Thursday, June 23, 2011

PCP synthetic positions - before expiration?


In most of the books I have seen, all the synthetic option positions (buy-write vs short put for eg) are analyzed at expiration, using the hockey stick PnL graphs. But what about valuations before-expiration -- is the synthetic also a substitute?
 
Let me give you a long answer. Bear in mind all the synthetics are based on PCP, applicable to European (E) options only.( For Europeans, real valuation happens only at expiration.)

By arbitrage analysis, and assuming 0 bid/ask spread 0 commission European style, I believe we can prove that n days (eg 5) before expiration, BW valuation must match the naked short put.

5 days before expiration, even with very low spot level, even with very high implied volatility, the option holder can't exercise and must wait till expiration. At expiration, the 2 portfolios have identical payoff. Therefore the 2 are equivalent any time before expiration.

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