Lesson 3 of 5 · All lessons in this module
  1. Fiduciary call, protective put and put–call parityVideo lesson
  2. Arbitrage when put–call parity fails
  3. Synthetic positions and option strategies from parityVideo lesson
  4. Put–call forward parity
  5. Put–call parity and the value of the firm

Lesson 3 of 5 · 12 min

Synthetic positions and option strategies from parity

Rearranging S0+p0=c0+X(1+r)−TS_0 + p_0 = c_0 + X(1+r)^{-T} shows how to build any one of the four instruments from the other three, which both prices it and gives its replicating portfolio.

In short

  • Move a term across the equals sign and its sign flips: a plus means long, a minus means short.
  • Synthetic put: p0=c0+X(1+r)−T−S0p_0 = c_0 + X(1+r)^{-T} - S_0 (long call, long bond, short share).
  • Synthetic call: c0=S0+p0−X(1+r)−Tc_0 = S_0 + p_0 - X(1+r)^{-T} (long share, long put, borrow PV(X)).
  • Synthetic share: S0=c0−p0+X(1+r)−TS_0 = c_0 - p_0 + X(1+r)^{-T} (long call, short put, long bond). The options' asymmetric payoffs cancel into a straight line.
  • A covered call (long share, short call) equals a long bond plus a short put: S0−c0=X(1+r)−T−p0S_0 - c_0 = X(1+r)^{-T} - p_0.

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