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(FINA222)[2009](s)final~2047^_10334.pdf
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FINA222 2009 Spring Final Exam

Name Student No.

Note: All interest rates are continuous compounding rates unless otherwise stated.


1.
Which of the following are always positively related to the price of a European call option on a stock (Circle there) (6)


(a)
The stock price


(b)
The strike price


(c)
The time to expiration


(d)
The volatility


(e)
The risk C free rate


(f)
The magnitude of dividends anticipated during the life of the option




2.
State whether you agree or disagree with the following statements, and say why.

The price of an American call option with strike 100 must be at least as great as the average price of two otherwise identical options (same underlying and expiration) with strikes 95 and 105.(5)




3.
What is the lower bound for the price of a two-year European call option on a stock when the stock price is $ 20, the strike price is $ 15, and the risk C free interest rate is 5% and there are no dividends? How does your answer to question change if the option is American? (10)





4.
Three-month European put options with strike prices of $50, $55, and $60 cost $2, $4, and $7, respectively.

(i) What is the maximum gain when a butterfly spread is created from the put options? (5)
(ii) What is the maximum loss when a butterfly spread is create from the put options? (5)
(iii) For what two values of ST does the holder of the butterfly spread breakeven with a profit of zero, where ST is the stock price in three months? (5)




5.
A power option pays off [max(ST C K), 0]2 at time T where ST is the stock price at time T and K is the strike price. Consider the situation where K=26 and T is one year. The stock price is currently $24 and at the end of one year it will be either $30 or $18. The risk-free interest rate is 5%

(i) What is the risk neutral probability of the stock rising to $30? (5)
(ii) What position in the stock is necessary to hedge a short position in one power option? (5)
(iii) What is the value of the power option? (5)






6.
For a European call option on a non-dividend-paying stock, the stock price is $30, the strike price is $29, the risk-free rate is 6% per annum, the volatility is 20% per annum and the time to maturity is three months. Expressed in terms of the cumulative normal function, N(x),

(i) What is the price of the option? (5)
(ii) What is the price of the option if it is a put? (5)
(iii) What is the price of the option if a dividend of $2 is expected in two months? (5)





7.
(Binomial Model.) Suppose that the annualized, continuously-compounded return on EBAY stock is normally distributed with mean 0.08 and standard deviation of 0.4. Also, the annualized, continuously compounded risk-free rate is 4%. The current price of EBAY stock is $50. Assume that no dividends