Comment by Bronek

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Bronek
May 28th, 2008 at 4:19 pm
Peter ref Premium loss estimate.
The premium for call is defined as the ((underlying price + option cost) – strike price). I understand that Phil approximates the premium decay by dividing above defined premium/# days to expiration. It is a constant number and this is not the same as theta. Theta, like most of Greeks, is not linear and depends on distance from the strike price. To illustrate check attached Apple modified risk graph http://i26.tinypic.com/okx4i1.jpg . The risk graph is rotated and flipped in a way that price axis is aligned with a typical stock price graph and the P/L is on the horizontal axis. The redline is the option value today, 23 days to expiration, as a function of the stock price with other Greeks held constant. The blue line approximates the option value after about 1/3 towards the expiration (16 days left), green line is eight days prior to and the black is on the expiration date. All estimates use current volatility value (highly unlikely that it will remain constant). Please note that the distances between the lines are not constant. That means that the magnitude of theta increases as the expiration date approaches. Also note that the max theta is ATM and at the price of ~$172 theta=0. As the price moves away from ATM in either direction theta gets smaller. To summarize, b/c most Greeks continuously vary, the risk graphs are crude approximations of the future option value, so IMO Phil’s simplified method is not worse nor it is any better that other pretty graphs provided by most platforms, but it is simply to estimate.