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IBBC CAPITAL ACADEMY / 2027

Replicate European options with put–call parity

Independent IBBC Capital draft content for self-study. Not affiliated with or endorsed by CFA Institute. New lessons await subject-matter review. No CFA designation or official PSM credit is awarded.

Learning goals

  • Explain matched contracts using mechanisms and limitations.
  • Explain synthetic positions using mechanisms and limitations.
  • Explain forward form using mechanisms and limitations.

Draft · approximately 25 minutes, excluding further revision.

Matched contracts

European put–call parity compares call plus present-value strike with put plus underlying for the same strike and maturity under compatible assumptions.

For a non-dividend stock, c+PV(K)=p+S; future dividends require an explicit present-value adjustment rather than ignoring the distribution.

Synthetic positions

A synthetic long stock combines long call, short put and a bond funding strike; match quantities and dates before concluding exposure equivalence.

A call-minus-put position replicates a forward-like terminal payoff ST−K, not the nonnegative payoff of a call alone.

Forward form

Forward parity expresses c−p as discounted (forward price−strike), using an appropriate forward and discount factor.

Apparent parity violations require executable quotes and funding, short-sale and exercise checks; American early exercise can break the simple European equality.

Formula and assumptions

c−p=S−PV(dividends)−PV(K)=DF×(F−K)

Original applied case: Replicate European options with put–call parity

  1. Non-dividend stock 100, strike present value 95 and European put price 7, matched maturity.
  2. Call=put+spot−PV(strike)=7+100−95=12.
  3. This is an arbitrage relationship under assumptions, not a forecast of the final asset price.

Errors to catch

  • Do not assume: Parity compares options with unrelated maturities.
  • Do not assume: Future dividends can always be omitted.
  • Do not assume: Long call plus long put exactly replicates long stock.

Original knowledge check

Answer every question before checking. Review explanations after submitting; retry starts a new attempt.

Sources and coverage status

These original lessons are drafts. Public outlines are used to check scope; the official learning-outcome text and proprietary question banks are not reproduced here. Follow the source for exam-year requirements and updates.