A 58-65-68 asymmetric butterfly spread is constructed using a total of 20 three-month call options. Let X1 and X2 be the spot prices of the underlying stock at expiration for which the spread would have a profit of 0, and such that X2 > X1. Calculate X2 - X1.
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- Using put-call parity formula, derive expressions for the lower bounds for European call and put options. What is a lower bound for the price of (i) a three-month call option on a non-dividend-paying stock when the stock price is R860, the strike price is R760, and the risk-free interest rate is 10% per annum? (ii) a three-month European put option on a non-dividend-paying stock when the stock price is R500, the strike price is R610, and the discrete risk-free interest rate is 9% per annum?You observe the price of a European put option that expires in nine months and has a strike price of$45 is $3. The underlying stock price is $49.50. The term structure is flat, with all risk-free interestrates being 8%.a. What is the price of a European call option that expires in nine months and has a strike priceof $45? b. You observe next that the price of the call option (in part (a)) in the market is $9.59. Statewhy an arbitrage opportunity exists and explain how you would take advantage of thisopportunity. (Hint: answer should include an outline general strategy, net cost ofstrategy at initiation and net profit at expiration using the numbers in the question)Compute the difference in price of American put option and European put option using 2- step binomial option on a stock that is selling at $42. The options will expire is 6-months and the risk-free rate is 12%. In each three-months period the price of stock will be either 10% high or 10% low. (A) $0.42 (B) $2.24 (C) $0.65 (D) S0.52
- You have the following information about LearnMore Inc.’s stock and a two-month call option with a strike price of $140.00. LearnMore Inc.’s current stock price is $100.00. You are using the multiperiod binomial option pricing model to find the value of the two-month option with two periods. ∏u∏u and ∏d∏d values given here apply to any period. Data Collected for LearnMore Inc. u 1.5032 d 0.5922 ∏u∏u 0.2357 ∏d∏d 0.3555 You work with a junior analyst to calculate the value of the option, and she submits her inferences to you. Which of the following points are true in the case of LearnMore Inc.’s stock options? Check all that apply. The option payoff if the stock goes up in two months will be $10.32. The value of the two-month call option with a strike price of $140.00 at the end of two months will be $2.43. The value of the call option will always remain $2.43, irrespective of the time until expiration. LearnMore Inc.’s stock price…Suppose the following for European options: Stock price $94 3-month call options with strike price $97 3-month put option with strike price $98 1-year risk-free rate is 3%. The put option is trading ot $5 and there is an identical call option that is trading for $4. The arbitrage gain that can be made is equal to: O a. $2.00 b. $0.27 Oc. $3.00 O d. $1.27 O e $227The following information is given about an Option on a stock: S(0)=$31, X=$34, rf=9%, variance (sigma squared)=20%, T=182.5 days, Dividend $1.75 in 45 days (1) Calculate the price of a European put option using the Black-Scholes pricing model (show all workings including d1, d2, N(d1), N(d2)) (2) Calculate the price of the corresponding European call option (hint: put call parity) (3) Suppose you feel that the put option is overpriced. What strategy should you use to exploit the apparent mispricing? (4) The market has entered a state of significant volatility, and you believe the implied volatility is incorrect. You believe it should be 10% higher. What trade would you undertake to exploit this arbitrage
- Consider a four-period binomial model in which a stock currently trades at a price of sh.30. The stock price can go up 13 percent or down 15 percent each period. The risk-free rate is 5 percent. Calculate the price of a European call option expiring in four periods with an exercise price of Ksh.32Find the current price of a one-year, R110-strike American put option on a non- dividend-paying stock whose current price is S(0) = 100. Assume that the continuously compounded interest rate equals r = 0.06. Use a two-period Binomial tree with u = 1.23, and d = 0.86 to calculate the price VP(0) of the put option.Given a one-year European call options with strike price, K are available on two differ- ent stocks P and Q. Then, given also the current stock prices of Stock P and Stock Q are 20.5 and 41.5 respectively. Over the next 15 days, the price of Stock P has increased to 26 while the price of Stock Q has decreased to 38. Given the following Greeks for the options under a Black-Scholes pricing model: 3. |Option Greek Call on Stock P Call on Stock Q Delta 0.6543 0.4313 Gamma 0.1145 0.0559 Theta(365 days) -12.4102 -10.9501 Then you are also given the prices of the option as below Call Option on Stock Price as of Today Price after 15 days 4.12 W 5.45 Determine the value of W – X.
- Suppose that a call option with a strike price of $48 expires in one year and has a current market price of $5.17. The market price of the underlying stock is $46.25, and the risk-free rate is 1%. Use put-call parity to calculate the price of a put option on the same underlying stock with a strike of $48 and an expiration of one year. The price of a put option on the same underlying stock with a strike of $48 and an expiration of one year is $. (Round to the nearest cent.)Suppose that the price of a stock today is at $25. For a strike price of K = $24 a 3-month European call option on that stock is quoted with a price of $2, and a 3-month European put option on the same stock is quoted at $1.5 Assume that the risk-free rate is 10% 3. per annum. (a) Does the put-call parity hold?Suppose the following for European options: Stock price = $94 3-month call options with strike price $97 3-month put option with strike price $98 1-year risk-free rate is 3%. The put option is trading at $5 and there is a similar put option with an exercise price of $101 is trading at $8.5. The arbitrage gain that can be made is equal to