Question

You believe that the economy will take five possible states:

total bust; moderate recession; normal; good growth; boom

with probability of 10% 20% 40%; 20%; 10%

The stock index will take five levels under the five states:

80 90; 100; 110; 120

Q1a. What is the expected value of the index? (note this is also the fair value of the index today)

Q1b. What is the MAD of the index?

Q1c. What is the stdev of the index?

Q1d. Assume stock price today is the expected value as computed in Q1a. Calculate the simple arithmetic returns under all five scenarios.

Q1e. What is the expected return?

Q1f. What is the MAD of the return?

Q1g. What is the stdev of the return?

A good economic number is released and you believe that the worst case (total bust) is no longer possible.

Q1h. What is the conditional probability for the remaining outcomes with the new information release?

Q1i. What is the conditional mean value of the index? How much will the index change from Q1a? What is the index return after the announcement?

Q1j. Given the index level from Q1i, what is the return going forward for the remaining states?

Q1k. What is the conditional expected return going forward?

Q1l. What is the conditional MAD of the return?

Q1m. What is the conditional stdev of the return?

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Use same assumption for 5 states of economy and related stock price performance as in Q1 before the release of econ number.

Q2. Consider a PUT option with strike at 95.

Q2a. What is the prob of PUT expiring ITM (ie the price for the 95 strike binary put that pays $1 if expiring ITM)?

Q2b. What is the expected value of underlying index price under the condition that PUT expires ITM?

Q2c. What is the conditional PUT payment when expiring ITM?

Q2d. How much should the PUT option be priced at today?

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Q3. Redo Q2 for a 105 strike CALL.

Answer 1