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1. An asset follows a binomial model every six months(length of each period). The current
price is 60. the US risk-free rate is 1% and the volatility of the asset is 30% per annum. What
is the early exercise privilege premium of a one year American lookback on the maximum
option?
2. Consider a stock currently priced at $60. Assume that in each period of one month, the
stock could either appreciate or depreciate by 10%. The risk-free rate is 2% per annum.
What would be the value of a 3-month 60 European call if a dividend of $1 would be paid
and the ex-dividend date is at the end of the second period? Justify your answer.
3.Consider a stock currently priced at $40. Assume that in each period of one month and for two
periods, the stock could either appreciate or depreciate by 10%. The risk-free rate is 2% per
annum. You have the right to shout at time 1. This means you lock in a profit payable at maturity
and rewrite the contract at a new exercise price equal to the underlying price at the time of the
shouting.
What is the value of the shouting?
4.Consider a stock currently priced at $40. Assume that in each period of one month, the stock
could either appreciate or depreciate by 10%. The risk-free rate is 2% per annum.
What would be the value of a 3-month American lookback option on the minimum of this stock?
5. The value of a project is $100 and the cost at t=0 is $104.The project value follows a
binomial model. It could go up to $180 or down to $60. The government posts a guarantee
of $78 at time 1. What is the value of the option? The required rate of return is 20% and the
risk free rate is 8% per period.
6. You have a project that costs $104. The current value of the project is $100. This value
could go to $180 or $60 in one period. You pay $44 now and borrow $60 at 2% per period
for one period.What is the value of the embedded option if the risk free rate is 2% per
period?
7. Consider a stock currently priced at $40. Assume that in each period of one month, the
stock could either appreciate or depreciate by 10%. The risk-free rate is 2% per annum.
8. The value of a company is 1000 expected to go up by 20% or down by 10%. The company
has a two-year zero-coupon debt with face value of 500. The risk free rate is 4%. The cost of
equity is 14%. What is the yield on the debt?
9. You have the following information:
Portfolio
Traded option
Gamma
-3,000
.1
Vega
-5,000
.3
Delta
0
.7
Could you create a delta-neutral, gamma-neutral portfolio?Justify your answer.
Could you create a delta-neutral, vega-neutral portfolio?Justify your answer.
Could you create a delta-neutral, gamma-neutral, and Vega Neutral portfolio? Justify your
answer.
10. GW Bank has the following positions:
* Short XY 100,000 calls with X=.95, T=2-Month, and delta=.533
* Long XY 200,000 calls with X=.96, T=3-Month, and delta=.568
Short XY 100,000 puts with X=.96, and T=3-Month
The risk-free interest rates is 4%.
What should the bank do to have a delta- neutral portfolio?Justify your answer.
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