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Chartered Financial Analyst Level 1

Chartered Financial Analyst Level 1

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An analyst gathers the following information for a European option:

  • Call price: $10
  • Stock price: $40
  • Exercise price: $60
  • Interest rate: 3%
  • Time to expiry: 1 year According to put-call parity, the price of the put option is closest to:

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Explanation:

The correct answer is A ($28.25). According to put-call parity for European options, the relationship is given by:

S0+P0=C0+X(1+r)TS_0 + P_0 = C_0 + \frac{X}{(1 + r)^T}S0​+P0​=C0​+(1+r)TX​

Where:

  • S0S_0S0​ is the spot price ($40),
  • P0P_0P0​ is the put premium,
  • C0C_0C0​ is the call premium ($10),
  • XXX is the strike price ($60),
  • rrr is the interest rate (3%),
  • TTT is the time to expiry (1 year).

Substituting the values:

40+P0=10+601.0340 + P_0 = 10 + \frac{60}{1.03}40+P0​=10+1.0360​

Solving for P0P_0P0​:

P0=10+601.03−40=28.25242718≈28.25P_0 = 10 + \frac{60}{1.03} - 40 = 28.25242718 \approx 28.25P0​=10+1.0360​−40=28.25242718≈28.25

**Option B (30.00)∗∗isincorrectbecauseitfailstodiscountthestrikepriceby30.00)** is incorrect because it fails to discount the strike price by 30.00)∗∗isincorrectbecauseitfailstodiscountthestrikepriceby(1 + r)^T$.

Option C ($108.25) is incorrect because it incorrectly adds the spot price instead of subtracting it from the discounted strike price.

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