Distribution Of Financial Returns Research Articles

Multivariate Option Pricing with Gaussian Mixture Distributions and Mixed Copulas

Recently, it has been reported that the hypothesis proposed by the classical black scholes model to price multivariate options in finance were unrealistic, as such, several other methods have been introduced over the last decades including the copulas methods which uses copulas functions to model the dependence structure of underlying assets. However, the previous work did not take into account the use of mixed copulas to assess the underlying assets' dependence structure. The approach we propose consists of selecting the appropriate mixed copula’s structure which captures as much information as possible about the asset’s dependence structure and apply a copulas-based martingale strategy to price multivariate equity options using monte Carlo simulation. A mixture of normal distributions estimated with the standard EM algorithm is also considered for modeling the marginal distribution of financial asset returns. Moreover, the Monte Carlo simulation is performed to compute the values of exotic and up and out barrier options such as worst of, spread, and rainbow options, which shows that the clayton gumble and clayton gaussian have relatively large values for all the options. Our results further indicate that the mixed copula-based approach can be used efficiently to capture heterogeneous dependence structure existing in multivariate assets, price exotic options and generalize the existing results.

Income and racial disparities in financial returns from solar PV deployment

Transitioning the U.S. energy system towards renewable sources of energy generation is critical to reducing global CO2 emissions. Solar photovoltaic (PV) technology is a promising source of renewable energy. Federal and state mandates, incentives, and subsidies increase solar PV adoption and hasten the energy transition. However, these policies are designed with adoption as the main metric of success and fail to consider differences in the stream of financial returns that accrue to households depending on the mode of adoption. Our research investigates financial returns to solar PV adoption by system ownership status (leased or owned). We examine the relationship of total and average financial returns to income and race using data on solar PV systems installed as part of the Massachusetts Solar Renewable Energy Certificate (SREC) program from 2014–2018. We find that financial returns that accrue to households for owned systems are over 300% higher on average than for leased systems. We also find that neighborhoods with more low-income and non-White households receive lower financial returns compared to neighborhoods with higher income and more White households, mostly because these households tend to lease their solar panels. Our results illustrate that the form of participation in the solar PV market (leasing or owning) has significant implications for the distribution of financial returns. Policymakers interested in prioritizing equity in the energy transition should account for this difference in financial returns when designing solar adoption programs, especially those targeted towards low-income and non-White communities.

Do realized higher moments have information content? - VaR forecasting based on the realized GARCH-RSRK model

In this paper, we develop a new model, the Realized GARCH-RSRK, to determine the time-varying distribution of financial returns with realized higher moments. Based on Gram-Charlier expansion (GCE) density, we first explicitly link the expansion parameters with moments that are calculated based on intraday returns using our new model. Then, the Cornish-Fisher expansion is applied to forecast Value-at-Risk (VaR) with estimated moments to demonstrate the economic significance of this new model. Compared with the daily-return-based dynamic higher moments models, the inclusion of realized higher moments significantly improves this model's ability to forecast extreme tails. The empirical results indicate that this new model outperforms the benchmark models when forecasting extreme VaR. In addition, we provide a formula to correct the moments associated with the commonly used squared transformation of GCE. Our empirical evidence highlights the importance of using corrected moments in VaR forecasting.

Financial Return Distributions: Past, Present, and COVID-19.

We analyze the price return distributions of currency exchange rates, cryptocurrencies, and contracts for differences (CFDs) representing stock indices, stock shares, and commodities. Based on recent data from the years 2017–2020, we model tails of the return distributions at different time scales by using power-law, stretched exponential, and q-Gaussian functions. We focus on the fitted function parameters and how they change over the years by comparing our results with those from earlier studies and find that, on the time horizons of up to a few minutes, the so-called “inverse-cubic power-law” still constitutes an appropriate global reference. However, we no longer observe the hypothesized universal constant acceleration of the market time flow that was manifested before in an ever faster convergence of empirical return distributions towards the normal distribution. Our results do not exclude such a scenario but, rather, suggest that some other short-term processes related to a current market situation alter market dynamics and may mask this scenario. Real market dynamics is associated with a continuous alternation of different regimes with different statistical properties. An example is the COVID-19 pandemic outburst, which had an enormous yet short-time impact on financial markets. We also point out that two factors—speed of the market time flow and the asset cross-correlation magnitude—while related (the larger the speed, the larger the cross-correlations on a given time scale), act in opposite directions with regard to the return distribution tails, which can affect the expected distribution convergence to the normal distribution.

