FRM一级模考
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FRM一级模拟题
1 . A stock currently trades at $10. At the end of three months, the stock will either be $11 0r $9. The continuously compounded risk-free rate of interest is
3.5 percent per year. The value of a 3-month European call option with a
strike price of $10 is closest to:
A. $1.07
B. $0.54
C. $0.81
D. $0.95
Answer: B
2.The current price of a non-dividend paying stock-is $75. The annual volatility of the stock is 18.25%, and the current continuously compounded risk-free interest rate is 5 %. A 3-year European call option exists that has a strike price of $90. Assuming that 'the price of the stock will rise or fall by a proportional amount each year, and that the probability that the stock will rise in any one year is 60 %, what is the value of the European call option?
A. $22.16
B. $12.91
C. $3.24
D. $7.36
Answer: D
3 . You have been asked to find the value of an Asian option on the short rate. The Asian option gives the holder an amount equal to the average value of the short rate over the period to expiration less the strike rate. To value this option with a one-factor binomial model of interest rates, what method would you recommend using?
A. The backward induction method, since it is the fastest.
B. The simulation method, using 'path averages since the option is path-dependent.
C. The simulation method, using path averages since the option is path-independent.
D. Either the backward induction method or the simulation method, since both methods return the same value.
Answer: B
The payoff for an Asian option (or average price option) on the short rate is dependent on the path of the average value of short rates. Furthermore, Asian options must be valued using simulation techniques because they cannot be exercised early.
4 . Suppose you believe that Company A's stock price is going to decline from its current level of $82.50 sometime during the next
5 months. For $510.25 you could buy a 5-month put option giving you the right to sell 100 shares at a price of $83.00 per share. If you bought the put option contract for $510.25 and Company A's stock price actually dropped to $63.00, your profit net of the premium paid would be
A. $1,950.00
B. $1,439.75
C. $1,489.75
D. $2,000.00
Answer: C
5 . We buy an SPX put (multiplieF$250) at l,250 for a premium of 20 points. The S&P500 closes at l,235 0n the settlement day. What is our profit/loss from this trade?
A. $0
B. $500
C. -$1,250
D. -$3,750
Answer: C
In return for buying this option, we paid a premium of 20x $250 = $5,000. As the settlement level is lower than the strike we make (1,250 - 1,235)x 250 = $3,750. Subtracting the premium from the profit made at settlement, our net loss is $1,250.。