# Construct a binomial tree for the price of a stock where the

Added on - 16 Sep 2019

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1.Construct a binomial tree for the price of a stock where the initial price is equal to 100, thevolatility= 30% per year, the length of the period is one day (h=1/252), the riskfree rate r = 1%per year, compounded continuously, u = exp[rh +(h^0.5)], d = exp[rh -(h^0.5)]. The stockdoes not pay dividends.a.Use this framework to calculate the price (at the beginning of the tree) of anAmericanoption whose payoff is equal to [max(S^2 – 100^2, 0)]^0.5 and expiring in 1 year.b.Repeat part a. with volatilities ranging from 20% to 40%, in increments of 5%, and plotthe option price as a function of volatility.c.Repeat part a. for a range of riskfree rates from 1% to 10%, in increments of 1%, andplot the option price as a function of the riskfree rate.d.Plot the Delta of the option as a function of the stock price on the path of the treewhere the stock price goes only up.e.Plot the cash in the replicating portfolio as function of the stock price on the path in thebinomial tree on which the stock price only goes up.Make your excel spreadsheetveryclear.2.Construct a binomial tree with three periods, such that the riskfree rate is zero, u=1.1, d=0.9 andthe initial stock price is $100. Calculate the price of the following convertible bond: you have thechoice between holding your security as a bond tha pays you $200 at maturity or converting(irreversibly) that security in two shares of stock.

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