Robust Conditional Variance Estimation and Value-at-Risk

A common approach to estimating the conditional volatility of short horizon asset returns is to use an exponentially weighted moving average (EWMA) of squared past returns. The EWMA estimator is based on the maximum likelihood estimator of the variance of the normal distribution, and is thus optimal when returns are conditionally normal. However, there is ample evidence that the conditional distribution of short horizon financial asset returns is leptokurtic, and so the EWMA estimator will generally be inefficient in the sense that it will attach too much weight to extreme returns. In this paper, we propose an alternative EWMA estimator that is robust to leptokurtosis in the conditional distribution of portfolio returns. The estimator is based on the maximum likelihood estimator of the standard deviation of the Laplace distribution, and is a function of an exponentially weighted moving average of the absolute value of past returns, rather than their squares. We employ the robust EWMA estimator to forecast the VaR of aggregate equity portfolios for the US, the UK and Japan using historical simulation. We find that the robust EWMA estimator offers an improvement over the standard EWMA estimator. In particular, the VaR forecasts that it generates are as accurate as those generated by the standard EWMA estimator, but are more efficient in the sense that the average level of capital required to cover against unexpected losses is lower and the root mean square deviation between the VaR forecast and actual returns is smaller. Moreover, the volatility of the VaR forecast itself is substantially lower with the robust EWMA estimator than with the standard EWMA estimator, reflecting its lower sensitivity to extreme returns.

Under what management and policy scenarios can alley cropping be a competitive alternative in the United States Southeast?

Despite statements that it can mitigate financial risk through farm diversification, alley cropping in the United States Southeast has not been comprehensively modeled to estimate potential financial returns and risks. We used a Monte Carlo method to model stochastic financial returns to monocropping agriculture, loblolly pine plantation, and loblolly pine alley cropping in North Carolina, USA, plotting the results from 25,000 iterations to understand financial risk. Under certain scenarios and assumptions, alley cropping did have financial returns comparable to, or potentially higher than, monocropping agriculture, but did not lower overall risk, as measured by the spread of the distribution of financial returns. Pine plantations, on the other hand, did have lower risk than both alley cropping and monocropping. Alley cropping with wider 24.4-m alleys performed better than narrow 12.2-m alleys. Allowing the producer to choose a timber rotation length that optimizes financial returns generated the best financial returns for alley cropping, but this assumes perfect knowledge of the manager and is unrealistic. Current policy programs of government payments for commodity crops and cost-share for tree planting, tend to favor monocropping over alley cropping or pine plantation. A hypothetical system of payments for carbon sequestration does increase pine plantation and alley cropping financial returns, but not to the extent that commodity crop programs currently increase monocropping financial returns, and does not reduce risk significantly. Overall, on average agricultural land in North Carolina, alley cropping may be of value to certain producers, but we find those possibilities to be somewhat limited.

A quantile function approach to the distribution of financial returns following TGARCH models

We develop a novel quantile function approach to the distribution of financial returns that follow threshold GARCH models. We propose a Bayesian method to do estimation and forecasting simultaneously, which ensures that the density forecasts can take account of the variation of model parameters. This method also allows us to handle multiple thresholds easily. We conduct extensive simulation studies and apply our method to Nasdaq returns. The results show that our approach is robust to model specification errors and outperforms some commonly used benchmark models.

Modeling the conditional distribution of financial returns with asymmetric tails

SummaryThis paper proposes a conditional density model that allows for differing left/right tail indices and time‐varying volatility based on the dynamic conditional score (DCS) approach. The asymptotic properties of the maximum likelihood estimates are presented under verifiable conditions together with simulations showing effective estimation with practical sample sizes. It is shown that tail asymmetry is prevalent in global equity index returns and can be mistaken for skewness through the center of the distribution. The importance of tail asymmetry for asset allocation and risk premia is demonstrated in‐sample. Application to portfolio construction out‐of‐sample is then considered, with a representative investor willing to pay economically and statistically significant management fees to use the new model instead of traditional skewed models to determine their asset allocation.

Fat tails in financial return distributions revisited: Evidence from the Korean stock market

This study empirically re-examines fat tails in stock return distributions by applying statistical methods to an extensive dataset taken from the Korean stock market. The tails of the return distributions are shown to be much fatter in recent periods than in past periods and much fatter for small-capitalization stocks than for large-capitalization stocks. After controlling for the 1997 Korean foreign currency crisis and using the GARCH filter models to control for volatility clustering in the returns, the fat tails in the distribution of residuals are found to persist. We show that market crashes and volatility clustering may not sufficiently account for the existence of fat tails in return distributions. These findings are robust regardless of period or type of stock group.

