FRM一级模拟题
1 . A bank has sold USD 300,000 0f call options on 100,000 equities. The equities trade at 50, the option strike price is 49, the maturity is in 3 months, volatility is 20%, and the interest rate is 5%. How does it the bank delta. hedge? (round to the nearest thousand share)
A. Buy 65,000 shares
B. Buy 100,000 shares
C. Buy 21,000 shares
D. Sell 100,000 shares
we know that N(0.3770) has to be between 0.5 and l.0, which means we need to buy somewhere between 50,000 and 100,000 shares. The only answer that fits is A, buy 65,000 shares. If you did have access to a probability table, you could determine that N(0.37'/0) = 0.6469, which means we need to buy exactly 64,690 shares to delta hedge the position. '
2 . Initially, the call option on Big Kahuna Inc. with 90 days to maturity trades at USD l.40. The option has a delta of 0.5739. A dealer sells 200 call option contracts, and to delta-hedge the position, the dealer purchases 11,478 shares of the stock at the current market price of USD 100 per share. The following day, the prices of both the stock and the call option increase. Consequently, delta increases t0 0.7040. To maintain the delta hedge, the dealer should
A. sell 2,602 shares
B. sell l,493 shares
C. purchase l,493 shares
D. purchase 2,602 shares
Answer: D
Changes of Stock number= (0.7040-0.5739) x200x100=2602
3 . To hedge delta, gamma, and Vega of a portfolio of derivatives, with futures, FRAs, and options, the easiest way to calculate the appropriate amount of the hedges is to evaluate the quantity of:
A. futures first and FRAs second
B. futures first and options second
C. options first and FRAs second
D. FRAs first and futures second
Answer: C
It is easiest to determine the number of options first in order to address the vega risk, then use FRAs to address the gamma risk, and then use futures to address the delta risk.
4.Which of the following options strategies is considered to be a short volatility trade?
A. Long a protective put
B. Short a covered call
C. Long a straddle
D. Long a strangle
Answer: C
A long straddle is an option strategy that is profitable when the price of the underlying is volatile.