Monte Carlo estimation of stochastic volatility for stock values and potential applications to temperature and seismographic data.
详细信息
文摘
The purpose of this research is to develop and apply numerical methods to the analysis of time series such as stock returns, temperature measurements and seismographic readings. In particular to measure and if possible predict a non-observable quantity ("volatility" in the case of stock returns). For a given time series of observations, a corresponding time series of volatility estimates is generated along with error estimates. From this we develop an n state Markov Chain description for the volatility. The program used to estimate volatility generates candidate distributions of volatility data and applies system dynamics to the generated data. Then the volatility is estimated by comparing the observed data to the outputs resulting from the a large number of test inputs (usually 10,000 to 125,000). To check accuracy test data is generated and compared to the resulting volatility estimates. To determine the n states of the Markov Chain the frequency distribution of volatility estimates is fitted with a mixture of normal distributions that best approximates it. Markov Chain volatility models are derived from minute data for several large companies for the week of the Bear Steams collapse (3-10-08； IBM, Lehmann Brothers, Bank of America, Chevron) and from daily data for some important indices (SP500, New York Stock Exchange, Nasdaq, Dow Jones) Other possible applications include temperature time series and seismographic earthquake recordings. The program estimates monthly and hourly "volatility" for temperature time series from NY State. Overall trends, trends in high and trends in low volatility intervals were compared [the linear temperature trend in both the high and low volatility months had a positive slope, the slope for the high volatility months being somewhat greater than for the lower volatility months]. Other trends observed were an increase in yearly average volatility in the last two years and an annual cycle of higher volatility in late winter/early spring and lower volatility in late fall Seismographic data was analyzed and shifts in "volatility" level were compared to threshold levels used in detecting and timing shock waves during earthquakes