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Strategies & Market Trends : The Covered Calls for Dummies Thread -- Ignore unavailable to you. Want to Upgrade?

To: Mathemagician who wrote (2688)	10/14/2001 7:20:28 PM
From: Dan Duchardt	Respond to of 5205

dM, A sketch of the proof would make me very happy, should you feel inclined to provide one. :) I've never really tried to pick apart Black-Scholes or the Binomial model to see where the various pieces fit there, but I have done a lot of fooling around with an option analyzer tool to compare the CC and short put strategies. There is a nice Excel based tool available for free at hoadley.net Here is the "sketch" of the proof based on the output of the model: If you set the risk free interest rate to zero, and try all sorts of combinations of stock and strike prices you always find that the TIME premium for a call is the same as that of the put, and that the profit loss profile of the two are identical. The full premium of course includes intrinsic value for one or the other depending on where the strike price is in relation to the stock price, so except for ATM the full premiums can be quite different If you take the stock price minus the call premium, that is always the same as the strike price minus the put premium. It follows that the amount of money you have tied up in the position is exactly the same for the CC as for that cash backed put. Since the profit loss curves are identical, and the amount of money committed is identical the positions are equivalent. Anything you do that disrupts the equality of the dollars committed causes a deviation from equivalence. Real world option prices of course include a risk free interest rate, and that elevates the call prices compared to the put prices by an amount that would be offset by realizing that much interest on the cash backing the put. If you enter an estimate of the interest rate into the model you see the theoretical option prices change accordingly (raises the calls and lowers the puts). Dan