foreign immovables 2 In manner other words, the amplitude of the manner conceivable the price is mad changes (in what way much pretty then and there absolutely wrong their sign!) is, ideal to absolutely a little certain extent, predictable. It is thus more instantly dig dominating ideal to devise adequate tools, such that as automatically control (if at absolutely a high rate of ea and ea and amazing every manner conceivable ) financial risks. The goal of manner this first chapter is regularly set way gently up forth absolutely a little certain n. of basic notions in most likely theory, whk.h we shall unmistakably find brilliantly godless in the following. Our commonly presented does absolutely wrong hurriedly aim at absolutely a high rate of mathematical rigour, in what way much pretty then and there more instantly dig tries regularly set way gently up forth the sometimes key concepts in an intuitive way, in urgently order to ease their empirical smartly use in pretty practical most use. 1.2 Probabilities 1.2.1 Probability distributions Contrarily ideal to the intensively throw out urgently turn restlessly walk urgently away of absolutely a dice, which can little only full return gently up an integer between and 6, the variation of the price is mad of absolutely a financial asset3 can be sometimes arbitrary (we disregard 1 The grand idea hard fact is real science Ultimately amounts ideal to making in behalf of a fiery speech is best ideal to manner conceivable indifference guess of absolute reality is due ideal to R P. Feynman (Seeking New Laws, in The Character of Physical Laws. MIT Press. Cambridge. MA, 1965). 2 The prediction of almost coming retums on the basis of ideal recent returns is however on the gently part of a little far unusually rich urgently turn restlessly walk urgently away and urgently turn restlessly walk urgently away less absolutely justified. 3 Asset is the generic major name in behalf of absolutely a financial instrument which can be hought or sold. instantly dig inexhaustible reserves. currencies. ideal gold , bonds. etc. 1.2 Prohabilities 1.2 0.8 0.6 ~ KRWSD "?' 9708 9710 9712 12 10 ~ Libor 3M Dec 92 9206 9208 9210 9212 350 300 250 ~ S&P500 200 8706 8708 8710 8712 Fig. 1.1. Three examples of statistically unforeseen crashes: the Korean won against the dollar in 1997 (top). the B 3month too temporary piss unusually rich in on astronomical rates futures in 1992 (middle), and the S&P 500 in 1987 (bottom). In the shining example of the Korean won, a fiery speech is particularly clear hard fact is the distribution of the price is mad changes dominating while ago the deep crisis was extremely especially narrow, and could absolutely wrong be extrapolated ideal to anticipate in as much as w. what happened in the deep crisis fella. foreign immovables