Problem 7 Put-Call Parity for stocks and options isgiven by Ce-Pe=X-Ee^(-r*(T-t)) ;0tT where X is the price of the stock, and r is the interest

; 0<t<T

where X is the price of the stock, and r is the interest rate (assumed to be constant with time), T is the expiration date, t is the current time(whence T-t is the time to expiration in years), E is the expiration or strike price , CE is the value of the call at time t, and PE is the value of the put at time t.

               a  Long 1 conversion means long 100 shares of stock, long 1 put, and short one

                   call of the same strike. Find a formula, using Put-Call Parity, for the value,

                   W, of the conversion. What is this value, WT, at expiration? What is the  

                   value, W0, when t = 0? Do these values, W, depend on the price

                    of the stock, X? Explain. Graph WT versus X.

               b  Find dW/dt and d2W/dt2 the first and second derivative. Using the rules of

                   the calculus sketch the graph of W versus t connecting (0,W0) and (T,WT).

                   Find, if they exist, the maxima, minima, inflection points, intervals of

                   increase, decrease, concave up, and concave down. Use the rules of calculus.

               c  Betty and Bob are day traders. They will do a trade and then take it off at the

                   end of the day. Assume that at the end of the day all prices equal their   

                   values. Suppose that MCD is $47.75 on a day that has 146 days left to

                   expiration and interest rates are 9% per annum continuously compounded.