in Derivatives2020, due Saturday 8/1/2020 at 10:00 am (Boston MA time).

Name (first, last) ______________________________________________________________

There are ten equally-weighted questions (10%). Please show all your work. Good luck.

1. Using the AAPL option chain and put call parity, assume the at the money strike of 225 and a Rf of 0.50%, also assume the actual mean put quote is $7.00. Derive the riskless arbitrage profits and explain all the arbitrage steps to accomplish this.

2. Using the AAPL option chain and 350,000 AAPL shares, devise a delta neutral call and put strategy. Prove each assuming a loss of $5 in APPL. You proof should include delta, gamma, and theta.

3. One Period Binomial Model, Using the AAPL option chain, solve for the at the money (X = 225) call and put options. Assume U = 1.2, πu= 0.6, Rf = 0.50%. Show all your work.

4. Using the AAPL option chain, assume you employ a covered call strategy with 1,000 shares of stock and the correct # of calls. Convert this to a delta neutral hedge with calls. Calculate the incremental (+ or -) # of calls you need. Calculate any required margin.

5. Using the AAPL option chain, establish a covered call with 2,000 stock shares. Determine the investment and ROI is S1 is $230 in 3 days. Use delta, gamma, and theta.

6. Assume you have a $500,000,000 portfolio: 50% equity with a beta of 1.2, and 50% fixed income, corporate bonds, average credit quality of BBB, duration of 5. You wish to design a portfolio: 75% equity asset allocation, beta 1.6, fixed income 25% asset allocation, duration 3. The available futures are: equity index 2,000, multiplier 250, fixed income Tbond $100,000 par, 97 price, 2 duration. The simulation is that in one day the market appreciates by 1.5% and the interest rates fall by 1%. Provide the correct number of contracts and do a proof.

7. Draw two graphs, one for the price yield relationship of a bond with its duration and convexity and the other a long call with the delta and gamma. Explain the mathematical analogy between delta/ duration and gamma/ convexity. Label all parts of the two graphs.

8. Using the AAPL option chain, using the at the money strike (225), if the stock rises by $5, calculate the new value of the call option, the new delta, and the new gamma.

9. Using the AAPL option chain, design a short strangle, where Xp = 215, and Xc = 235. If S1 = 225 in two days, calculate the margin, 2-day profit (using delta, theta, and gamma), ROI for 2 days and annualized, maximum gain and maximum loss.

10. Time-adjusted standard deviation. Using the current VIX, (you need to look it up), determine the daily standard deviation, assuming 252 trading days, and the 2-year standard deviation. Explain the relationship between VIX and asset pricing.