Answer to Question #12661 in Other Management for John
4. The current price of a stock is $22, and at the end of one year its price will be either $27 or $17. The annual risk-free rate is 6.0%, based on daily compounding. A 1-year call option on the stock, with an exercise price of $22, is available. Based on the binominal model, what is the option's value?
Answer is c ($ 2,99)The stock’s range of payoffs in one year is $27 - $17 = $10. At expiration, the option will be worth $27 - $22 = $5 in case the stock price is $27, and zero if the stock price is $17.
The range of payoffs for the stock option is $5 – 0 = $5. We equalize the range to find the number of shares of stock:
Option range / Stock range = $5/$10 = 0.5
With 0.5 shares, the stock’s payoff will be either $13.5 or $8.5. The portfolio’s payoff will be $13.5 - $5 = $8.5, or $8.5 – 0 = $8.5.
The present value of $8.5 at the daily compounded risk-free rate is: PV = $8.5 / (1+ (0.06/365))365 = $8.005.
The option price is the current value of the stock in the portfolio minus the PV of the payoff: V = 0.5($22) - $8.005 = $3.00.
From a young age, our brains develop to the world around us, the environment we live in, and the people…
APPROVED BY CLIENTS
Dear Assignment Expert!
Thank you so much. Your service is really great, and experts are smart as well, they know their job. Excellent job. I checked the assignment, it seems it works perfectly as the requirements. I will give it a final check on Tuesday, and if i need anymore help, i will message you. And yes , you are right. it wasn’t in my mind that for dynamic array, I don’t need that pre-condition. Thanks