# Volatility Futures & Options

## Apr 14, 2015

### MATLAB Computational Finance Conference 2015

MATLAB Computational Finance Conference was a great event that I attended last year. There is a lot to learn for average Matlab user, and anyone working in finance. The agenda looks especially exciting this year. Ping me if you want to meet during the event.

## Apr 8, 2015

### Volatility Arbitrage Mutual Fund?

Indeed; just came across this article:

No other information about the fund available on American Beacon website.

More detailed information in the SEC filing. Ionic was managing the strategy since August 2013, and the performance has not been stellar: the fund returned only 3.2% since inception til end of 2014. Proposed managed fee is little over 1%. However this is not particularly surprising - afaik Ionic strategy is specifically long convexity, and would likely to underperform at times of stagnant volatility, like we had in the past few years.The American Beacon Ionic Strategic Arbitrage Fund ... [through it's] sub-advisor, Ionic Capital Management, will pursue ... a market-neutral ... strategy that consists of ...40-50% of the fund’s assets will be allocated to convertible arbitrage;20-30% will be allocated to credit/rates relative value arbitrage;30-40% will be allocated to equity arbitrage; and5-15% to volatility arbitrage.

No other information about the fund available on American Beacon website.

## Mar 26, 2015

### High / Low Timing Patterns, Part 2

Comment from reader Rich on yesterday's post prompted me to run a quick investigation - does adjusting bars helps to bring distribution of highs and lows closer to theory? The answer is definitely yes, but as everything else in life the reality is complicated. Here's what I found:

Using SPY data for 2013 and 2014, and dividing trading day into 7 equal time intervals of about 56 minutes the percentages of highs and lows (and theoretical from arcsine law) are as follows:

Using SPY data for 2013 and 2014, and dividing trading day into 7 equal time intervals of about 56 minutes the percentages of highs and lows (and theoretical from arcsine law) are as follows:

highs | lows | theoretical |
---|---|---|

30% | 42% | 25% |

11% | 14% | 11% |

9% | 8% | 10% |

6% | 4% | 9% |

7% | 7% | 10% |

11% | 9% | 11% |

27% | 16% | 25% |

So the numbers are clearly different, especially for beginning of the day, and for daily lows. However, if we divide every day into 7 buckets of equal volume, the distribution of highs and lows is actually much closer to theoretical:

highs | lows | theoretical |
---|---|---|

23% | 28% | 25% |

12% | 15% | 11% |

10% | 14% | 10% |

9% | 10% | 9% |

11% | 11% | 10% |

13% | 11% | 11% |

23% | 11% | 25% |

Both highs and lows are quite similar to what is predicted by theory. But as Rich noted in the comment, lows tend to happen more often at the start of the day than predicted by theory, even if we normalize the data by volume. This, I believe, is a legitimate pattern - although I'm not sure how to systematically capitalize on it.

## Mar 25, 2015

### High / Low Timing Patterns

Just few days ago stock.nu published a post with charts showing that empirical distribution of daily lows follows a U-shaped pattern, i.e. daily low is not equally likely to happen at any time during the trading day, rather low is more likely to occur near the open or the close. Similar (symmetric) U pattern exists for distribution of daily highs - they also more likely to happen near the open or the close.

This particular distributions of daily extremes is actually

This phenomenon is known as arcsine law (law in this context means probability distribution) and has several manifestations. The one displayed in the charts is described in Wikipedia as Third Arcsine Law

This particular distributions of daily extremes is actually

*not*surprising - it is one of the properties of random walk process. To re-phrase: if we were to simulate a random walk process, we would not see a uniform distribution of highs and lows throughout the day, rather we would see this U-shape pattern of highs and lows.This phenomenon is known as arcsine law (law in this context means probability distribution) and has several manifestations. The one displayed in the charts is described in Wikipedia as Third Arcsine Law

This is theoretical distribution of lows (or highs) that we would expect according to the formula. If you compare it to the original (empirical distribution) chart, the numbers are quit similar.

However I must note that I cheated a little bit: both the empirical chart from stock.nu and mine below have seven columns, but time intervals are not the same - in the top chart the first bar corresponds to the first half-hour, while the rest are one hour. In theoretical chart all time intervals are the same.

So how much do these distributions really differ? If we recalculate the theoretical chart, we still see the U-shaped pattern, but it would look somewhat different from empirical.

What explains the differences? Well - really one thing - there is a difference in trading activity in different parts of the day. I speculate that if were to adjust the time intervals for equal trading volume, or equal number of trades, the resulting empirical distribution will be very similar.

Check out my follow-up post.

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