Stochastic Volatilities and Correlations

STOCHASTIC VOLATILITIES AND CORRELATIONS, EXTREME VALUES AND MODELING THE MACROECONOMIC ENVIRONMENT, UNDER WHICH BRAZILIAN BANKS OPERATE
By: Theodore M. Barnhill, Marcos Rietti Souto

Abstract:

Forecasting stochastic volatilities has been a topic under intense scrutiny, particularly after the 1987 crash in the U.S. market. However, only few studies have focused on emerging economies and on variables other than stock market index and foreign exchange rate. This study expands the empirical literature on many fronts: (i) we utilize monthly data on several different macroeconomic time series from Brazil; (ii) we assess forecast performance for both variance and covariance models; (iii) we conduct a Monte Carlo exercise to examine the distribution of simulated returns via exponentially weighted moving average model, and test for heavy-tailed distributions; and (iv) we simulate Credit Transition Matrix for two Brazilian banks and compare the results with results obtained in Barnhill, Souto, and Tabak (2003), with the same banks, when volatilities and correlations were treated as time-invariant. Our findings add evidence to the bulk of research done in this area. First, there is no single stochastic model that consistently outperformed other models, a finding that is robust to different forecast error measures. However, differences in out-of-sample forecast errors among models are reasonably small. We opted for the autoregressive exponentially weighted moving average process for a matter of computational time and effort. Second, estimation of fat tail index for historical data on returns on interest rates, FX rate, commodities prices, and on stock price indices, both daily and monthly, were consistent with empirical and anecdotal evidence of heavy-tailed distributions for these series. The simulated return distributions for the same variables have also produced tail index of similar magnitude, which corroborate our claim that our Monte Carlo simulation methodology is capable of producing simulated returns that are reasonably close to what is observed in historical data. Finally, when stochastic volatilities and correlations are incorporated within our Monte Carlo simulation framework, (further results forthcoming).