# Greek Alphabet

May 13th, 2015
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Dipylon inscription, one of the oldest known samples of the use of the Greek alphabet, ca. 740 BCThe Greek alphabet is a set of twenty-four letters that has been used to write the Greek language since the 8th century BC.[2] It is still in use today.

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FE610 Final Exam 2008FE610FinalExam 2011SProblem1: (15 pts)A four-step binomial tree for the price of a stock St is to be calculated using up and down ticks given as follows: u = 1.1; d = 1/uThese up and down movements apply to one-month periods denoted by = 1: Then St follows the following dynamicsandwith "up" and "down" describing the two states of the world at each node. Suppose that time is measured in months and t=4 is the expiration date for a European call option Ct written on St: The stock does not pay dividends and its price is expected to grow at the annual rate of 15%. The risk free interest rate r is known to be constant at 5%. a) Calculate the four-step binomial trees for St and Ct:b) Calculate the arbitrage-free price C0 of the option at t=0. c) Construct a binomial tree corresponding to the trees in a) and b) containing the delta hedging ratio at each node.FE610FinalExam 2011SProblem2:(10pts)Calculatetheresultofthefollowing:(Pleaseproveitmathematicallyandshowyourcalculationprocedurestepbystep.Onlyaresultwillnot earnthefullgrade)3(1) E[Wt ]2(2) Var [Wt ] FE610FinalExam 2011SProblem3:(15pts)LetWtbeaWienerprocessandtdenotethetime,arethefollowingstochasticprocessesmartingales? Explainwhy.(1) X t = Wt 3(2) X t = e t Wt(3) X t = W

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