IN the absence of transactions costs, w otherwise similar European Options on non-Dividend paying stocks the NO-Arb relation is S+P = C + pv(K) LHS=Protective Put Hedge = buy stock and buy put= RHS = fiduciary call (lend money and buy calls).

a) Suppose T=1 year, K=50, S(t)= 55, pv(K)=48.50, C=10... compute fair no arb price for P. If the market price of the Put is 2.50, what would you do to make profit?

b) A big hint from the algebra to a strategy: this relation holds at all times t until T! A second inference --- with an equality in this relation you can interpret the plus sign on either side as shorting...an inflow of cash ... hence +pv(K) as borrowing money at the riskless rate. SO we try the following synthetic positions w eur0-style options with zero dividends: + S = ? P + C + pv(K) shorting the stock can synthesized by buying the put (bearish), selling the call (bearish) and borrowing pv(K) today.

Use the following table, make the relevant entries and compare the LHS of this bold red relationship to the RHS, now and at T. Use the data for in part (a) together with your assessment of the fair value of P, which should have been $3.50!.

c) Following the logic in (b) above: how can you find a synthetic position that imitates riskless lending of money (an outflow today), trading only the stock and its associated euro-put and call? [This is a way in which a broker-dealer looks at the inventory of his net positions in puts, calls and net short and long positions typically just before the market closes, and decides to CONVERT his position into a riskless strategy! That's why the

Strategy CF Today At T, S(T) 250 Remarks Today S(T)