Question

5. Option pricing - Single-period binomial approach A Aa The value of an option can be calculated by using a step-by-step approach in the case of single periods or by using sophisticated formulas that can be easily created through a spreadsheet. In the real world, two possible outcomes for a stock price in six months is an assumption. The stock markets are volatile, and stocks move up and down based on market- and firm-specific factors. Consider the case of Canada Tel Inc.: Shares of Canada Tel Inc., a manufacturer of cell phones, sell for $30.00. (Assume that you get the option for freel) Existing options allow for the option holder to purchase one additional share at an exercise price of $22.00. The option will expire within one year. Assume that at that time there will be an 90% chance that Canada Tel Inc. shares will sell for $38.00 and a 10% chance that the shares will be selling at $20.00. Using the steps to the binomial approach, determine the following: The expected end-term share price and return on Canada Tel Inc. shares are: Based on the binomial approach, the range of payoff values at expiration for Canada Tel Inc.'s shares and options is: $18.00 (share) and $16.00 (option) $28.00 (share) and $26.00 (option) $20.00 (share) and $30.00 (option) $25.00 (share) and $20.00 (option) Given this information, it is possible to create a riskless portfolio by selling one option and purchasing shares. Assuming that the risk-free rate is 8% and is compounded daily, current option price (Vc) of the call option is

Answer 1

I have answered the question below

Please up vote for the same and thanks!!!

Do reach out in the comments for any queries

Answer:

1)

Expected share price = (Probability Price(P)) +(Probability Price(P))

= 0.9*38 + 0.1*20 = 36.20

Expected return = Expected share price --1 Selling price

= 36.2/30 - 1= 20.7%

2)

Share price range = 38 - 20 = $18

Option price range = MAX Price(P1)- Exercise price, $0 Upper price -MAX Price(P)- Exercise price, $0 Lower price

= MAX(38-22,0)-MAX(20-22,0) = $16

3)

Hedge ratio Change in call price(Range of option) Change in share price Range of share price)

= 16/18 = 0.8889

4)

u = 38/22 = 1.727

d = 20/22 = 0.91

365 1+ -d Call Payoff risk-free rate 365 u-d 365 --{1+ risk-freerate 365 u-d +Call Payoff Don Value of call option (V.) 365 risk-free rate 365

= 3.14