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Principles of Corporate Finance (9th Edition) See this solution in the app

Problem

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.

Step-by-step solution

Options are contracts which provide the holder the right to sell or buy a specified quantity of an underlying asset at a fixed price on or before the expiration of the option date. Options provide a right n and not the obligation to buy or sell.

Comment

Option delta is the ratio which contrasts the change in the prices of the asset or stock with the change in the price of the option r derivative.

Comment

Here, stock price of R will halve to $50 from the current price of $100 or it will rise to $200. The interest rate is 10%

Comment

a.

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Here calculate the Delta in the price is $100

Therefore, the Delta is .

Comment

b.

Here calculate the value of the call:

Comment

c.

Here calculate the probability of R’s stock will rise:

Therefore, probability of R’s stock will rise is .

Comments (1)

d.

Here calculate the value of the call:

Therefore, the value of the call is .

Comment

e.

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No. The factual probability of a rise in the price of the stock is nearly positively superior to the risk-neutral probability, but it does not assist to value the option.

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