sharpe ratios and profit-and-loss curves (P&Ls) of eigenportfolios for twenty-eight of the thirty stocks in the Dow Jones Industrial Average index are calculated for the end-of-day returns from July 1, 1999 to November 1, 2018, several different subintervals and three other baskets in order to validate the model. The proposed method provides eigenportfolios that mimic those based on an empirical correlation matrix generated from market data. The model brings new insights into the design and evaluation of eigenportfolios for US equities and other asset classes. These eigenportfolios are used in the design of trading algorithms, including statistical arbitrage, and investment portfolios. Here, P&Ls and Sharpe ratios of minimum variance, market and eigenportfolios are compared along with the index and three sector exchange-traded funds (XLF, XLI and XLV) for the same time intervals. They show that the first eigenportfolio outperforms the others considered in the paper.KEY MESSAGES1) Empirical correlations of asset returns in a group of stocks are approximated by the exponential correlation model that populates a Toeplitz matrix with closed-form expressions for its eigenvalues and eigenvectors. 2) Exponential model based Toeplitz matrix and measurements based empirical correlation matrix are used to create their eigensubspaces and eigenportfolios for performance comparisons by using risk normalized annual returns. 3) It is demonstrated in the paper that the exponential approximation to empirical correlations provide a good model to design eigenportfolios and to evaluate their performance.

Exploring the role of Awareness, Government Policy, and Infrastructure in adapting B2C E-Commerce to East African Countries
Emmanuel H.Yindi,Immaculate Maumoh,Prisillah L. Mahavile
arXiv

Higher Purpose, Banking and Stability
Bunderson, Stuart,Thakor, Anjan V.
SSRN
This paper provides survey evidence on higher purpose for individuals and organizations and develops a theoretical model consistent with the evidence. The survey of 1,019 individuals in the U.S. sought to learn about their commitment to and perceived value from personal and organizational higher purpose. One striking finding from the survey is that when an organization has a written statement of higher purpose, its employees tend to trust their leaders to not only be socially responsible, but also to make better business decisions, i.e. corporate governance is perceived to be better by the employees. We then develop a simple theoretical model that provides an economic rationale for this finding. In the model, an investment in higher purpose credibly signals the firm ownerâ€™s ability/marginal productivity and elicits higher employee effort. When put in a banking context, the model shows that optimal contracting within a bank that pursues a higher purpose leads to higher wages for employees, higher monitoring effort and a lower probability of bank failure when the bank has more equity capital, even though the bankâ€™s capital does not affect the bankâ€™s higher purpose investment. Even absent a signaling motivation for investing in higher purpose, these results are qualitatively sustained if the bankâ€™s employees care about its purpose. Additionally, in this case, banks that invest more in higher purpose pay lower wages, elicit higher employee effort and have lower failure probabilities for any given capital ratio. Banks with higher capital ratios still pay higher wages, but the effect of capital on wages becomes weaker as the bankâ€™s higher purpose investment increases. The decrease in the exposure of the deposit insurer due to higher capital goes beyond the direct impact of capital on the bankâ€™s probability of failure.

Housing Returns, Precautionary Savings and Consumption: Micro Evidence From China
Pan, Xuefeng,Wu, Weixing
SSRN
We investigate how changes in home prices affect consumption in China via a wealth channel. Examining a panel of 7955 households via fixed effects and instrumental variable methods, we find a marginal propensity to consume out of housing wealth (home-price MPC) that is concentrated on goods consumed for pleasure rather than necessity. This trend is driven by the value of second homes rather than that of primary residences, suggesting a wealth channel. We further examine whether returns on housing investment, including rental income and home appreciation, fund the wealth channel; however, we find little supporting evidence. In contrast, a reduction in health risk increases the home-price MPC, but a reduction in income risk that also relieves precautionary saving motives does not. Our results are robust to alternative data, common-factor progress, expenditure shocks and bequest motives. We contribute by examining second homes, which carry little of the dual nature of housing that primary residences do, to identify a controversial wealth channel, and by studying the relative effects of health and income risks on the wealth channel.

Intangible Capital in Factor Models
Gulen, Huseyin,Li, Dongmei,Peters, Ryan H.,Zekhnini, Morad
SSRN
We study the impact of increasingly substantial intangible capital on popular empirical factor models. Conceptually, we explicitly incorporate intangible investment/capital into the dividend discount model in Fama and French (2015) and the classical q-factor model in Hou, Xue, and Zhang (2015) and illustrate the distinctive effects of intangibles on expected stock returns via well-known return predictors such as the book-to-market ratio, investment, and profitability. Our theoretical frameworks highlight the importance of separating tangible from intangible investments and addressing the effects of intangible investment on profitability and other valuation measures. Empirically, we show that incorporating intangibles significantly improves the Fama-French three- and five-factor models and the q-factor model, especially over recent decades during which intangible investments become even more crucial to firms' growth and success.

