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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

York University - MFIN 5800 MFIN 5800 (M) Question 1)Suppose that you are considering an exchange traded option contract on 100 shares

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York University - MFIN 5800

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

  1. What type of changes in the yield curve is duration­based hedging appropriate for?
  2. If convexity is included as well, what types of yield curve changes can be accommodated?
  3. Are there any types of yield curve changes that duration and convexity alone are inappropriate for? If so, how can these changes be accommodated?

 

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:

  1. The weighting of observations method;
  2. The volatility updating method;
  3. Use of Extreme Value Theory.

 

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.

  1. Express E1  in terms of A0  and L0.
  2. How large does A0  have to be to have Prob(E1  > 0) = 99%?
  3. How large does A0  have to be to have Prob(E1  > 0) = 99.9%?

 

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.

  1. Identify what action you should take now (i.e. when you have just written the option contract) to make your position delta neutral.
  2. After the option is written, if the stock price falls to $99 per share, identify what action should be taken at that time, later, to rebalance your delta­hedged position.

 

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.

  1. What tests might you perform to determine if one model produces “better” derivative prices than the other?
  2. Would you ever consider using both models?

 

  1. Could one be a “research” model, and the other an “official” model? If so, how would you decide which to use for which purpose?

 

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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