The Black-Scholes option valuation model, developed by Fisher Black and Myron Scholes in 1973 is without doubt the most popular option analysis and pricing model in use today, attempting as it does to predict fair option prices using rigorous mathematical models based on a security's price and volatility, time until expiration, and the current market interest rate. The Put/Call price is the main output of the Black-Scholes model, helping to answer the question of whether the option is overpriced or underpriced. Unfortunately the main use of this (to find and exploit over or underpriced options) is now less useful than it was, as everyone has access to the same equation, and barring machine failure, will generally price their options correctly. Long Term Capital management (yes, THAT turkey) used the model to try and create a "riskless" hedge to earn arbitrage profits (e.g. by buying underpriced calls and then shorting the underlying stock, having only to wait for the option to return to its fair market value resulting in arbitrage profits). The success (or otherwise!) of LTCM is well documented, but the model itself is still generally regarded as valid, it was the application of it that was at fault.

An associated term is Delta (the relative amount an option's price will change if the underlying security's price changes, hardly ever 1 for 1). Deep in-the-money options tend to have high Deltas, because almost all of the gain/loss in the security will be reflected in the option price. Deep out-of-the-money options tend to have a low Delta, because they are already dogs, and how bad can it get? As expiration approaches, Delta 'firms up' one way or the other - the Delta of in-the-money options approaches 1 because there is simply less time for them to soften into 'out-of-the-money' options.

A further associated term is Gamma, which indicates the risk involved with an option. Large Gammas suggest higher risk, because the value of the option is likely to change fast (it is geared). Other options terms, and the calculation of the Black-Scholes equations are outside the scope of this article. Day traders often try to create a 'riskless' position, but transaction costs and time decay on these options (and the unwillingness of the market to behave) usually conspire to thwart them..

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