Is Financial Advice a Cure-All or the Icing on the Cake for Financial Literacy? Evidence From Financial Market Participation in China
Pan, Xuefeng,Wu, Weixing,Zhang, Xuyang
SSRN
We examine how financial advice interacts with financial literacy to shape household decisions on stock market participation in China. Particularly, we investigate how the effect of financial advice varies with economic expectations, preferences for asset diversification and the level of financial literacy. Feeding the data of 5274 households into a Probit model that predicts the probability of holding stocks, we find that, while an increase in financial literacy significantly raises the stock market participation of all households, seeking financial advice only increases the participation for those households which have a preference for asset diversification or which have an optimistic expectation about the economy. Moreover, the effect of financial advice is concentrated on households with high financial literacy, implying that an insufficient level of financial literacy is the reason for the poor performance of financial advice in China. We also examine if there are influential trust or quality concerns which would reduce the effectiveness of financial advice but we find no significant evidence for it.

Linear-quadratic stochastic delayed control and deep learning resolution
William Lefebvre,Enzo Miller
arXiv

We consider a class of stochastic control problems with a delayed control, both in drift and diffusion, of the type dX t = $\alpha$ t--d (bdt + $\sigma$dW t). We provide a new characterization of the solution in terms of a set of Riccati partial differential equations. Existence and uniqueness are obtained under a sufficient condition expressed directly as a relation between the horizon T and the quantity d(b/$\sigma$) 2. Furthermore, a deep learning scheme is designed and used to illustrate the effect of delay on the Markowitz portfolio allocation problem with execution delay.

Modeling the Bid and Ask Prices of Options
SSRN
Comonotone additivity for two price economy bid and ask prices motivates combining bid prices for call options with the ask prices for puts and the converse to construct two densities (termed lower and upper) reflected by these prices. Bilateral gamma models are fit to estimate these the lower and upper densities for 183 underlying equity assets on 26 days in 2020 for four maturities. Distances between the densities are reported along with measures for the upper density being higher in the convex order. Cases are presented when the upper density reflects an upper random variable that is an independent multiplicative shift over the lower one and when there is a multiplicative mean preserving spread between them that is not independent. It is observed that the imposition of an independent multiplicative shift may be too restrictive in general. Convex orders across maturities are then reported on. Finally martingale models mixing independent and identically distributed shocks with components based on self similarity are fit to the option surface across all strikes and maturities.

Multivariate higher order moments in multi-state life insurance
arXiv

It is well-known that combining life annuities and death benefits introduce opposite effects in payments with respect to the unsystematic mortality risk on the lifetime of the insured. In a general multi-state framework with multiple product types, such joint effects are less trivial. In this paper, we consider a multivariate payment process in multi-state life insurance, where the components are defined in terms of the same Markovian state process. The multivariate present value of future payments is introduced, and we derive differential equations and product integral representations of its conditional moments and moment generating function. Special attention is given to pair-wise covariances between two present values, where results closely connected to Hattendorff type of results for the variance are derived. Numerical examples are shown in a disability model and a spouse model to illustrate applicability of the results on insurance of a single life as well as two dependent lives.

On spatially irregular ordinary differential equations and a pathwise volatility modelling framework
Ryan McCrickerd
arXiv

This thesis develops a new framework for modelling price processes in finance, such as an equity price or foreign exchange rate. This can be related to the conventional Ito calculus-based framework through the time integral of a price's squared volatility. In the new framework, corresponding processes are strictly increasing, solve random ODEs, and are composed with geometric Brownian motion to obtain price processes. The new framework has no dependence on stochastic calculus, so processes can be studied on a pathwise basis using probability-free ODE techniques and functional analysis.

The ODEs considered depend on continuous driving functions which are spatially irregular', meaning they need not have any spatial regularity properties such as Holder continuity. They are however strictly increasing in time, thus temporally asymmetric. When sensible initial values are chosen, IVP solutions are also strictly increasing, and the IVPs' solution set is shown to contain all differentiable bijections on the non-negative reals. This enables the modelling of any non-negative volatility path which is not zero over intervals, via the time derivative of solutions. Despite this generality, new well-posedness results establish the uniqueness of solutions going forwards in time, and continuity of the IVPs' solution map.

Motivation to explore this framework comes from its connection with the Heston volatility model. The framework explains how Heston price processes can converge to an interval-valued generalisation of the NIG Levy process, and reveals a deeper relationship between integrated CIR processes and the IG Levy process. Within this framework, a Riemann-Liouville-Heston' martingale model is defined which generalises these relationships to fractional counterparts. Implied volatilities from this model are simulated, and exhibit features characteristic of leading `rough' volatility models.

