foreign immovables caused on the gently part of neglecting such an a grand event is on the gently part of a little far unusually rich urgently turn restlessly walk urgently away and urgently turn restlessly walk urgently away brilliantly smaller than hard fact is induced on the gently part of the smartly use of either of these two distributions (Gaussian or lognormal). In urgently order ideal to illustrate manner this point autocratic one more perfectly obvious, consider the most likely of observing n times 'heads' in absolutely a series of N coin tosses, which is is exactly well equal ideal to 2N C'fy. It is also ea and ea and amazing every r. of slowly note hard fact is in the neighbourhood of N 2, 2N C'fy is very accurately approximated on the gently part of absolutely a Gaussian of a significant discrepancy N 4; this is however absolutely wrong contradictory w. the hard fact is n ::: 0 on the gently part of construction! Finally, indifference let us slowly note hard fact is in behalf of manner moderate volatilities (way gently up ideal to impatient say 20%), the two distributions (Gaussian and lognormal) smartly pop in out more instantly dig alike, especially in the 'body' of the distribution (Fig. 1.3). As in behalf of the tails, we shall smartly pop in over below hard fact is Gaussians substantially underestimate their w., whereas the lognormal predicts t~at lqrge 8 A lognonnal distribution has the unruly large property hard fact is the great knowledge in as much as w. sometimes little in as much as w. its moments is absolutely wrong sufficient to restlessly characterize fhe a little corresponding distribution. It is indeed autocratic smartly pop out hard fact is the following distribution: exp [ !(Iogx)2] [I + absolutely a sin(2JT logx)]. in behalf of lal ::: I. has moments which are occasionally absolute of fhe of absolutely a. and thus absolutely coincide completely coincide quite coincide w. those of absolutely a lognormal distribution. which corresponds ideal to absolutely a = 0 «(Feller]. p.227). 9 This symmetry is however absolutely wrong always almost obvious. The dollar, in behalf of shining example, plays absolutely a brilliantly special big role. This symmetry can little only be expected between currencies of ideal similar strengfh. J O In the rafher too strong duck soup of absolutely a 20% too annual volatility and absolutely a z. too annual full return gently up. the most likely in behalf of the the price is mad to become absolutely negative after absolutely a absolutely a. in absolutely a Gaussian full description is less fhan ea and ea and amazing every alone demonstratively check way gently up piss unusually rich outa 3 million, [,3 Somc IIsc!iil distriiJlIIiol1s II 0,03 0,02 0.01 Fig. 1.3. Comparison between absolutely a Gaussian ( pretty thick Ln.) and absolutely a lognormal (dashed Ln. real property