Organizer:

Jianming Ye, jmy@quest.baruch.cuny.edu

Speakers

1:30 p.m.
Extreme Value Analysis of Financial Data
Ruey S. Tsay, Graduate School of Business, University of Chicago

Large price movements in security markets are relatively rare, but important. They are the main focus of some applications such as risk management. In this paper, we apply extreme value theory to investigate the occurrence times and excesses over some high thresholds of financial time series. We separate positive returns from negative ones and study properties of both returns. In particular, we investigate the effect of changes in U.S. daily interest rates on daily returns of the S&P 500 index from 1962 to 1997. The effect is found highly significant and contributes to the heavy-tailed behavior of stock returns. We found strong evidence that the tail behavior of index returns evolves over time, but no evidence that the daily mean rate of the return exceeding a high threshold is increasing. However, for negative returns, there is an increasing probability of large excesses over high thresholds if exceedances occur. The analysis also confirms volatility clusterings in stock markets and shows an increased volatility of daily returns in October, November, and December. Finally, our models indicate that daily returns of the S&P 500 index do not follow a log-normal distribution.

2:00 p.m.
Nonparametric Prediction of Volatility, and its Application to Finance
Per Mykland, Department of Statistics, University of Chicago

The problem of hedging options under uncertainty of volatility is discussed. We display ways of constructing prediction intervals for future cumulative volatility, and then discuss how to convert such an interval into a trading strategy that is valid whenever the realized outcome is in the interval. An algorithm is presented that will do this conversion in the presence of the underlying security and options on this security.

2:30 p.m.
Nonlinear and Nonparametric Accounting-based Valuation Models
Mark Finn, Kellogg School of Management, Northwestern University

We explore nonlinear accounting-based valuation as an alternative to traditional linear valuation. We first outline statistical problems with the linear approach and describe pronounced nonlinear features in the empirical relationship between stock prices and accounting numbers. Next we identify the economic rationale behind such nonlinearity, which is due to real (both investment and abandonment) options. We show that the autoregressive assumption put forward by Ohlson (1995) does not generate such features, and offer an analytical derivation of a nonlinear alternative. We then test the linear model against an array of nonlinear and nonparametric competitors. We find rather striking and clear-cut evidence of large improvements in the fit of the nonlinear, and particularly the nonparametric, models. These models are then used to construct a parsimonious parametric model that fits the data very well out-of-sample.