Has Solly Got Synthetic Shorts?, page-7

Hi andrewk4,

The arbitrage opportunity is identified as a breach of the fundamental put-call parity relationship.

For European Options:

CallPremium - PutPremium = StockPrice - PresentValue of ExercisePrice.

For American Options:

CallPremium - StockPrice + PresentValue of ExercisePrice <= PutPremium <= CallPremium - StockPrice + ExercisePrice

The exercise was fudged by crossing from ETO market into Warrant market, and by disregarding interest rates, funding costs, present values, etc.

From memory:

CallPremium = 00.09
PutPremium = 00.94
StockPrice = 17.63
ExercisePrice = 18.50

American Style:

(00.09 - 17.63 + 18.50 = 00.96) > PutPremium of 0.94 < (00.09 - 17.63 + 18.50 = 00.96)

Breach on left-hand side.

The Put Warrant was cheap so the arbitrage is constructed around the purchase of the put. This type of arbitrage (identifying cheap puts) does not involve short selling the underlying. If the call option was the underpriced option, the arbitrage would require a short sell.

GK