NO.PZ201702190300000408
问题如下：
Trident Advisory Group manages assets for high-net-worth individuals and family trusts.
Alice Lee, chief investment officer, is meeting with a client, Noah Solomon, to discuss risk management strategies for his portfolio. Solomon is concerned about recent volatility and has asked Lee to explain options valuation and the use of options in risk management.
Options on Stock
Lee begins: "We use the Black-Scholes-Merton (BSM) model for option valuation. To fully understand the BSM model valuation, one needs to understand the assumptions of the model. These assumptions include normally distributed stock returns, constant volatility of return on the underlying, constant interest rates, and continuous prices" Lee uses the BSM model to price TCB, which is one of Solomon’s holdings. Exhibit 1 provides the current stock price (S), exercise price (X), risk-free interest rate (r), volatility (σ), and time to expiration (T) in years as well as selected outputs from the BSM model. TCB does not pay a dividend.
BSM Model for European Options on TCB
Options on Futures
The Black model valuation and selected outputs for options on another of Solomon’s holdings, the GPX 500 Index (GPX), are shown in Exhibit 2. The spot index level for the GPX is 187.95, and the index is assumed to pay a continuous dividend at a rate of 2.2% (5) over the life of the options being valued, which expire in 0.36 years. A futures contract on the GPX also expiring in 0.36 years is currently priced at 186.73.
After reviewing Exhibit 2, Solomon asks Lee which option Greek letter best describes the changes in an option’s value as time to expiration declines.
Solomon observes that the market price of the put option in Exhibit 2 is $7.20. Lee responds that she used the historical volatility of the GPX of 24% as an input to the BSM model, and she explains the implications for the implied volatility for the GPX.
Options on Interest Rates
Solomon forecasts the three-month Libor will exceed 0.85% in six months and is considering using options to reduce the risk of rising rates. He asks Lee to value an interest rate call with a strike price of 0.85%. The current three-month Libor is 0.60%, and an FRA for a three-month Libor loan beginning in six months is currently 0.75%.
Hedging Strategy for the Equity Index
Solomon’s portfolio currently holds 10,000 shares of an exchange-traded fund (ETF) that tracks the GPX. He is worried the index will decline. He remarks to Lee, "You have told me how the BSM model can provide useful information for reducing the risk of my GPX position" Lee suggests a delta hedge as a strategy to protect against small moves in the GPX Index.
Lee also indicates that a long position in puts could be used to hedge larger moves in the GPX. She notes that although hedging with either puts or calls can result in a delta-neutral position, they would need to consider the resulting gamma.
8.The strategy suggested by Lee for hedging small moves in Soiomon‘s ETF position would most likely involve:
选项：
A. selling put options.
B. selling call options.
C. buying call options.
解释：
B is correct
because selling call options creates a short position in the ETF that would hedge his current long position in the ETF.
Exhibit 2 could also be used to answer the question. Solomon owns 10,000 shares of the GPX, each with a delta of +1; by definition, his portfolio delta is + 10,000. A delta hedge could be implemented by selling enough calls to make the portfolio delta neutral:
老师 如果A说buy put对吗？
