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Q6

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Q6. Suppose call and put prices are given by

a. What no-arbitrage properties are violated? (Hint: Check out equations 9.17 and 9.18 of the textbook. They are C(K1) – C (K2) < = K2-K1, and P (K2)- P(K1) <= K2-K1.)

b. How can you take advantage of this arbitrage opportunity, if any?

c. Demonstrate the payoffs involved.that the premium on this insurance VCA T. As Bodie notes, however, this proposito on has outp ernment bonds in the imple. Siegel, 1998). ome to suggest that if period of time, stocks ve to risk-free bonds sing put option premi m that stocks are safe what would it cost to hat after 7 years your orth at least as much red in a zero-coupon hent was you could be true for any valid option pricing model. The this insurance must increase with T or else payoffs in Table 9.5 demonstrate that the an arbitrage opportunity. Whatever the retum statistics appear to say, the cost of por insurance is increasing with the length of which you insure the portfolio return. Unte cost of insurance as a measure, Stocksale in the long run i difference between otherwise identical calls with different strike price rater than the difference in strike prices: (9.17 C(K)-C(K) K2 - K difference for otherwise identical puts also cannot be greater than the strike prices P(ky) - P(K) SK,- K 9.18 line at a decreasing rate as we consider calls with progressively higher The same is true for puts as strike prices decline. This is called convexity price with respect to the strike price: C(K) - CK2) C(K) - C(K) K? - K? 19.19 K? - Ki (9.20 P(K) - P(1) POK) - P(K) K? - Ki K? K? nts are all true for both European and American options." Algebra in Appendix 9.B. It turns out, however, that these three proposition e Farupean, the second stalenient can be strengthened: The difference in opcion on the present salar of the difference in strikes