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...

One of the central elements in modern finance theory is that of a risk-return tradeoff. The idea is simply that investors are risk averse, and accordingly must be paid to incur risk. T here is, then, a constant trade-off in the investment world: safe investments carry low return, high-return investments aren’t so safe. Fortunately, this conforms with almost everyone’s intuitions. What exactly is risk, though? Yes, we have an intuitive idea. The guy jumping out of an airplane is taking a risk that the appreciative audience standing on firm ground below is not. Further, if he has neglected to    check his gear properly he is taking an extra, unwarranted, risk. But we can be a good deal more specific about what the word means in the world of investments. It means the size of the standard deviation of return. It means the width of that bell curve we've discussed in earlier posts.   Standard Deviation A standard deviation is the “average distance from ...