Answered step by step
Verified Expert Solution
Link Copied!

Question

1 Approved Answer

Question 5. a. Find the Black-Scholes value of a put option on the following non-dividend paying stock: Time to maturity: 6 months Standard Deviation: 50%

image text in transcribed

Question 5. a. Find the Black-Scholes value of a put option on the following non-dividend paying stock: Time to maturity: 6 months Standard Deviation: 50% per year Exercise price: $50 Current stock price: $50 Interest rate: 10% (4 marks) b. You found that the put option is trading at the fair value you calculated in part a) but the call option with the same exercise price and maturity is currently selling for 9 dollars. Is there an arbitrage opportunity? If so, identify a trading strategy. Explain what actions you would take at the inception and expiry of the strategy to capture an arbitrage profit and calculate the amount of this profit. Show that your strategy eliminates all risk irrespective of the value of the underlying stock at the maturity of the put and call options. (4 marks) c. You decided to establish a position (unrelated to part a and b) by buying a share of the stock for $50, buying a 6-month put option with exercise price $45, and writing a 6- month call option with exercise price $55. Explain what is the maximum payoff (not profit and loss) of this position? (4 marks) Question 5. a. Find the Black-Scholes value of a put option on the following non-dividend paying stock: Time to maturity: 6 months Standard Deviation: 50% per year Exercise price: $50 Current stock price: $50 Interest rate: 10% (4 marks) b. You found that the put option is trading at the fair value you calculated in part a) but the call option with the same exercise price and maturity is currently selling for 9 dollars. Is there an arbitrage opportunity? If so, identify a trading strategy. Explain what actions you would take at the inception and expiry of the strategy to capture an arbitrage profit and calculate the amount of this profit. Show that your strategy eliminates all risk irrespective of the value of the underlying stock at the maturity of the put and call options. (4 marks) c. You decided to establish a position (unrelated to part a and b) by buying a share of the stock for $50, buying a 6-month put option with exercise price $45, and writing a 6- month call option with exercise price $55. Explain what is the maximum payoff (not profit and loss) of this position? (4 marks)

Step by Step Solution

There are 3 Steps involved in it

Step: 1

blur-text-image

Get Instant Access to Expert-Tailored Solutions

See step-by-step solutions with expert insights and AI powered tools for academic success

Step: 2

blur-text-image

Step: 3

blur-text-image

Ace Your Homework with AI

Get the answers you need in no time with our AI-driven, step-by-step assistance

Get Started

Recommended Textbook for

Hotel Finance

Authors: Anand Iyengar

1st Edition

0195694465, 978-0195694468

More Books

Students also viewed these Finance questions

Question

In Problems 21100, establish each identity. 1 + tan (-0) = sec0

Answered: 1 week ago