Question
In: Finance
Suppose today's stock price of McDonald’s is $150. With probability, 60% the price will rise to...
Suppose today's stock price of McDonald’s is $150. With probability, 60% the price will rise to $175 in one year and with probability, 40% it will fall to $140 in one year. What is the current price of a European call option with one year until maturity with a strike price of $160 if the risk-free rate of interest is 4%? Use a binomial tree.
Solutions
Expert Solution
| Stock Price | 150 | |
| Strike Price | 160 | |
| Stock Price after one year with 60% probability | 175 | |
| Stock Price after one year with 40% probability | 140 | |
| Risk Free Rate | 4% | |
| Value of the european call at the expiration | max( 0, (Stock Price-Strike Price)) | |
| Value of the Call, when stock reaches to 175 | max(0, (175-160) | 15 |
| Value of the Call, when stock reaches to 140 | max(0, (140-160) | 0 |
| These values of the call is at the end of year one with different different probability. | ||
| To compute the call price today, we need to calculate the present value of the call options at both end and calcualted the expected value on the basis of probability | ||
| Call price with 60% probability at t=0 with discounted factor | 15/1.04 | 14.42 |
| Call price with 40% probability at t=0 with discounted factor | 0/1.04 | 0.00 |
| At t=0 estimated call price will be the weighted average number of both the end | 60%*14.42+40%*0 | 8.65 |
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