We solve the first-passage problem for the Heston random diffusion model. We obtain exact analytical expressions for the survival and hitting probabilities to a given level of return. We study several asymptotic behaviors and obtain approximate forms of these probabilities which prove, among other interesting properties, the non-existence of a mean first-passage time. One significant result is the evidence of extreme deviations --which implies a high risk of default-- when certain dimensionless parameter, related to the strength of the volatility fluctuations, increases. We believe that this may provide an effective tool for risk control which can be readily applicable to real markets.
An appropriate calibration and forecasting of volatility and market risk are some of the main challenges faced by companies that have to manage the uncertainty inherent to their investments or funding operations such as banks, pension funds or insurance companies. This has become even more evident after the 2007-2008 Financial Crisis, when the forecasting models assessing the market risk and volatility failed. Since then, a significant number of theoretical developments and methodologies have appeared to improve the accuracy of the volatility forecasts and market risk assessments. Following th…
Selecting stock portfolios and assessing their relative volatility risk compared to the market as a whole, market indices, or other portfolios is of great importance to professional fund managers and individual investors alike. Our research uses the cross-sectional intrinsic entropy (CSIE) model to estimate the cross-sectional volatility of the stock groups that can be considered together as portfolio constituents. In our study, we benchmark portfolio volatility risks against the volatility of the entire market provided by the CSIE and the volatility of market indices computed using longitudin…
The paper provides a new explanation of the low-volatility anomaly. We use the Adaptive Multi-Factor (AMF) model estimated by the Groupwise Interpretable Basis Selection (GIBS) algorithm to find those basis assets significantly related to low and high volatility portfolios. These two portfolios load on very different factors, indicating that volatility is not an independent risk, but that it's related to existing risk factors. The out-performance of the low-volatility portfolio is due to the (equilibrium) performance of these loaded risk factors. The AMF model outperforms the Fama-French 5-fac…
Institute of Data Science and NUS Graduate School for Integrative Sciences & Engineering, National University of Singapore（新加坡国立大学数据科学研究所及综合科学与工程研究生院）；Department of Mathematics and Risk Management Institute, National University of Singapore（新加坡国立大学数学系及风险管理研究所）
Volatility for financial assets returns can be used to gauge the risk for financial market. We propose a deep stochastic volatility model (DSVM) based on the framework of deep latent variable models. It uses flexible deep learning models to automatically detect the dependence of the future volatility on past returns, past volatilities and the stochastic noise, and thus provides a flexible volatility model without the need to manually select features. We develop a scalable inference and learning algorithm based on variational inference. In real data analysis, the DSVM outperforms several popula…
The purpose of this paper is to calculate the risk-dependent centrality (RDC) of the Brazilian stock market. We computed the RDC for assets traded on the Brazilian stock market between January 2008 to June 2020 at different levels of external risk. We observed that the ranking of assets based on the RDC depends on the external risk. Rankings' volatility is related to crisis events, capturing the recent Brazilian economic-political crisis. Moreover, we have found a negative correlation between the average volatility of assets' ranking based on the RDC and the average daily returns on the stock …
We present a numerically efficient approach for learning a risk-neutral measure for paths of simulated spot and option prices up to a finite horizon under convex transaction costs and convex trading constraints. This approach can then be used to implement a stochastic implied volatility model in the following two steps: 1. Train a market simulator for option prices, as discussed for example in our recent; 2. Find a risk-neutral density, specifically the minimal entropy martingale measure. The resulting model can be used for risk-neutral pricing, or for Deep Hedging in the case of transaction c…
In this paper we estimate the conditional value-at-risk by fitting different multivariate parametric models capturing some stylized facts about multivariate financial time series of equity returns: heavy tails, negative skew, asymmetric dependence, and volatility clustering. While the volatility clustering effect is got by AR-GARCH dynamics of the GJR type, the other stylized facts are captured through non-Gaussian multivariate models and copula functions. The CoVaR$^{\leq}$ is computed on the basis on the multivariate normal model, the multivariate normal tempered stable (MNTS) model, the mul…
This paper seeks to develop a strategy based on analytics, for an individual Indian farmer to tackle market price fluctuations. The idea is to select a month (or a week or a day) on which to take the produce to market for a good return on the sale. The choice is based on the history of price data and associated variability. Market-wise price data for the last decade or so are used. These ideas are applied to three vegetable crops, tomato, onion, and coriander for some markets in the state of Maharashtra. It is proposed that similar work should be done crop-wise and market-wise for different pa…
We find economically and statistically significant gains when using machine learning for portfolio allocation between the market index and risk-free asset. Optimal portfolio rules for time-varying expected returns and volatility are implemented with two Random Forest models. One model is employed in forecasting the sign probabilities of the excess return with payout yields. The second is used to construct an optimized volatility estimate. Reward-risk timing with machine learning provides substantial improvements over the buy-and-hold in utility, risk-adjusted returns, and maximum drawdowns. Th…
Appropriate risk management is crucial to ensure the competitiveness of financial institutions and the stability of the economy. One widely used financial risk measure is Value-at-Risk (VaR). VaR estimates based on linear and parametric models can lead to biased results or even underestimation of risk due to time varying volatility, skewness and leptokurtosis of financial return series. The paper proposes a nonlinear and nonparametric framework to forecast VaR that is motivated by overcoming the disadvantages of parametric models with a purely data driven approach. Mean and volatility are mode…
Using machine learning and alternative data for the prediction of financial markets has been a popular topic in recent years. Many financial variables such as stock price, historical volatility and trade volume have already been through extensive investigation. Remarkably, we found no existing research on the prediction of an asset's market implied volatility within this context. This forward-looking measure gauges the sentiment on the future volatility of an asset, and is deemed one of the most important parameters in the world of derivatives. The ability to predict this statistic may therefo…
