Stock ABC, whose current price is $42, has several 5-month European options written on it. The call and put prices are $5.4 and $3.8 respectively for the same exercise price of $40. The risk-free interest rate (continuous compounding) is 5% p.a. Which of the following statement is correct?

Group of answer choices

1. There are definitely some arbitrage opportunities.

2. If the option prices are correct then there is definitely a dividend payment of at least $1.5 within the next five months.

3. There is definitely at least one dividend payment within the next five months.

4. None of the other four.

5. The corresponding American call value should be $5.4 and the American put value is higher than $3.8.

The strike price of a six-month European put on futures is $19, the risk-free rate is 6% per annum compounded continuously, and the value of the option is $1.5. The current futures price is $21. Then the value of a call option with the same strike price and time to maturity is

Group of answer choices

$4.062.

$2.000.

$3.441.

$3.500.

A stocks price is observed monthly with S_i being the ith observation. Let u_i = ln(S_i / S_i-1). Suppose that there are 20 observations on the u_i and the sum of u_i is 0.24 and the sum of the squared u_i is 0.08. Then the standard error of the annual volatility estimate is

Group of answer choices

0.0494.

0.0349.

0.2207.

0.0637.

A forward rate agreement for a 3-year, $2 million loan has just reached its maturity. The contract rate is 9% and the current 3-year rate is 10.5% p.a. compounded continuously. To settle the contract, the borrowing party will

Group of answer choices

1. receive $65,681 from the lending party.

2. pay the lending party $90,639.78.

3. receive $2 million in net from the lending party.

4. pay the lending party $65,681.

5. receive $90,639.78 from the lending party.

The spot price of an asset is positively correlated with the market. Then, the futures prices are most likely to be in

Group of answer choices

1. contango and backwardation simultaneously

2. normal contango and normal backwardation simultaneously

3. normal contango only

4. contango only

5. contango and normal backwardation