Jamesian Philosophy Refreshed

The above graph is a visual representation of the Black-Scholes model. Or Black-Scholes- Merton if you want credit shared equitably and "you're not into the whole brevity thing," Mr Lebowski. As you can see, there are three axes. The x axis (the width of the box) is the price of the underlying asset, the stock price, treating the strike price in the center as 1. The y axis (the height of the box) is the volatility of that option. The z axis (the depth of the box) is the time to maturity [and either exercise or expiration].   As you can see, the plane of various shades of blue (the darker the blue, the higher) has a sharp crease at the front/center/bottom of the box, where the sharp difference between winners and losers on the lottery’s drawing date is indicated. We should also mention that the volatility that goes into the calculations as we’ve described them above is historical volatility. One of the assumptions of the BSM model is constant volatilit...

  You’ll remember that in earlier posts I've discussed a hypothetical widget-making company, XYZ, and said that we could enter various reasonable assumptions about this company’s stock in a calculator available in any of several websites, and receive for our troubles the value of a proposed put or call. How does the calculator do that?   A skeptic may sneer at the whole idea and say, “only supply and demand determine the value of a financial instrument. The demand for an option on a particular stock may change from day to day – as may the supply, as new writers enter or leave the market – so surely no formula or algorithm can tell us in advance what the value is.” That’s a plausible response, but it is in error. The value of stock options can be defined mathematically in ways that the value of the underlying stocks cannot. After all, we know intuitively what the value of a stock option is on the expiration date. If it has expired worthless, we know the value i...