2. a) Using put-call parity and bounds on a European call, or otherwise, show that the price of a European put on a stock paying no dividends satisfies max{0, KZ(t, T) − St} ≤ PK(t, T) ≤ KZ(t, T).
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2. a) Using put-call parity and bounds on a European call, or otherwise, show that the price of a European put on a stock paying no dividends satisfies max{0, KZ(t, T) − St} ≤ PK(t, T) ≤ KZ(t, T).
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- A) Does this model satisfy the no-arbitrage assumption? B) Calculate the risk-neutral probabilities of up and down movements in the share price. C) Determine the no-arbitrage price of a European call option on the share with strike price K=70 and expiry time T=2.Please help me prove this question: Show that for a European put on a stock which pays continuous dividends, P(S,t)=Ker(T-t)N(-d*2)-Se-q (T-t)N(-d*1). Here d*1 and d*2 are the usual d1 and d2 but with r replaced by r-q.Imagine a situation where European options on some underlying stock have the following relationship. p+S > c+ K*exp(-rT). (a) Describe the arbitrage opportunities that are available with an example. (b) Now change those options to American-style options. Does the arbitrage strategy still work? Explain your answer.
- Under the assumptions of the Black-Scholes model, which value does not affect the price of a European call option: Select one: a. the interest rate r b. the spot price S c. the strike price K d. the return of the stock µ e. the volatility of the stock σLet C be the price of a call option that enables its holder to buy one share of a stock at an exercise price K at time t; also, let P be the price of a European put option that enables its holder to sale one share or the stock for the amount K at time t. Let S be the price of the stock at time 0. Then, assuming that interest is continuously discounted at a nominal rate r, either S+P-C=Ke-rt or there is an arbitrage opportunity. Question: How do I verify that the strategy of selling one share of stock, selling one put option, and buying one call option always results in a positive win if S+P-C>Ke-rt ?European plain vanilla call options with strikes 30 and 35 on the same non- dividend paying asset with spot price $ 35 are trading for $ 11.50 and $ 7, respectively. Does arbitrage exist, and if so, how do you take advantage of it?
- State and prove the Put-Call Parity Theorem that gives the relation between a European Call and a Put option price where the options are written on the same stock, same time to maturity and have the same exercise price.D6) Derive the lower bound for European call options on both non-dividend-paying stocks and dividend-paying stocks.Suppose that C is the price of a European call option to purchase a security whose present price is S.Show that if C > S then there is an opportunity for arbitrage (i.e. riskless profit). You may assume theinterest rate is r = 0 so that present value calculations are unnecessary.
- 3. Explain why it is or isn’t optimal to exercise early (a) an American call and (b) an American put when the underlying stock does not pay dividend?Suppose that C is the price of a European call option to purchase a security whose present price is S. Show that if C>S then there is an opportunity for arbitrage (ie. riskless profit). Assume the interest rate r=0 so present value calculations are unnecessary.2. An investor buys a European put on a share for Rs. 3. The stock price is Rs. 42 and the Strike price is Rs. 40. Under what circumstances does the investor make a profit? Under what circumstances will the option be exercised? Draw a diagram showing the variation of the investor's profit with the stock price at the maturity of the option.