Autoregression

Log Heston Model for Monthly Average VIX ArXiv ID: 2410.22471 “View on arXiv” Authors: Unknown Abstract We model time series of VIX (monthly average) and monthly stock index returns. We use log-Heston model: logarithm of VIX is modeled as an autoregression of order 1. Our main insight is that normalizing monthly stock index returns (dividing them by VIX) makes them much closer to independent identically distributed Gaussian. The resulting model is mean-reverting, and the innovations are non-Gaussian. The combined stochastic volatility model fits well, and captures Pareto-like tails of real-world stock market returns. This works for small and large stock indices, for both price and total returns. ...

The VIX as Stochastic Volatility for Corporate Bonds ArXiv ID: 2410.22498 “View on arXiv” Authors: Unknown Abstract Classic stochastic volatility models assume volatility is unobservable. We use the Volatility Index: S&P 500 VIX to observe it, to easier fit the model. We apply it to corporate bonds. We fit autoregression for corporate rates and for risk spreads between these rates and Treasury rates. Next, we divide residuals by VIX. Our main idea is such division makes residuals closer to the ideal case of a Gaussian white noise. This is remarkable, since these residuals and VIX come from separate market segments. Similarly, we model corporate bond returns as a linear function of rates and rate changes. Our article has two main parts: Moody’s AAA and BAA spreads; Bank of America investment-grade and high-yield rates, spreads, and returns. We analyze long-term stability of these models. ...

Electricity Spot Prices Forecasting Using Stochastic Volatility Models ArXiv ID: 2406.19405 “View on arXiv” Authors: Unknown Abstract There are several approaches to modeling and forecasting time series as applied to prices of commodities and financial assets. One of the approaches is to model the price as a non-stationary time series process with heteroscedastic volatility (variance of price). The goal of the research is to generate probabilistic forecasts of day-ahead electricity prices in a spot marker employing stochastic volatility models. A typical stochastic volatility model - that treats the volatility as a latent stochastic process in discrete time - is explored first. Then the research focuses on enriching the baseline model by introducing several exogenous regressors. A better fitting model - as compared to the baseline model - is derived as a result of the research. Out-of-sample forecasts confirm the applicability and robustness of the enriched model. This model may be used in financial derivative instruments for hedging the risk associated with electricity trading. Keywords: Electricity spot prices forecasting, Stochastic volatility, Exogenous regressors, Autoregression, Bayesian inference, Stan ...