Reference no: EM133048561

Engineering Questions:

Question 1) The current stock price is 100. It pays 6% continuous dividend yield. Its volatility is 30%. The risk free interest rate is 3% flat. Use the closed form results from BSM theory to compute the price, delta and theta (round your numerical results to 4 decimal places) for
a) a 10 year European style call option with strike 150;
b) a perpetual American style call option with strike 150.
c) Greek "phi" for a derivative f is defined as its sensitivity to the changes of dividend yieldq:

Φ = ∂f/∂q
Compute phi for the above two options. Please present both the analytical expressions and the numerical results.

Question 2) The current price of a non-dividend paying stock is 100. The risk free interest rate is 2%. A 5 year European cash binary call option with barrier level K = 110 and cash notional H = 100000 is traded at 31669.34. What is the fair value of a European cash binary put option of the same maturity and barrier level?

Question 3) A portfolio consists of two stocks SA and SB. Their shares, prices, expected return rates, annualized volatility and beta are given below:

The correlation between SA and SB returns is 0.65. The expected return rate of the market is 12%, the market return volatility is 30%, and the risk free rate is 2%. Returns of all risky assets follow normal distributions.

a) According to CAPM, are SA and SB under-valued, over-valued or fair valued?

b) What is the expected return rate of the portfolio? What is the variance of its return?

c) What is the beta of the portfolio?

d) To weather short term market volatility the portfolio manager (PM) decided to make her position market neutral (i.e., beta = 0). The market index future is traded at 112500 per contract. Assuming the beta of the index future = 1.0, how many contracts should the PM long or short?

e) What is the 1-day, 97.5% confidence level VaR of the portfolio before and after adding the future position? Use 252 as the annualization factor, and assume the index future has the same statistical properties of the market index itself.

Question 4) A 2 year zero coupon corporate bond with notional N = 1000 is traded 895.5. The risk free interest rate r is 2%. Assume the bond default recovery rate R is 40%, and assume r, R and default (hazard) rate λ are all constant, what is the fair value of a 5 year zero coupon bond with the same seniority (i.e., R) by the same issuer?