ABC Ltd. Is currently trading at $27.00 per share. A one-year European put option on ABC with a strike price of $30.00 is currently trading for $2.60. If the risk-free interest rate is 6.00% per year, then the price of a one-year call option on ABC with a strike price of $30.00 will be closest to:

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We start by identifying the key inputs: current stock price S0 = 27, strike price K = 30, one-year maturity T = 1 year, risk-free rate r = 6% per year, and the observed price of a one-year European put with strike 30 is P = 2.60.

To value the corresponding call using put-call parity for European options on a non-dividend-paying stock, we use the relationship:
C + K e^{-rT} = P + S0  (continuous compounding), or equivalently C = P + S0 − K e^{-rT}.

We compute K e^{-rT} first. If we assume continuous compounding, e^{-rT} = e^{-0.06} ≈ 0.941764, so K e^{-rT} ≈ 30 × 0.941764 ≈ 28.25.

Plugging into the parity formula: C ≈ P + S0 − K e^{-rT} ≈ 2.60 + 27 − 28.25 ≈ 1.35.

If instead we use annual (discrete) compounding, K/(1 + r)^T = 30 / 1.06 ≈ 28.30, and C ≈ 2.60 + 27 − 28.30 ≈ 1.30.

Both methods yield a call price in the vicinity of 1.30–1.35. Since the question asks for the price closest to the call, the result typically rounded to two decimals would be about $1.30. The slight difference between the two compounding conventions explains why the parity calculation can land near 1.30 rather than exactly 1.35 in the continuous- vs discrete-compounding interpretations.

In summary, applying put-call parity with the given data leads to a call price around $1.30 to $1.35, with $1.30 being the closest rounded value commonly used in such problems.

MGT232H5 F LEC0101 Quiz 8

ABC Ltd. Is currently trading at $27.00 per share. A one-year European put option on ABC with a strike price of $30.00 is currently trading for $2.60. If the risk-free interest rate is 6.00% per year, then the price of a one-year call option on ABC with a strike price of $30.00 will be closest to:

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