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Posted: July 13th, 2022
Vanda Pharmaceutical is a biopharmaceutical company with a focus on the development and commercialization of clinical-stage product candidates for central nervous system disorders. On July 28, 2008 the company was waiting for FDA response on a Drug Approval Application submitted for "iloperidone", an investigational atypical antipsychotic that was reviewed for the treatment of schizophrenia. We will analyze FDA approval implications on Vanda stock price using binomial trees.
, t=0, is July 28, 2007; in 1 year time, that is t=1, depending on whether FDA approves the drug application, analysts believe that Vanda stock price can either be S1,u = 21 with probability q=0.7 or S1,d = 10 with probability (1-q) = 0.3. Assume that the firm has a CAPM beta equal to 2, that the annualized continuously-compounded risk-free rate is 5%, and that the annually-compounded expected excess return on the market (or market risk premium) is 6.44%.
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(1) What is the expected return on the stock according to the CAPM? (Tip: note that the risk-free rate provided is continuously-compounded, but in the CAPM equation you need to plug the annually-compounded equivalent). (2 points)
(2) Use your answer in part (1) to compute the value S0 of the stock on July 28, 2007, that is one year before FDA's approval decision (Tip: recall, asset values are discounted expectations of future cash flows). (2 points)
(3) Compute the value of an at-the money European call option with maturity t=1 using the risk-neutral methodology. (6 points)
(i) Compute the risk-neutral probabilities.
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(ii) Compute the expected stock price at time t=1 (July 28, 2008) under the risk neutral probabilities.
(iii) Compute the expected stock price at time t=1 (July 28, 2008) under the probabilities assumed by the analysts. Are the two time t=1 expected prices computed above equal/different? Discuss.
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(iv) Compute the option value under the risk-neutral probabilities.
(4) Assume that the strike price is equal to the time t=0 stock price computed in point (2) above. How would the value of the option computed in Point (3) change if .... (6 points)
(i) The probability (assumed by the analysts) that FDA approves the drug becomes 80%? Provide some intuition.
(ii) The probability (assumed by the analysts) that FDA approves the drug becomes 80% and the CAPM beta of the firm becomes 3.14? Provide some intuition.
(5) What is the value of an at-the-money European put option? (3 points)
(6) What is the value of an at-the-money forward contract? (3 points) Get
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