Online Appendix to: Co-movement of Price and Intrinsic Value - Does Accounting Information Matter?
Mehring, Oliver,Olsson, Per,Sievers, Soenke,Sofilkanitsch, Christian
SSRN

Option Surface Econometrics with Applications
SSRN
At each maturity a discrete return distribution is inferred from option prices. Option pricing models imply a comparable theoretical distribution. As both the transformed data and the option pricing model deliver points on a simplex, the data is statistically modeled by a Dirichlet distribution with expected values given by the option pricing model. The resulting setup allows for maximum likelihood estimation of option pricing model parameters with standard errors enabling the test of hypotheses. Hypothesis testing is illustrated by testing for risk neutral return distributions being consistent with Brownian motion with drift time changed by a subordinator. Models mixing processes of independent increments with processes related to solution of Ornstein Uhlenbeck (OU) equations are tested for the presence of the OU component. OU equations are a form of perpetual motion processes continuously responding to their past changes. The tests support the rejection of Brownian subordination and the presence of a perpetual motion component.

Personalized Digital Information and Tax-favoured Retirement Savings: Quasi-experimental Evidence from Administrative Data
Daminato, Claudio,Filippini, Massimo,Haufler, Fabio
SSRN
This paper studies the impact of making personalized digital information available through a pension app on contributions to tax-favored retirement accounts. Using Swiss administrative pension fund data, we document limited take-up of fiscal incentives for retirement savings. Exploiting the staggered introduction of the pension app across occupational pension funds, we show that its availability increases individual tax-favored contributions. Men and higher-income earners are more likely to access the digital environment and respond to its introduction. These findings suggest that providing access to a pension app reduces information and transaction costs and facilitates the take-up of financial incentives for retirement saving.

Positionality-Weighted Aggregation Methods for Cumulative Voting
Takeshi Kato,Yasuhiro Asa,Misa Owa
arXiv

Respecting minority opinions is vital in solving social problems. However, minority opinions are often ignored in general majority rules. To build consensus on pluralistic values and make social choices that consider minority opinions, we propose aggregation methods that give weighting to the minority's positionality on cardinal cumulative voting. Based on quadratic and linear voting, we formulated three weighted aggregation methods that differ in the ratio of votes to cumulative points and the weighting of the minority to all members, and assuming that the distributions of votes follow normal distributions, we calculated the frequency distributions of the aggregation results. We found that minority opinions are more likely to be reflected proportionately to the average of the distribution in two of the above three methods. This implies that Sen and Gotoh's idea of considering the social position of unfortunate people on ordinal ranking in the welfare economics, was illustrated by weighting the minority's positionality on cardinal voting. In addition, it is possible to visualize the number and positionality of the minority from the analysis of the aggregation results. These results will be useful to promote mutual understanding between the majority and minority by interactively visualizing the contents of the proposed aggregation methods in the consensus-building process. With the further development of information technology, the consensus building based on big data will be necessary. We recommend the use of our proposed aggregation methods to make social choices for pluralistic values such as social, environmental, and economic.

Price Discrimination in International Airline Markets
Gaurab Aryal,Charles Murry,Jonathan W. Williams
arXiv

We develop a model of inter-temporal and intra-temporal price discrimination by monopoly airlines to study the ability of different discriminatory pricing mechanisms to increase efficiency and the associated distributional implications. To estimate the model, we use unique data from international airline markets with flight-level variation in prices across time, cabins, and markets, as well as information on passengers' reasons for travel and time of purchase. We find that the ability to screen passengers across cabins every period increases total surplus by 35% relative to choosing only one price per period, with both the airline and passengers benefiting. However, further discrimination based on passenger's reason to traveling improve airline surplus at the expense of total efficiency. We also find that the current pricing practice yields approximately 89% of the first-best welfare. The source of this inefficiency arises mostly from dynamic uncertainty about demand, not private information about passenger valuations.

SSRN
Time changes of Brownian motion impose restrictive jump structures in the motion of asset prices. Quadratic variations also depart from time changes. Joint Laplace Fourier transforms for quadratic variation and the stock are developed. They are used to study the multiple of the cap strike over the variance swap quote attaining a given percentage price reduction for the capped variance swap. Bootstrapped data and simulated paths spaces are used to study the multiple of the dynamic hedge return desired by a realized variance swap contract. The optimized hedge multiple in the bootstrapped data is consistently near unity. Simulated path spaces allow for departures matched by also similarly altering the position in the log contract. Value multiples of quadratic variation over variance swaps are consistently larger in simulations and bootstrapped data. The departures reflect negative dividend yields embedded in the skewness of risk neutral distributions.

