Given a text T, and several options, according to the question posed in the text T to choose the most appropriate option from the options as the answer, please directly output the most appropriate option, do not need to output the explanation.

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 StockLee 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.
| Exhibit lBS M Model for European Options on TCB |
| BSM Inputs |
| SXrT |
| $57.03550.22%32%0.25 |
|  |
| BSMOutputs |
| BSMBSMdN(d)dN(da)Call PricePut Price |
| 0.31000.62170.15000.5596$4.695$2.634 |


Options on FuturesThe 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.
| Exhibit 2.Black Model for European Options on the GPX Index |
| Black Model Inputs |
| GPX Index | X | r | 8 Yield |
| 187.95 | 180 | 0.39% | 24% | 0.36 | 2.2% |
| Black | Black | Market | Market |
| Model | Model | Call Price | Put Price |
| Call Value | Put Value |
| $14.2089 | $7.4890 | $14.26 | $7.20 |
| Option Greeks |
| Vega |
| Delta(cal) Delta(put) | Gamma(call or | Theta(cal) | Rho(cal) | per% |
| put) | daily | per% | (call or |
| put) |


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 RatesSolomon 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 IndexSolomon'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.
To determine the long put option value on TCB stock in Exhibit 1, the correct BSM valuation approach is to compute:
Option A:0.4404 times the present value of the exercise price minus 0.6217 times the price of TCB stock.
Option B:0.4404 times the present value of the exercise price minus 0.3783 times the price of TCB stock.
Option C:0.5596 times the present value of the exercise price minus 0.6217 times the price of TCB stock.

Answer: B