LOL Ltd has a current share price of $40. A call option written on LOL, which has a strike price has $38 and 9 months to expiry, is trading at $4.94. If the riskfree rate of interest is 3% pa (continuously compounded), what is the correct price for a put option on LOL with $38 strike price and 9 months to expiry? Do not enter the dollar sign "$" in your answer. Your answer should have at least two decimals places.

Question

BlackTom AI · Accepted Answer

Put-call parity for European options states C - P = S - K e^{-rT}. Here C = 4.94, S = 40, K = 38, r = 0.03 (continuously compounded), and T = 9/12 = 0.75 years.

Step-by-step computation:
1. Compute the present value of the strike: K e^{-rT} = 38 × exp(−0.03 × 0.75).
   - Exponent: −0.03 × 0.75 = −0.0225.
   - exp(−0.0225) ≈ 0.977751 (using the exponential series or a calculator).
   - So K e^{-rT} ≈ 38 × 0.977751 = 37.15454 (intermediate value).
2. Rearrange put-call parity to solve for the put price P:
   - C - P = S - K e^{-rT}  ⇒  P = C - S + K e^{-rT}.
3. Substitute numbers:
   - P = 4.94 − 40 + 37.15454
   - P = 4.94 − 2.84546
   - P ≈ 2.09454.

Rounding to two decimal places gives P = 2.09.

Why this is correct: put-call parity is an arbitrage-free identity for European options on non-dividend-paying stocks; it links call and put prices through the current stock price and the discounted strike. Using continuous compounding requires K e^{-rT} rather than simple discounting; using a wrong discount method (e.g., K/(1 + rT) or ignoring discounting) would produce a different (incorrect) put price. Also, ignoring the stock price or misplacing signs in the parity rearrangement would give incorrect results.

Conclusion: The correct put price is 2.09, which matches the provided answer.

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