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Technology Stocks : Dell Technologies Inc.
DELL 133.74-0.1%3:59 PM EST
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To: Geoff Nunn who wrote (82435)11/26/1998 1:16:00 PM
From: BGR  Read Replies (1) of 176387
 
Geoff,

If E(Y) = 0, doesn't there remain an arbitrage opportunity where you sell options with expected return = 0 (ignoring transaction costs) and loan the money thus raised at the risk-free interest rate (r) with expected return > 0 (everywhere except in Japan, that is)?

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. Volatility makes the average growth of the asset/liability different from r% in individual transactions but the expected value remains r% in the long run, thus ensuring that the option market is fair.

Hence E(Y) = r%. This is very similar to the future price vs. cash price relation (B-S may be used to derive that as well). Thus if X and Y represented risk premiums rather than real rates of returns your model holds. If that is true (i.e if B-S holds) strange as it may sound, risk premium being 0, options are risk-free by definition. As the Wall Street saying goes, there are no rich and old option players - it is a wash in the long run.

IMO, options traders can only make money from spotting mispriced options based on implied volatility and fundamental analysis.

-Apratim.
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