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Homework answers / question archive / York University - MFIN 5800 MFIN 5800 (M) Question 1)Suppose that you are considering an exchange traded option contract on 100 shares
MFIN 5800 (M)
Question 1)Suppose that you are considering an exchange traded option contract on 100 shares. The current price of the option is quoted as $600 (i.e. $6 for an option on a single share). You are considering using an identical overthecounter option instead. You estimate the probability of default by the dealer during the life of the contract at 2.5%. After deducting the option dealer’s fee for agreeing to serve as counterparty to the contract, what would you expect the dealer’s price for selling the option to be? If the dealer’s price for the option is greater than $600, would it ever make sense to use the overthecounter option rather than the exchangetraded one?
Question 2
Question 3
In the historical simulation approach to market risk VaR, explain the motivation for each of the following adjustments to the straightforward application of the definition of VaR to the historical loss data:
Question 4
A bank estimates that its profit next year is normally distributed with a mean of 0.8% of assets and a standard deviation of 2% of assets, i.e. ROA (return on assets) is distributed N(0.8%, 2%2). Let A0 = assets, L0 = liabilities, and E0 = A0 – L0 be shareholder equity, all at the start of the year. Assume that liabilities at the end of the year remain the same as at the beginning of the year. Let E1 denote shareholder equity at the end of the year, and ignore taxes.
Question 5
A nondividendpaying stock has a current price of $100 per share. You have just sold a sixmonth European call option contract on 100 shares of this stock at a strike price of
$101 per share. You want to implement a dynamic delta hedging scheme to hedge the risk of having sold the option. The option has a delta of 0.50. You believe that the delta would fall to 0.44 if the stock price falls to $99 per share.
Question 6
Suppose there are two models of a stock price, one with a small number of parameters that does a reasonable job of capturing historical variations in the price, and another with many more parameters that does a much better job of capturing historical variations in the price.
Question 7
Calculate the volatility a trader would use for an 11month option with a strike price of 0.98 using the following table:
Time to Maturity |
Strike Price |
||||
0.90 |
0.95 |
1.00 |
1.05 |
1.10 |
|
1month |
14.2% |
13.0% |
12.0% |
13.1% |
14.5% |
3months |
14.0% |
13.0% |
12.0% |
13.1% |
14.2% |
6months |
14.1% |
13.3% |
12.5% |
13.4% |
14.3% |
1year |
14.7% |
14.0% |
13.5% |
14.0% |
14.8% |
2years |
15.0% |
14.4% |
14.0% |
14.5% |
15.1% |
5years |
14.8% |
14.6% |
14.4% |
14.7% |
15.0% |
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