Jan 28, 2015

Machine Learning in Finance Workshop

The Data Science Institute at Columbia University and Bloomberg are holding a workshop on Machine Learning in Finance. The presentations look interesting and the price is
right - just $30 if you have a valid student ID, or $100 if you don't.

Some research articles are already available for download - Shawn Mankad's research or regulatory feedback is available on his website, Marti Subrahmanyam's research on options is available here. I'm probably going; if you're looking to network send me an email.

Jan 22, 2015

Opalesque.tv Volatility Interviews

Opalesque.tv has two most interesting interviews: first, from 2012 with Michael Wexler of Maple Leaf, and second , posted earlier this month, with Dr Andrew Cumming of Blackheath Volatility Arbitrage. It is not often that you hear detailed interviews from volatility arbitrage managers, so I thought to post the links in case my readers missed it.

Volatility trading is complex, and there are many more volatility strategies than there are equity strategies, but the funds mentioned above do run a similar core strategy - both sell ATM options and buy / overbuy wings (similar strategy is purportedly traded by ex-Nassim Taleb's hedge fund). The first payout strategy is fly - which is easy to understand as short vol position; the second - short ATM longs extra wings, looks like letter W with peak at the money, and extra wings on the side. The strategy is called dragonfly, and it is much harder to provide a simple explanation. It pays off in a really calm market, loses money in a moderately volatile market, and makes money in very very volatile conditions. The payoff is obviously highly nonlinear.

Both funds are extremely diversified across all asset classes, and geographic markets. Michael Wexler notes that equities is probably the most difficult asset class for short vol, given the high level of cross-correlations at times of crisis, and competition.

Jan 14, 2015

Notes From Academia: Exercise Boundary Violations in American-Style Options

Here is the link to the research paper - Exercise Boundary Violations in American-Style Options: The Rule, not the Exception

Abstract: An exercise boundary violation (EBV) occurs when the current bid price for an American option in the market is below intrinsic value. A seller at this price leaves money on the table and the buyer receives an arbitrage profit. In a liquid market, competition among dealers should drive up the bid prices and eliminate the arbitrage. An analysis of intraday data shows that EBVs are the norm, not the exception, with near-term in-the-money equity calls and puts the most affected. In March 2010 48.6% of all in-the-money call options had EBV bid quotes and 11.5% of trading volume in those options occurred below the intrinsic value, costing the sellers an estimated $39 million. EBVs are highly persistent throughout the day, making it rational to liquidate an option by exercise rather than selling it in the market, in sharp contrast to textbook theory. Our empirical results show early exercise is strongly related to an option's EBV. 

The findings are not at all surprising: options market makers do not like to provide tight quotes for ITM options, especially high-delta options, because of pick-off risk. If market makes a sudden move, HFT stock traders, or options market makers with faster infrastructure can quickly trade against a slower market maker, locking in free premium. OTM options don't move as fast, and are not as risky from this angle.

So it is only natural that bids are below the exercise boundary. Majority of option traders know as much - if only 11.5% of volume is below intrinsic value, 88.5% presumably do not make that mistake.

Jan 9, 2015

Volatility of Average

Different commodity including some volatility and bitcoin futures settle to an average value. For example VSTOXX settles to 1 minute sampled average value of the index in the last half hour of trading, Bitmex XBT/USD futures settle to 1 minute sampled average value of the last two hours of trading, Atlas ATS BTC/USD futures and options settle to a 24 hour average of the last calendar day of the month.
Correct modelling of this is interesting for both options and futures pricing, as average process has obviously less volatility than "regular" process. How much less? Well, apparently I fell asleep during a class because I have no recollection of the formula until I recently researched it.
B(t) is ABM, then has variance of


In simple terms, average has 1/sqrt(3), or about 58% of volatility. 

Simple example: assume BTC/USD volatility of 100% per year. Expected volatility over 30 days should be  sqrt(100 * 100 * 30/365)  = 28.67%. However if the contract settles to the last day's average, for options pricing we should use volatility of sqrt(100 * 100 * 29/365 + 100 * 100 * 1/365 / 3)  = 28.35%, slightly lower. 

In conclusion: average settlement - interesting, but of little practical importance from pricing perspective. 

P.S. Re: Atlas ATS - could not get their API to work, waiting for LedgeX.