Options and Speculative Markets RevConv # 121 Professor André Farber Solvay Business School Université Libre de Bruxelles

August 23, 2004 OMS 04 IR Derivatives |2 Decomposition of plain vanilla RC For the investor: RC = Bond – n Put. As: Stock + Put = Call + PV(Strike) RC = n Stock – n Call + (Bond – n PV(Strike))

August 23, 2004 OMS 04 IR Derivatives |3 Valuing a plain vanilla RC Step 1: # shares / bond n = 1,000 / Step 2: Bond valuation PV(Coupons) + PV(1,000) Step 3: Put Valuation Strike price = Adjust stock price for dividend payments »Continuous dividend yield q = (4*0.10)/14.30 = 2.78% »Adjusted stock price = – PV(next 4 dividends)

August 23, 2004 OMS 04 IR Derivatives |4 Delta hedging The issuer is long on puts (long on volatility) The delta of a put option is negative To hedge its position, it should buy: - n * Delta put shares

August 23, 2004 OMS 04 IR Derivatives |5 Knock-in option (down-and-in put) Option alive if the stock price hits the lower barrier

August 23, 2004 OMS 04 IR Derivatives |6 In this situation, the option is not initiated

August 23, 2004 OMS 04 IR Derivatives |7 A standard put option would end up in the money. This is not the case for the d&i put option

August 23, 2004 OMS 04 IR Derivatives |8 Valuing the down-and-in put option For a standard put option: Risk neutral probability of being in the money at maturity

August 23, 2004 OMS 04 IR Derivatives |9 Proba(S T <H) Proba(S T ≥H & Hit) Proba(S T ≥K & Hit)