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To: BGR who wrote (82439)	11/27/1998 8:29:00 AM
From: Geoff Nunn	Read Replies (1) \| Respond to of 176387

Apartim: re returns on call options You are right on target about Black Scholes. You wrote: My understanding of B-S is that in naked option transactions the buyer parts with cash that could have earned r% and gets an asset that grows at r% on average while the seller gets cash that may be invested at r% while assuming a liability that grows at r% on average. That is it exactly. Suppose the price of a particular call option is P and its value is F at expiry. What is the relationship between P and F? Under B-S it is: E(F) = P(1+r) where E(F) is the option's average value at expiry, and r is the rate of interest. This means that if a call option is priced at $5 its value at expiry on average should be $5.50, assuming the interest rate is 10%. Your noting of the fact that B-S can be applied to future price v. cash price relationships is well taken, although I believe it holds only for certain financial instruments - not commodities. One example would be a pure discount instrument such as a zero coupon bond. Buying a call option is similar to buying a ZCB since, in both cases, the expected appreciation rate is the market rate of interest. What would be the expected return if an investor buys either a call or a ZCB? In one sense it is the rate of interest, but in another sense it is zero if you consider opportunity costs. To illustrate, suppose you "write" (sell) a ZCB which I purchase. Let's assume the maturity value is 100, and interest rates are 6%. The fair price for this bond is the present value of 100, which is 94.34. If you sell this bond to me and repurchase it at maturity, what are our respective rates of return? It may be said that in both cases it is zero! You, the seller, receive 94.34 cash which can be invested at 6%. Don't forget you will need every penny of interest when you later repurchase at 100. I, the buyer, gave up 94.34 cash that could have been invested elsewhere at 6%. Because 6% is my cost (opportunity cost) I also just break even. I receive a 6% return but 6% is my cost, so my profit is zero. That's how economists think about profit! Turning to the question about arbitrage, I see no such opportunity. The option writer receives cash which can be invested at r%. Let's not forget though that every penny of interest will be needed, on average, when the writer goes to cover his liability. At expiry, the option will on average have appreciated by r% compared to the original purchase price. If that is the case, the writer will only be able to cover his costs, and will merely break even in the long run. As you said Apratim, it is a wash in the long run! Geoff