Given the following inputs:

Interest rate 7.25

Dividend rate 7.50

and the following option prices:

Strike Price CallPrice Put Price

29.00 4.49

1.83

32.00 4.06 4.25

39.00 1.06 7.88

1. Construct an arbitrage portfolio.

2. Graph the payo and pro t diagrams for your portfolio from a), labelling key points.

For the next set of options use the same interest and dividend rates as above along, with a spot price of 36.14 and an expiry of 9 months.

Given the following option prices:

Strike Price CallPrice Put Price

29.00 7.99

1.09

32.00 5.71 1.65

39.00 2.67 5.24

3. Construct an arbitrage portfolio. Graph the payoff and profit diagrams.

4. Explain the terms fat tails and skew (in the context of volatility)d) Compute the implied volatilities for each of the call options (to the nearest 1%). Are these volatilities consistent with what we expect from fat tails and skew ? Explain.