Discuss the below:
1. Your are considering writing 1 year Call options and a 1 year Put options on Mantis.com. The stock is currently trading at $20. The exercise price you have selected is $20. The risk-free rate is 10%. The historic standard deviation of the stock is 1% per day.
A. Employ the Risk Neutral Pricing method to find the price (value) of the European Call and Put option. Use a two step Binomial tree in each case.
B. Find the price for the American Put option. Use a two step Binomial tree.
2. Solve the following options employing the Black-Scholes model:
A. European call option on HPQ: 5413, X=12, r--6%, a=20%, T=6 months, In dividend $1 in 2 months, rd dividend of $1 in 5 months.
B. American call option for HPQ (Black's Approximation).
3. Using competitive-market/arbitrage arguments, determine the Fair Credit Default Swap Spread for the following contract:
- 3 year contract with payments to seller made at the end of the each year.
- Expected recovery rate of 0.40; i.e., the CDS seller is expected to pay $.60s on $1.
- Default probabilities: Year 1: 0.08, Year 2: 0.05, Year 3: 0.03.
- Default can only occur year-end.