You hold a stock with price $100 that can increase by 10% or decrease by 10% m a year. The interest rate is 5%

a) Suppose that you want to ensure that you'll get a minimum of $I00 in a year regardless of the evolution of the stock price. Which derivative security will you have to purchase to ensure that your financial position will be at least $100 m a year? Be precise

(Note You are allowed to purchase just one derivative securin' Please describe the simplest securin' that allows you to get a minimum of $100 regardless of what happens to stock X Also, please ignore the cost of purchasing such securin', i.e., assume that in a year you want to have $100 gross of the cost of acquiring such securin'. )

b) Value the derivative securin' described Value the derivative securin' described in a).

c) Suppose that there is no derivatives market but that bonds and the stock can be traded (and short-sold if needed). Design a portfolio position in stock and T-bills that ensures you a payoff similar to the derivative securin' described in a)