LOL Ltd has a current share price of $52. A put option written on LOL, which has a strike price has $55 and 8 months to expiry, is trading at $5.34. If the riskfree rate of interest is 7% pa (continuously compounded), what is the correct price for a call option on LOL with $55 strike price and 8 months to expiry? Do not enter the dollar sign "$" in your answer. Your answer should have at least two decimal places.

Question

BlackTom AI · Accepted Answer

Put-call parity for European options (no dividends) is the core concept: C + K e^{-rT} = P + S.

1) Relevant knowledge points and concepts
- Put-call parity relates the prices of European calls (C) and puts (P) with the same strike (K) and expiry (T): C = P + S - K e^{-rT}, where r is the continuously compounded risk-free rate.
- This formula assumes no dividends on the underlying; if dividends exist, the parity must be adjusted.

2) Step-by-step reasoning
- Identify given values: S = 52, K = 55, P = 5.34, r = 0.07 (continuously compounded), T = 8 months = 8/12 = 2/3 year ≈ 0.6666667 year.
- Apply put-call parity and solve for C.

3) Calculations (all intermediate steps)
- Compute rT: rT = 0.07 × (8/12) = 0.07 × 0.6666667 = 0.046666667.
- Compute discount factor e^{-rT}: e^{-0.046666667} ≈ 0.954405506 (using series/expansion).
- Discounted strike: K e^{-rT} = 55 × 0.954405506 ≈ 52.4923028.
- Call price: C = P + S - K e^{-rT} = 5.34 + 52.00 - 52.4923028 = 57.34 - 52.4923028 = 4.8476972 ≈ 4.85.

4) Why this answer is correct
- The calculation directly implements the arbitrage-free put-call parity under continuous compounding. It properly discounts the strike to present value and combines known market prices (put and underlying) to infer the fair call price. Any deviation would create an arbitrage opportunity.

5) Why common mistakes are incorrect
- Forgetting to discount the strike (using K instead of K e^{-rT}) overstates or understates C.
- Using simple interest instead of continuous compounding gives a slightly different (incorrect) price.
- Reversing the parity formula sign would produce a wrong result.

6) Conclusion
- The correct call price is 4.85, which matches the provided answer.

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Question at position 1 Other things equal, a put option's value increases as the strike price increases TrueFalse

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