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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.
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.
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.
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.
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