I\'m currently doing part (B) and cannot seem to understand why in the solutions

Question

I'm currently doing part (B) and cannot seem to understand why in the solutions the risk neutral probability is calculated by (25.69)(q) + (3)(1-q) = 10.1

should it not be equal to 1.01 (risk free return) rather than 10.1?

also, since this is not a binomial situation, will there be two different risk neutral probabilities at each year since the probabilities of an increase/decrease will change?

Many thanks!!

A small biotech firm is commencing trials for an anti-cancer treatment. These trials will take one year to complete. The firm's shares are currently trading at $10 per share. The firm pays no dividends, and is not expected to do so in the next two years. If the trail is unsuccessful, the firm will be closed and its patents sold for $3 per share. if the trial is successful, the firm will apply for FDA approval, which will require further trials which will also take one year to complete and its share price will increase to $25.69. If the FDA approval is gained, the firm will be sold to a major pharmaceuticals company for $50 per share. If approval is not gained, the firm will be closed and its (now more valuable) patents sold for $15 per share. At each stage, the probability of success is the name. Use the following data to illustrate the relevant demand curve: If the price increases from $4 to $8, by how much does the quantity demanded decline? If a successful advertising campaign increases the quantity demanded at every price by 4 units. Draw the new demand curve D2. How many units are now purchases at $8?

Explanation / Answer

Hello friend i think You have not read the solution correctly. The solution of B is correct.

Probability of success is q=0.312866 given by either:

10=(q*25.69+(1-q)*3)/1.01 Or

25.69=(q(50+(1-q)*15)/1.01

The implied option price in the middle age is then (q*40+(1-q)*5)/1.01=15.79 conditional on success in stage 1 and zero conditional on failure. The initial price is then q*15.79/1.01=4.89. This is the value of her option to acquire the share. We need to assume no intermidiate dividends.

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