This paper by Anderson, Bollerslev, Diebold and Labys documents an empirical finding about standardized returns. If one needs to obtain standardized returns, the usual way is to divide the returns by volatility estimated by ARCH, GARCH type of models. This does not eliminate fat tails though. This paper studies 10 years of high frequency returns for USD-Yen. It begins by showing that the unstandardized returns are fat tailed(obvious to everyone in today’s world).

Let’s say you want to compute the annualized monthly volatility of your portfolio. There are two ways to go about doing it : Compute the monthly volatility of each month for your portfolio, average it and multiply by sqrt(12) Create a moving window to capture monthly volatility, average it, and then multiply by sqrt(12). In this case, there will many more data points that give you an estimate of monthly volatility as compared to the first case.

The title is meant to convey the message that many problems in mathematics can be solved using elementary tools, more of a street fighting kind than some heavy weight combat type tools. There have been many other books in this genre that highlight the importance of smart guessing and approximations but this book is exceptional in one way - It shows that math problems like solving differentiation, integration, differential equations, etc.

CBOE introduced VIX to measure the market’s expectation of 30-day volatility implied by at-the-money S&P 100 Index option prices. This was in 1993. Ten years later in 2003, CBOE with Goldman Sachs updated the VIX to reflect a new way to measure expected volatility, one that continues to be widely used by financial theorists, risk managers and volatility traders. The new VIX is based on S&P 500 Index and is estimated via averaging the weighted prices of SPX puts and calls over a wide range of strike prices.

Via Eran Raviv: The big plus of non-parametric bootstrap is that it is strictly data-based, without any distributional assumption, the big minus is the same, it is strictly data-based. Possible “futures” for the rate series in green and the red line is the actual realization