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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Q2: Given the following inputs for YMMV: Interest rate 3.25 Dividend rate 3.00 Spot Price Volatility (%) 30.21 12.00 Strike Price 30.00 Expiry (months) T Option type 12 European Put a) Compute u, d, Pup; Pdn, Construct a 3 step tree and price the option.
Question 5 Consider an option on a non-dividend-paying stock when the stock price is $30, the exercise price is $29, the risk-free interest rate is 5% per annum, the volatility is 25% per annum, and the time to maturity is four months. What is the price of the option if it is a European call? b. What is the price of the option if it is a European put? c. Verify that put-call parity holds. a.
Question 2 (a) Use the Black-Scholes formula to find the current price of a European call option on a stock paying no income with strike 60 and maturity 18 months from now. Assume the 20%, and the constant current stock price is 50, the lognormal volatility of the stock is a = continuously compounded interest rate is r 10% (b) Repeat part (a) for a European put with strike 60 and maturity 18 months from now
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 $227
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
Question Two (a) A six-month European Call option on a non-dividend paying Stock Index has a strike price of $4900. The index price is $5000, the risk-free rate is 5% per annum, and the value of u and d are 1.06 and 0.94, respectively. Use a two-step binomial tree to calculate the option price.
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.
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.
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.
Q.3Determine the risk-neutral value for a European put option (for a FLB (First Local Bank) share) that expires in eight months. The strike price is R500 and the current price is R650. The interest rate is 11%, and the volatility of the security is 0.026.

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