Question 3 - (2Consider a European call option on a non-dividend-paying stock where thestock 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 optionusing the risk neutral approach.(d) Verify that the European call and European put prices found in (b)and (c) satisfy the put-call parity.

(b) Value of European Call Option (Non-Arbitrage Argument):Since we cannot short sell the stock in a…

Answered: Question 3 - (2 Consider a European…

Fundamentals of Financial Management (MindTap Course List)

14th Edition

ISBN:9781285867977

Author:Eugene F. Brigham, Joel F. Houston

Publisher:Eugene F. Brigham, Joel F. Houston

Chapter18: Derivatives And Risk Management

Section18.A: Valuation Of Put Options

Problem 1P

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Question 4 Which of the following are always positively related to the price of a European call option on a stock (circle three) NOTE: "All or Nothing" Scoring Question options: The stock price The strike price The time to expiration The volatility The risk-free rate The magnitude of dividends anticipated during the life of the option Question 8 Six-month call options with strike prices of $35 and $40 cost $6 and $4, respectively. What is the maximum potential gain when a bear spread is created from the calls? Question options: $2.00 $2.50 $3.00 None of the above Question 11 Six-month call options with strike prices of $35 and $40 cost $6 and $4, respectively. What is the maximum potential loss when a bear spread is created from the calls? Question options: $2.00 $2.50 $3.00 None of the above
Problem 4c: State whether the following statements are true or false. In each case, provide a brief explanation. c. An investor would like to purchase a European call option on an underlying stock index with a strike price of 210 and a time to maturity of 3 months, but this option is not actively traded. However, two otherwise identical call options are traded with strike prices of 200 and 220 respectively, hence the investor can replicate a call with a strike price of 210 by holding a static position in the two traded calls.
Put–Call Parity The current price of a stock is $33, and the annual risk-free rate is 6%. A call option with a strike price of $32 and with 1 year until expiration has a current value of $6.56. What is the value of a put option written on the stock with the same exercise price and expiration date as the call option?
3 Using Black-Scholes find the price of a European call option on a non-dividend paying stock when the stock price is $69, the strike price is 70, the risk-free interest rate is 12% per annum, the volatility is 30% per annum, and the time to maturity is three months? What is the value of a put using theses parameters (use put-call parity)? What happens to the price of the call if volatility is 10% and 50%? Show the prices at these volatilites.
Aa.8 A put with 1-year to maturity is written on a stock. The current underlying stock price is $20. The option’s exercise price is $18, the interest rate is 3.74%, and the stock’s volatility is 32.7%. The price of a call written on the same stock with the same exercise price and time to maturity is $4.3. Use BSM pricing to determine if put-call parity holds.
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.
Q4 Using the Put-Call Parity relationship, find the value of a put option (same strike, expiration as the call option) using the following information: Current stock price 6% Call option strike price $6.56 Option time to maturity $33 $32 1 years risk-free rate Call option current value SHOW WORK HERE, HIGHLIGHT FINAL ANSWER IN YELLOW
A6 Consider a one-period binomial model (a two-state contingent claim model) with the right to sell (a put option), stock price S0 = 100, exercise price K=110, and compound factor 1+r = 1.10, where r is the interest rate. The two possibilities for the stock price at time T are 130 and 80. Discuss the one-period binomial model, highlighting its underlying assumptions. Derive the formula for the delta hedge. Using the data above compute the hedge ratio of this type of contingent claim and the value of the riskless portfolio at time 0.
QUESTION: 2. What is the fair value for a six-month European call option with a strike price of $135 over a stock which is trading at $138.15 and has a volatility of 42.5% when the risk free rate is 1.85% using the two step binomial tree? a) What is the delta of this option? b) What is the probability of an up movement in this stock? c) What is the probability of a down movement in this stock? d) What is the proportional move up for this stock e) What is the proportional move down for this stock f) What would be the value of the put option with the same strike price?
5. A stock index is currently trading at 50.00. The annual index standard deviation is 20 percent. Paul Tripp, CFA, wants to value two-year index options using the binomial model. To correctly value the options, he needs the formulas in Exhibit 1. The annual risk-free interest rate is 6 percent. Assume no dividends are paid on any of the underlying securities in the index. Exhibit 1. e-D U = e = 1.2214 d==- π₂ where e 1.06184 U-D Where: U = up movement factor D = down movement factor T = probability of an upward price movement
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