Volatility filtering in estimation of kurtosis (and variance)

Abstract The kurtosis of the distribution of financial returns characterized by high volatility persistence and thick tails is notoriously difficult to estimate precisely. We propose a simple but effective procedure of estimating the kurtosis coefficient (and variance) based on volatility filtering that uses a simple GARCH model. In addition to an estimate, the proposed algorithm issues a signal of whether the kurtosis (or variance) is finite or infinite. We also show how to construct confidence intervals around the proposed estimates. Simulations indicate that the proposed estimates are much less median biased than the usual method-of-moments estimates, their confidence intervals having much more precise coverage probabilities. The procedure alsoworks well when the underlying volatility process is not the one the filtering technique is based on. We illustrate how the algorithm works using several actual series of returns.

Inverted anhamonic oscillator model for distribution of financial returns

We construct a quantum-mechanical model to explain the distribution of financial returns in a stock market when it exhibits an upward trend. By combining a critical phenomenon effect in the form of a power law and the Schrodinger equation, we show that an appropriate potential of the financial returns is given by a time-dependent inverted anharmonic oscillator, whose coefficients depend on the critical time and exponent, which are empirically obtained from the Stock Exchange of Thailand (SET) from 1992 to 1994, during the critical phase of the Asian financial crisis. With the derived potential, we simulate the dynamics of returns as a function of time by employing the time-dependent variational method and the fourth-order Runge-Kutta method. Then we compute key characteristics of the return distribution such as mean, variance, skewness, and kurtosis and compare them with real financial data from SET. The results are found that the mean, skewness and kurtosis show good agreement with actual data computed from SET, but the variance is higher than that from the SET data.

Portfolio selection based on predictive joint return distribution

ABSTRACTA predictive joint return distribution can provide more useful information than moment-based risk measures in portfolio selection. This article develops a D-vine copula-CAViaR method to estimate and predict the joint probability distribution of multiple financial returns. Furthermore, we construct a portfolio model via the generalized Omega ratio inferred from the predicted joint return distribution. The superiority of our method is illustrated through an empirical application on five international stock market indices.

Exploiting tail shape biases to discriminate between stable and student t alternatives

SummaryThe nonnormal stable laws and Student t distributions are used to model the unconditional distribution of financial asset returns, as both models display heavy tails. The relevance of the two models is subject to debate because empirical estimates of the tail shape conditional on either model give conflicting signals. This stems from opposing bias terms. We exploit the biases to discriminate between the two distributions. A sign estimator for the second‐order scale parameter strengthens our results. Tail estimates based on asset return data match the bias induced by finite‐variance unconditional Student t data and the generalized autoregressive conditional heteroscedasticity process.

Dynamic Quantile Function Models

We offer a novel way of thinking about the modelling of the time-varying distributions of financial asset returns. Borrowing ideas from symbolic data analysis, we consider data representations beyond scalars and vectors. Specifically, we consider a quantile function as an observation, and develop a new class of dynamic models for quantile-function-valued (QF-valued) time series. In order to make statistical inferences and account for parameter uncertainty, we propose a method whereby a likelihood function can be constructed for QF-valued data, and develop an adaptive MCMC sampling algorithm for simulating from the posterior distribution. Compared to modelling realised measures, modelling the entire quantile functions of intra-daily returns allows one to gain more insight into the dynamic structure of price movements. Via simulations, we show that the proposed MCMC algorithm is effective in recovering the posterior distribution, and that the posterior means are reasonable point estimates of the model parameters. For empirical studies, the new model is applied to analysing one-minute returns of major international stock indices. Through quantile scaling, we further demonstrate the usefulness of our method by forecasting one-step-ahead the Value-at-Risk of daily returns.

A COMPARATIVE STUDY OF MONOTONE QUANTILE REGRESSION METHODS FOR FINANCIAL RETURNS

Quantile regression methods have been used widely in finance to alleviate estimation problems related to the impact of outliers and the fat-tailed error distribution of financial returns. However, a potential problem with the conventional quantile regression method is that the estimated conditional quantiles may cross over, leading to a failure of the analysis. It is noticed that the crossing over issues usually occur at high or low quantile levels, which are the quantile levels of great interest when analyzing financial returns. Several methods have appeared in the literature to tackle this problem. This study compares three methods, i.e. Cai & Jiang, Bondell et al. and Schnabel & Eilers, for estimating noncrossing conditional quantiles by using four financial return series. We found that all these methods provide similar quantiles at nonextreme quantile levels. However, at extreme quantile levels, the methods of Bondell et al. and Schnabel & Eilers may underestimate (overestimate) upper (lower) extreme quantiles, while that of Cai & Jiang may overestimate (underestimate) upper (lower) extreme quantiles. All methods provide similar median forecasts.