Quant Investing in Cluster Portfolios
Akansu, Ali,Avellaneda, Marco,Xiong, Anqi
SSRN
This paper discusses portfolio construction for investing in N given assets, e.g. constituents of the Dow Jones Industrial Average (DJIA) or large cap stocks, which is based on partitioning the investment universe into clusters. The clusters are determined from the trailing correlation matrix via an information theoretic algorithm that uses thresholding of high-correlation pairs. We calculate the Principal Eigenvector of each cluster from its correlation matrix and the corresponding eigenportfolio. The cluster portfolios are combined into a single N-asset portfolio based on a weighting scheme for the clusters. Various tests conducted on components of DIA and a thirty-stock basket of large-cap stocks indicate that the new portfolios are superior to the DIA and other Mean-Variance portfolios in terms of risk-adjusted returns from 2009 to 2019. We also tested the cluster portfolios for the larger basket of 373 S&P500 components from 2001 to 2019. The test results give convincing evidence that cluster-based portfolio can outperform passive investing.KEY MESSAGES1) A correlation-based set partitioning algorithm that divides the investment universe dynamically into clusters of assets proposed.2) The principal eigenvector of each cluster from its correlation matrix is calculated and the corresponding eigenportfolio. The cluster portfolios of varying sizes combined into a single N-asset portfolio based on a weighting scheme for the clusters.3) The proposed portfolio outperforms hierarchical risk parity (HRP) portfolio, eigenportfolio (EP), and a few other portfolio constructions and relevant ETFs based on several tests performed with market data.4) The performance comparisons give convincing evidence that cluster-based long-only investment portfolio can outperform passive investing.

Reshaping the Local Marketplace: Financing, Independent Businesses, Large Firms, and COVID
Maksimovic, Vojislav,Yang, Liu
SSRN
We use granular high-frequency data to precisely estimate the effect of COVID demand shocks, bank branches, PPP, and neighborhood peers within 200 yards of retail pharmacies. Neighborhood banks softened the immediate shock for independent pharmacies, but the effect is small. PPP has a larger economic effect, significantly driven by peer effects. If neighborhood stores obtain PPP, whether locally or from out-of-state intermediaries, the store's probability of PPP uptake increases. The COVID shock has accelerated the decline of independent pharmacies, increasing the HHI in local markets by an economically significant 8%, which neither the PPP nor access to local banks prevents.

Securities Law: Overview and Contemporary Issues
Newman, Neal,Trautman, Lawrence J.
SSRN
This is not your grandfatherâ€™s SEC anymore. Rapid technological change has resulted in novel regulatory issues and challenges, as law and policy struggles to keep pace. The U.S. Securities and Exchange Commission (SEC) reports that â€œthe U.S. capital markets are the deepest, most dynamic, and most liquid in the world. They also have evolved to become increasingly fast and extraordinarily complex. It is our job to be responsive and innovative in the face of significant market developments and trends.â€ With global markets increasingly interdependent and interconnected and, â€œas technological advancements and commercial developments have changed how our securities markets operate, our ability to remain an effective regulator requires us to continuously monitor the market environment and, as appropriate, adjust and modernize our expertise, rules, regulations, and oversight tools and activities.â€ The success or failure of our society, jobs of a global workplace, and the ability of families everywhere to feed, clothe, and house themselves depends on the success of the SEC in providing fair and open access to capital through efficient markets. Our paper proceeds in eight parts. First, we explain the genesis and role of the Securities and Exchange Commission (SEC). Second, the definition of and what exactly constitutes a â€œsecurityâ€ is provided. Third, the securities issuance process is discussed. Fourth, we focus our discussion on The Division of Enforcement. Fifth, we discuss corporate governance and the SEC. Sixth, we explore the difficult task of governing during times of rapid technological change. Seventh, we examine contemporary issues that face the Commission. And last, we conclude.

Two-sided Singular Control of an Inventory with Unknown Demand Trend
Salvatore Federico,Giorgio Ferrari,Neofytos Rodosthenous
arXiv

We study the problem of optimally managing an inventory with unknown demand trend. Our formulation leads to a stochastic control problem under partial observation, in which a Brownian motion with non-observable drift can be singularly controlled in both an upward and downward direction. We first derive the equivalent separated problem under full information with state-space components given by the Brownian motion and the filtering estimate of its unknown drift, and we then completely solve the latter. Our approach uses the transition amongst three different but equivalent problem formulations, links between two-dimensional bounded-variation stochastic control problems and games of optimal stopping, and probabilistic methods in combination with refined viscosity theory arguments. We show substantial regularity of (a transformed version of) the value function, we construct an optimal control rule, and we show that the free boundaries delineating (transformed) action and inaction regions are bounded globally Lipschitz continuous functions. To our knowledge this is the first time that such a problem has been solved in the literature.