Financial Market Risk

5 Frequency analysis of financial risk

 

 

 

 

5.1 Introduction

In Chapter 3 we analyzed the marginal distribution and in Chapter 4 the temporal dependence of investment returns identified as Fractional Brownian Motion (FBM). We'll now prepare to look at these two aspects of the research problem to characterize the long-term temporal risks of such returns simultaneously in their frequency and time domains. As we discussed in the preceding four chapters, Geometric Brownian Motion (GBM) increments are, per definition, independent and stationary (i.i.d.). Their stationarity allows for Fourier analysis, i.e., linear analysis in the frequency domain, since their (co-) variances and therefore their (co-) frequencies are constant. These increment series ...