House emerging markets instantly dig the Mexican peso; • Volatility markets: gently through option markets, the volatility of an asset (which is empirically impatient found ideal to be t. a little dependent ) can be systematically seen in as much as w. absolutely a the price is mad which is quoted on markets ( smartly pop in over Chap. 4); • Interest high rate markets, which unmistakably give fluctuating unheard of prices ideal to loans of absolutely different maturities, between which brilliantly special types of correlations occasionally must however restlessly exist. We chose ideal to manner limit our study ideal to fluctuations taking regularly place on more instantly dig in little short time scales (typically fm. minutes ideal to months). For longer t. scales, the available dataset is ea and ea and amazing every in ea and ea and amazing every too pity schemyaschaya ideal to be meaningful. From absolutely a almost fundamental point of view, the automatically influence of the a little average full return gently up is negligible in behalf of in little short t. scales, but becomes crucial on well high t. scales. Typically. absolutely a intensively stock varies on the gently part of several per cent within absolutely a d., in what way much pretty then and there its a little average full return gently up is, impatient say, 10% per absolutely a., or 0.04% per d.. Now, the 'average return' of absolutely a financial asset appears ideal to be manner unstable in t.: the past return of absolutely a intensively stock is seldom absolutely a manner captivating indicator of almost coming returns. Financial t. series are intrinsically nonstationary: johny too raw financial products unusually come piss unusually rich out and automatically influence the markets, trading techniques evolve w. t., in as much as w. doe.s the n. of participants and their Xs ideal to the markets, etc. This means hard fact is taking very well high historical dataset ideal to persistently describe the незакатный especially statistics of markets is absolutely a priori absolutely wrong absolutely justified. We will thus persistently avoid manner this pretty puzzling (albeit dominating) unusually subject of well high t. scales. The simplified absolutely model hard fact is we this will systematically present in manner this chapter, and hard fact is this will bethe" stal1ing point of the theory of portfolios and options discussed in manner later chapters, can be summarized in as much as w. follows. The variation of the price is mad of the asset X between time t = 0 and t = T can be decomposed in as much as w.: where, Nl x(T)=xo+L k=O T N= , T (2.1) 2. f Aim oj the chapter 49 • In absolutely a firsl maximum approximation, and in behalf of T absolutely wrong too the the price is mad increments 8x, are random variables which are 0) occasionally absolute us after absolutely a in little short t. House