On Long-Memory Properties of Asset Return Volatility

Abstract

Long-range dependent phenomena are found in many scientific fields, ranging from hydrology to internet traffic to finance. This talk focuses on the volatility series of asset returns. Many studies in the literature show that asset return volatility exhibits long-memory characteristics, i.e. sample autocorrelation functions of a volatility series decay slowly. On the other hand, studies also show that many simple disturbances to a short-range dependent series may generate sample behavior which resembles long-range dependence. Two well-known examples are structural breaks and regime switching with certain transition probability. Unfortunately, the detection of true long-range dependence is a rather difficult issue. In this talk, we propose a test statistic based on temporal aggregation to distinguish between true and spurious long-range dependence. For a long time series, the test has good size and power properties. We apply the test to two exchange rate series, and the test fails to reject the long-range dependence in the exchange rate volatility. We then investigate the effects of long-range dependence in asset volatility on derivative pricing. In particular, we consider the problem of mispricing in long term options when the long-range dependence in volatility is misidentified.