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- 1. Suppose you have the following information concerning a particular options.Stock price, S = RM 21Exercise price, K = RM 20Interest rate, r = 0.08Maturity, T = 180 days = 0.5Standard deviation, � = 0.5 The Call option value is 3.7739. and put option value is 1.8101 Suppose a European put options has a price higher than that dictated by the putcall parity. a. Outline the appropriate arbitrage strategy and graphically prove that the arbitrage is riskless. Note: Use the call and put options prices above)b. Name the options/stock strategy used to proof the put-call parity. c. What would be the extent of your profit in (a) depend on?*NoChatGPT answers please 6A) What is the price of a European call option on a non-dividend-paying stock when the stock price is $52, the strike price is $50, the risk-free interest rate is 12% per annum, the volatility is 30% per annum, and the time to maturity is 3 months? 6B) What is the assumption of the Black–Scholes–Merton stock option pricing model about the probability distribution of the stock price in one year? What is the assumption about the probability distribution of the continuously compounded rate of return on the stock during the year?The stock price of Google is $32. The price of an American call option with strike price $32 and a six-month expiration date is $5 and the price of the corresponding Amertican put option (same maturity and expiration date) is $6. The risk-free interest rate is 5%. Are these prices compatible with the absence of arbitrage opportunities? Why? O1. No, because the put-call parity relationship suggests that ct - Pt = St - K exp(-Ro (T-t)) and this is not satisfied in this case. O II. Yes, because the price of the American put option is greater than the price of the American call option violating the inequality conditions defining the put-call parity relationship. O II. No, because the put-call parity relationship for American options suggests that St - Ks t - Pt s St - K exp(-Ro (T-t)). O V.It depends on whether the stock pays dividends or not.
- 2. Suppose you have the following information concerning a particular options.Stock price, S = RM 21Exercise price, K = RM 20Interest rate, r = 0.08Maturity, T = 180 days = 0.5Standard deviation, = 0.5a. What is correct of the call options using Black-Scholes model? b. Compute the put options price using Black-Scholes model. 3Suppose a European put options has a price higher than that dictated by the putcall parity.a. Outline the appropriate arbitrage strategy and graphically prove that the arbitrage is riskless.Note: Use the call and put options prices you have computed in the previous question 2 above.b. Name the options/stock strategy used to proof the put-call parity. c. What would be the extent of your profit in (a) depend on?1. Suppose you have the following information concerning a particular options.Stock price, S = RM 21Exercise price, K = RM 20Interest rate, r = 0.08Maturity, T = 180 days = 0.5Standard deviation, � = 0.5 The Call option value is 3.77. and put option value is 1.99 Suppose a European put options has a price higher than that dictated by the putcall parity. a. Outline the appropriate arbitrage strategy and graphically prove that the arbitrage is riskless. Note: Use the call and put options prices above)b. Name the options/stock strategy used to proof the put-call parity. explainc. What would be the extent of your profit in (a) depend on? explain1. Consider a family of European call options on a non - dividend - paying stock, with maturity T, each option being identical except for its strike price. The current value of the call with strike price K is denoted by C(K) . There is a risk - free asset with interest rate r >= 0 (b) If you observe that the prices of the two options C( K 1) and C( K 2) satisfy K2 K 1<C(K1)-C(K2), construct a zero - cost strategy that corresponds to an arbitrage opportunity, and explain why this strategy leads to arbitrage.
- In this problem we assume the stock price S(t) follows Geometric Brownian Motion described by the following stochastic differential equation: dS = µSdt + o Sdw, where dw is the standard Wiener process and u = 0.13 and o = current stock price is $100 and the stock pays no dividends. 0.20 are constants. The Consider an at-the-money European call option on this stock with 1 year to expiration. What is the most likely value of the option at expiration? Please round your numerical answer to 2 decimal places.Consider a European call option on a non-dividend-paying stock where the stock price is $33, the strike price is $36, the risk-free rate is 6% per annum, the volatility is 25% per annum and the time to maturity is 6 months. (a) Calculate u and d for a one-step binomial tree. (b) Value the option using a non arbitrage argument. (c) Assume that the option is a put instead of a call. Value the option using the risk neutral approach. (d) Verify that the European call and European put prices found in (b) and (c) satisfy the put-call parity.The stock price of Google is $32. The price of an American call option with strike price $32 and a six-month expiration date is $5 and the price of the corresponding Amertican put option (same maturity and expiration date) is $6. The risk-free interest rate is 5%. Are these prices compatible with the absence of arbitrage opportunities? Why? O I. No, because the put-call parity relationship suggests that ct - Pt = St - K exp(-Ro (T-t)) and this is not satisfied in this case. O II. Yes, because the price of the American put option is greater than the price of the American call option violating the inequality conditions defining the put-call parity relationship. O II. No, because the put-call parity relationship for American options suggests that St - K s ct - Pt s St - K exp(-Ro (T-t)). O IV. It depends on whether the stock pays dividends or not.
- The stock price of Google is $32. The price of an American call option with strike price $32 and a six-month expiration date is $5 and the price of the corresponding Amertican put option (same maturity and expiration date) is $6. The risk-free interest rate is 8%. Are these prices compatible with the absence of arbitrage opportunities? Why? O I. No, because the put-call parity relationship suggests that ct - Pt = St - K exp(-Ro (T-t)) and this is not satisfied in this case. O II. It depends on whether the stock pays dividends or not. O III. Yes, because the price of the American put option is greater than the price of the American call option violating the inequality conditions defining the put-call parity relationship. O IV. No, because the put-call parity relationship for American options suggests that St - Ks ct - Pt < St - K exp(-RO (T-t)).A call option with X = $55 on a stock priced at S = $60 is sells for $12. Using a volatility estimate of σ = 0.35, you find that N(d1) = 0.7163 and N(d2) = 0.6543. The risk-free interest rate is zero. Is the implied volatility based on the option price more or less than 0.35?Consider a European call option and a European put option that have the same underlying stock, the same strike price K = 40, and the same expiration date 6 months from now. The current stock price is $45. a) Suppose the annualized risk-free rate r = 2%, what is the difference between the call premium and the put premium implied by no-arbitrage? b) Suppose the annualized risk-free borrowing rate = 4%, and the annualized risk-free lending rate = 2%. Find the maximum and minimum difference between the call premium and the put premium, i.e., C − P such that there is no arbitrage opportunities.