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.

Bruno Sousa has been hired recently to work with senior analyst Camila Rocha. Rocha gives him three option valuation tasks.Alpha CompanySousa's first task is to illustrate how to value a call option on Alpha Company with a one-period binomial option pricing model. It is a non-dividend-paying stock, and the inputs are as follows.● The current stock price is 50, and the call option exercise price is 50.● In one period, the stock price will either rise to 56 or decline to 46.● The risk-free rate of return is 5% per period.Based on the model, Rocha asks Sousa to estimate the hedge ratio, the risk-neutral probability of an up move, and the price of the call option. In the illustration, Sousa is also asked to describe related arbitrage positions to use if the call option is overpriced relative to the model.Beta CompanyNext, Sousa uses the two-period binomial model to estimate the value of a European- style call option on Beta Company's common shares. The inputs are as follows.● The current stock price is 38, and the call option exercise price is 40.● The up factor (u) is 1.300, and the down factor (d) is 0.800.● The risk-free rate of return is 3% per period.Sousa then analyzes a put option on the same stock. All of the inputs, including the exercise price, are the same as for the call option. He estimates that the value of a European-style put option is 4.53. Exhibit 1 summarizes his analysis. Sousa next must determine whether an American-style put option would have the same value.Exhibit 1. Two-period Binomial European-Style Put Option on Beta Company
| Item | Valu c |
| Underlying | 64.22 |
| Put |  |

| I tom | Valu c |
| Underlying | 49.4 |
| Put | 0.2517 |
| Hedge Ratio | -0.01943 |

| Item | Valu c |
| Underlying | 38 |
| Put | 4.5346 |
| Hedge Ratio | -0.4307 |

| Item | Value |
| Underlying | 30.4 |
| Put | 8.4350 |
| Hedge Ratio | -1 |

| Item | Value |
| Und cr lying | 39.52 |
| Put | 0.48 |
|  |
| Item | Value |
| Underlying | 24.32 |
| Put | 15.68 |


Sousa makes two statements with regard to the valuation of a European-style option under the expectations approach.Statement 1: The calculation involves discounting at the risk-free rate.Statement 2: The calculation uses risk-neutral probabilities instead of true probabilities.Rocha asks Sousa whether it is ever profitable to exercise American options prior to maturity. Sousa answers, “I can think of two possible cases. The first case is the early exercise of an American call option on a dividend-paying stock. The second case is the early exercise of an American put option.”Interest Rate OptionThe final option valuation task involves an interest rate option. Sousa must value a two-year, European-style call option on a one-year spot rate. The notional value of the option is 1 million, and the exercise rate is 2.75%. The risk-neutral probability of an up move is 0.50. The current and expected one-year interest rates are shown in Exhibit 2, along with the values of a one-year zero-coupon bond of 1 notional value for each interest rate.Exhibit 2. Two-Year Interest Rate Lattice for an Interest Rate Option
| Maturity | Value | Rate |
| 1 | 0.952381 | 5% |

| Maturity | Value | Rate |
|  | 0.961538 | 4% |

| Maturity | Value | Rale |
| 1 | 0.970874 | 3% |

| Maturi y | Value | Rate |
| 1 | 0.970874 | 3% |

| Maturity | Valu c | Rate |
|  | 0.980392 | 2% |

| Maturity | Val us | Rate |
| 1 | 0.990099 | 1% |


Rocha asks Sousa why the value of a similar in-the-money interest rate call option decreases if the exercise price is higher. Sousa provides two reasons.Reason 1: The exercise value of the call option is lower.Reason 2: The risk-neutral probabilities are changed.
The optimal hedge ratio for the Alpha Company call option using the one- period binomial model is closest to:
Option A:0.60.
Option B:0.67.
Option C:1.67.

Answer: A