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Suppose you purchased the following options at fair value:

1. Suppose you purchased the following options at fair value:

Number of options Option type Strike

-100 calls 96
+ 50 calls 98
+ 50 puts 102
- 100 puts 104

Time to maturity, T = 90 days
σ = 15%
R = 4%
S(0) = 100

Sketch the payoff diagram. Compute , , , and vega at various times as time tends to expiration with S (t) = 100 for all t from 0 to 90 i.e. just do for one price of the underlying.

2. Using any bond option routine at your disposal, create a MATLAB program for valuing callable bonds and puttable bonds, their option-adjusted duration, convexity and OAS (given a current price or ytm). This should also work for non-callable bonds.

3. You are asked to create a simple one year CBO with two tranches, a senior and a junior. There are four underlying bonds, each has a principal of $100 and pays a coupon of 6%. Give several alternative structures. How much would be issued in each tranche and what coupon would each tranche pay?

4. Write a Matlab program to price CDS’s. Describe how the user would find the values for each of the input variables.

5. Program a Monte Carlo model for options on Energy. It should be mean-reverting and include spikes.
Give several alternative structures. How much would be issued in each tranche and what coupon would each tranche pay?

6. Write a Matlab program to value a swing swap

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