Research articles for the 2019-11-17

An approximate solution for the power utility optimization under predictable returns
Dmytro Ivasiuk

This work presents an approximate solution of the portfolio choice problem for the investor with a power utility function and the predictable returns. Assuming that asset returns follow the vector autoregressive process with the normally distributed error terms (what is a popular choice in financial literature to model the return path) it comes up with the fact that portfolio gross returns appear to be normally distributed as a linear combination of normal variables. As it was shown, the log-normal distribution seems to be a good proxy of the normal distribution in case if the standard deviation of the last one is way much smaller than the mean. Thus, this fact is exploited to derive the optimal weights. Besides, the paper provides a simulation study comparing the derived result to the well-know numerical solution obtained by using a Taylor series expansion of the value function.

Capital Budgeting and Idiosyncratic Risk
H. Décaire, Paul
Using an NPV-based revealed-preference strategy, I find that idiosyncratic risk materially affects the discount rate that firms use in their capital budgeting decisions. I exploit quasi-exogenous within-region variation in project-specific idiosyncratic risk and find that, on average, firms inflate their discount rate by 5 percentage points (pp) in response to an 18 pp increase in idiosyncratic risk. Moreover, these discount rate adjustments are negatively associated with various measures of firm profitability. I then explore how proxies for costly external financing and agency frictions relate to discount rate adjustments. I find that firms appear to adjust their discount rate upward as a form of risk management when facing costly external financing frictions. Also, I provide evidence that firms partially insure managers against project-specific underperformance to mitigate discount rate adjustments due to agency frictions.

Cyber bonds and their pricing models
Oleg Kolesnikov,Alexander Markov,Daulet Smagulov,Sergejs Solovjovs

Motivated by the developments in cyber risk treatment in the finance industry, we propose a general framework of cyber bond, whose main purpose is to insure (compensate) losses of a cyber attack. Based on a database of publicly available cyber events, we determine cyber loss distribution parameters and use them to numerically simulate cyber bond price, yield, and other characteristics. We also consider two possible approaches to cyber bond coupon calculation.

Determining Fundamental Supply and Demand Curves in a Wholesale Electricity Market
Sergei Kulakov,Florian Ziel

In this paper we develop a novel method of wholesale electricity market modeling. Our optimization-based model decomposes wholesale supply and demand curves into buy and sell orders of individual market participants. In doing so, the model detects and removes arbitrage orders. As a result, we construct an innovative fundamental model of a wholesale electricity market. First, our fundamental demand curve has a unique composition. The demand curve lies in between the wholesale demand curve and a perfectly inelastic demand curve. Second, our fundamental supply and demand curves contain only actual (i.e. non-arbitrage) transactions with physical assets on buy and sell sides. Third, these transactions are designated to one of the three groups of wholesale electricity market participants: retailers, suppliers, or utility companies. To evaluate the performance of our model, we use the German wholesale market data. Our fundamental model yields a more precise approximation of the actual load values than a model with perfectly inelastic demand. Moreover, we conduct a study of wholesale demand elasticities. The obtained conclusions regarding wholesale demand elasticity are consistent with the existing academic literature.

Idiosyncratic Volatility and the Intertemporal Capital Asset Pricing Model
Li, Gang
When the true asset pricing model cannot be identified, the idiosyncratic volatility obtained from a misspecified model contains information of the hedge portfolio in Merton’s (1973) ICAPM. Empirically, I find that from 1815 to 2018, more than two centuries, neither equal-weighted idiosyncratic volatility (EWIV) nor value-weighted idiosyncratic volatility (VWIV) can forecast stock market returns. However, EWIV and VWIV when applied together are strong predictors of stock market returns over short- and long-term horizons. The explanatory power is economically significant with an out-of-sample forecasting r-squared around 1% for one month and 12% for one year. This finding suggests that EWIV and VWIV together are linked to state variables that capture time-varying investment opportunities. Furthermore, EWIV and VWIV jointly can explain the cross-section of average stock returns with a beta quintile spread of 7.88% per year. I argue that the combination of EWIV and VWIV is a proxy for the conditional covariance risk in the ICAPM. I revisit the debate between Goyal and Santa-Clara (2003) and Bali, Cakici, Yan, and Zhang (2005) and reconcile their mixed findings between the idiosyncratic volatility and future stock market returns. Finally, this paper also gives new insights for the tail risk measure proposed by Kelly and Jiang (2014).

