Binomial model* Over the coming year, Ragwort’s stock price will halve to $50 from its current level of $100 or it will rise to $200. The one-year interest rate is 10%.
- a. What is the delta of a one-year call option on Ragwort stock with an exercise price of $100?
- b. Use the replicating-portfolio method to value this call.
- c. In a risk-neutral world, what is the probability that Ragwort stock will rise in price?
- d. Use the risk-neutral method to check your valuation of the Ragwort option.
- e. If someone told you that in reality there is a 60% chance that Ragwort’s stock price will rise to $200, would you change your view about the value of the option? Explain.
a.
To compute: The delta of one year call option on R stock with a strike price of $100.
Explanation of Solution
The formula to calculate delta is:
The calculation of delta is as follows:
b.
To discuss: Apply the replicating portfolio technique to value this call.
Explanation of Solution
The replicating portfolio technique of valuing call is as follows.
c.
To discuss: The probability of increasing stock R price in a risk neutral world.
Explanation of Solution
The probability of increasing stock R calculated as follows:
The computation as follows:
Foot note: The probability is calculated on the basis of expected return.
d.
To compute: The value of stock R using the risk neutral method.
Explanation of Solution
The option value is calculated using the following formula:
Hence, the value of call is $36.36
e.
To discuss: Whether person X change his option regarding the value of option.
Explanation of Solution
Person X does not change his opinion regarding the value of option. The chance of price increase is most likely higher than the risk- neutral probability, but it does not aid to value the option.
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