Quantile Regression Model for Measurement of Equity Portfolio Risk a Case Study of Nairobi Securities Exchange

Quantile regression provides a method of estimating quantiles from a conditional distribution density. It is achieves this by minimizing asymmetrically weighted sum of absolute errors thus partitioning the conditional distribution into quantiles. Lower conditional quantiles are of interest in estimation of Value-at-Risk because they indicate downward movement of financial returns. Current risk measurement methods do not effectively estimate the VaR since they make assumptions in the distribution tails. Financial data is sampled frequently leading to a heavier tailed distribution compared to a normal and student t distribution. A remedy to this is to use a method that does not make assumptions in the tail distribution of financial returns. Little research has been done on the usage of quantile regression in the estimation of portfolio risk in the Nairobi Securities Exchange. The main aim of this study was to model the portfolio risk as a lower conditional quantile, compare the performance of this model to the existing risk measurement methods and to predict the Value-at-Risk. This study presents summary of key findings and conclusion drawn from the study. From the fitted conditional quantile GARCH model 62.4% of VaR can be explained by past standard deviation and absolute residual of NSE 20 share index optimal portfolio returns. The fitted model had less proportion of failure of 7.65% compared to commonly used VaR models.

Quantification of VaR: A Note on VaR Valuation in the South African Equity Market

The statistical distribution of financial returns plays a key role in evaluating Value-at-Risk using parametric methods. Traditionally, when evaluating parametric Value-at-Risk, the statistical distribution of the financial returns is assumed to be normally distributed. However, though simple to implement, the Normal distribution underestimates the kurtosis and skewness of the observed financial returns. This article focuses on the evaluation of the South African equity markets in a Value-at-Risk framework. Value-at-Risk is estimated on four equity stocks listed on the Johannesburg Stock Exchange, including the FTSE/JSE TOP40 index and the S & P 500 index. The statistical distribution of the financial returns is modelled using the Normal Inverse Gaussian and is compared to the financial returns modelled using the Normal, Skew t-distribution and Student t-distribution. We then estimate Value-at-Risk under the assumption that financial returns follow the Normal Inverse Gaussian, Normal, Skew t-distribution and Student t-distribution and backtesting was performed under each distribution assumption. The results of these distributions are compared and discussed.

Influences of Trading Volume on Financial Return Distributions: A Reassessment and a Step Further

We assess investors' reaction to new information arrivals in financial markets by examining the relationships between trading volume and the higher moments of returns in 18 international equity and currency markets. Our volume-volatility results support extant information theories and further contribute new evidence of cross market relations between volume and volatility. We also find that the direct impact of volume on the level of negative skewness is less significant for more diversified regional portfolios. Furthermore, the negative interaction between volume and kurtosis can be explained by the differences of opinion in financial markets. We observe stronger interdependence among higher moments in reaction to significant events, but the strength is dampened by trading volume. This result is consistent with trading volume being a source of heteroskedasticity in asset returns.

How does trading volume affect financial return distributions?

We assess investors' reaction to new information arrivals in financial markets by examining the relationships between trading volume and the higher moments of returns in 18 international equity and currency markets. Our volume-volatility results support extant information theories and further contribute new evidence of cross market relations between volume and volatility. We also find that the direct impact of volume on the level of negative skewness is less significant for more diversified regional portfolios. Furthermore, the negative interaction between volume and kurtosis can be explained by the differences of opinion in financial markets. We observe stronger interdependence among higher moments in reaction to significant events, but the strength is dampened by trading volume. This result is consistent with trading volume being a source of heteroskedasticity in asset returns.

The effects of sovereign rating drifts on financial return distributions: Evidence from the European Union

We develop a framework that allows a multivariate system of long memory processes to be conditional on specific regimes to investigate the effects of credit rating agencies' (CRAs) sovereign credit re-ratings on European stock and currency return distributions over the period from 1996 to 2012. We find evidence across rating regimes to support the usefulness of our proposed model in accommodating both long memory and regime switching features. Furthermore, we reveal that the total effects (both direct and indirect forces) of sovereign credit assessments on the first four realized moments of return distributions can be different to their direct effects on individual moments. Thus, we find the rank orders among the three major CRAs to differ for each realized moment and asset market.