Explanation

This question tests the understanding of put-call parity and how market prices may deviate from theoretical Black-Scholes prices.

Put-Call Parity Formula

Put-call parity states that for European options with the same strike price and expiration date:

C + PV(K) = P + S

C + PV(K) = P + S

Where:

• C = Call price
• P = Put price
• PV(K) = Present value of strike price
• S = Current stock price

Applying the Information

Given:

• Market call price = $3.00
• Black-Scholes call price = $3.50
• Black-Scholes put price = $2.00

From put-call parity using Black-Scholes prices:

`$3.50` + PV(K) = `$2.00` + S

`$3.50` + PV(K) = `$2.00` + S

From put-call parity using market prices:

`$3.00` + PV(K) = Market Put Price + S

`$3.00` + PV(K) = Market Put Price + S

Solving for Market Put Price

Subtract the first equation from the second:

(`$3.00` + PV(K)) - (`$3.50` + PV(K)) = (Market Put Price + S) - (`$2.00` + S)
`$3.00` - `$3.50` = Market Put Price - `$2.00`
-`$0.50` = Market Put Price - `$2.00`
Market Put Price = `$2.00` - `$0.50` = `$1.50`

(`$3.00` + PV(K)) - (`$3.50` + PV(K)) = (Market Put Price + S) - (`$2.00` + S)
`$3.00` - `$3.50` = Market Put Price - `$2.00`
-`$0.50` = Market Put Price - `$2.00`
Market Put Price = `$2.00` - `$0.50` = `$1.50`

Verification

The difference between the market call price and Black-Scholes call price is -$0.50. Due to put-call parity, the market put price should also be $0.50 less than the Black-Scholes put price:

`$2.00` - `$0.50` = `$1.50`

`$2.00` - `$0.50` = `$1.50`

Therefore, the correct market price for the put option is $1.50.