Improvement of Neural Networks with Swarm Intelligence Algorithm for Credit Scoring
Zhang, Runchi,Qiu, Zhiyi
Neural networks are widely used in automatic credit scoring systems with high accuracy and outstanding efficiency. However, in the absence of prior knowledge, it is difficult to determine the combination of parameters, which makes its application limited in practice. This paper presents a higher accurate and robust credit scoring model based on neural networks that have been trained with the optimal swarm intelligence algorithm. Specifically, we trained neural network with seven different swarm intelligence algorithm (bat algorithm, chicken swarm optimization, cuckoo search optimization, firefly algorithm, particle swarm optimization, social spider algorithm, and whale swarm algorithm) to find out the superior combination of parameters in the neural network and to identify the swarm intelligence algorithm seeking the superior solution most efficiency. It shows that the neural networks trained with swarm intelligence algorithm outperforms competing models (logistic regression, naive Bayesian, determinant analysis, K nearest neighbor, decision tree, and support vector machine), inter alia, the neural network trained with social spider algorithm performs the best. Better performance of the neural network is particularly salient with larger dataset, thus making it amenable for real-time implementation.

Minimum Relative Entropy Inference for Normal and Categorical Distributions
Colasante, Marcello,Meucci, Attilio
We represent affine sub-manifolds of exponential family distributions as minimum relative entropy submanifolds. With such representation we derive analytical formulas for the inference from partial evidence on expectations and covariances of multivariate normal distributions; and we improve the numerical implementation via Monte Carlo simulations for the inference from partial evidence of generalized expectation type.

Option pricing in exponential L\'evy models with transaction costs
Nicola Cantarutti,João Guerra,Manuel Guerra,Maria do Rosário Grossinho

We present an approach for pricing European call options in presence of proportional transaction costs, when the stock price follows a general exponential L\'{e}vy process. The model is a generalization of the celebrated work of Davis, Panas and Zariphopoulou (1993), where the value of the option is defined as the utility indifference price. This approach requires the solution of two stochastic singular control problems in finite horizon, satisfying the same Hamilton-Jacobi-Bellman equation, with different terminal conditions. We introduce a general formulation for these portfolio selection problems, and then we focus on the special case in which the probability of default is ignored. We solve numerically the optimization problems using the Markov chain approximation method and show results for diffusion, Merton and Variance Gamma processes. Option prices are computed for both the writer and the buyer.

Pricing Variance Swaps on Time-Changed Markov Processes
Peter Carr,Roger Lee,Matthew Lorig

We prove that the variance swap rate (fair strike) equals the price of a co-terminal European-style contract when the underlying is an exponential Markov process, time-changed by an arbitrary continuous stochastic clock, which has arbitrary correlation with the driving Markov process, provided that the payoff function $G$ of the European contract satisfies an ordinary integro-differential equation, which depends only on the dynamics of the Markov process, not on the clock. We present examples of Markov processes where the function $G$ that prices the variance swap can be computed explicitly. In general, the solutions $G$ are not contained in the logarithmic family previously obtained in the special case where the Markov process is a L\'evy process.

Simulation of Stylized Facts in Agent-Based Computational Economic Market Models
Maximilian Beikirch,Simon Cramer,Martin Frank,Philipp Otte,Emma Pabich,Torsten Trimborn

We study the qualitative and quantitative appearance of stylized facts in several agent-based computational economic market (ABCEM) models. We perform our simulations with the SABCEMM (Simulator for Agent-Based Computational Economic Market Models) tool recently introduced by the authors (Trimborn et al. 2019). Furthermore, we present novel ABCEM models created by recombining existing models and study them with respect to stylized facts as well. This can be efficiently performed by the SABCEMM tool thanks to its object-oriented software design. The code is available on GitHub (Trimborn et al. 2018), such that all results can be reproduced by the reader.

Tracking the circulation routes of fresh coins in Bitcoin: A way of identifying coin miners with transaction network structural properties
Zeng-Xian Lin,Xiao Fan Liu

Bitcoin draws the highest degree of attention among cryptocurrencies, while coin mining is one of the most important fashion of profiting in the Bitcoin ecosystem. This paper constructs fresh coin circulation networks by tracking the fresh coin transfer routes with transaction referencing in Bitcoin blockchain. This paper proposes a heuristic algorithm to identifying coin miners by comparing coin circulation networks from different mining pools and thereby inferring the common profit distribution schemes of Bitcoin mining pools. Furthermore, this paper characterizes the increasing trend of Bitcoin miner numbers during recent years.

Winners from Winners: A Tale of Risk Factors
Chib, Siddhartha,Zhao, Lingxiao,Huang, Dashan,Zhou, Guofu
Taking the union of the risk factors recently proposed by Fama and French (1993, 2015, 2018), Hou, Xue, and Zhang (2015), Stambaugh and Yuan (2017), and Daniel, Hirshleifer, and Sun (2019), a pool we refer to as the “winners”, we ask what collection of winners from winners emerge when each factor is allowed to play the role of a risk factor, or a non-risk factor. Our comparison of 4,095 models shows that a six factor model consisting of Mkt, SMB, MOM, ROE, MGMT, and PEAD as risk factors has the largest Bayesian posterior probability. Moreover, this collection displays superior out-of-sample predictive performance, higher Sharpe ratios, and greater ability in pricing anomalies, than the preceding models. These results suggest that both fundamental and behavioral factors play an important role in explaining the cross-section of expected equity returns.