Sunday, 10 April 2016

Some new updates

Looks as though I haven't updated this page in about a month. Technically, I have been writing, except they've been appearing on Canadian Running. Check them out if you'd like.

Conference:

I'm going to present some of my research at the EGU in Vienna in exactly one week. Check out my abstract here. I'm flying out Tuesday night, and hoping to see some of the city and culture. Thanks to Duolingo, I'm now 4% fluent in German, yay!

Montreal 5k:

Originally I was going to run 21.1k in Montreal,  but since the conference is eating up the chance for proper training, plus since I'm slightly injured with a forever tight hamstring. So it's the 5k for me (turns out lots of sitting and running do not cancel each other out). Also my wife Heather is running the 5k and raising money for the MOSD (Montreal Oral School for the Deaf ) on her personal fundraiser page.  You even get a tax voucher if you happen to contribute.

Finally, Stocks and options:

I'm learning a little more about stocks, and to a lesser extent options. It began with Jason Kottke's blog citing theBlack-Scholes as among the equations that changed the world, and realized I have never heard of it. It is useful (apparently) with options traders, who need to know what a 'good' price is for a call/put option. I had never understood options trading either. Figured it wasn't too late to learn.

Basically if you try solving for the brownian-type motion of stock movement, normalized to one-year periods, you get their famous equation, which is:


Where C is the option price, S is the strike price, sigma is the volatility, r is the interest rate if you bought a bond of some sort, and t is time. The sigma value is known as the implied stock volatility (IV), it might range from 0% (rock-steady) to 100% (stock could lose all or double its value in a year's time). Normally it takes some doing to calculate the number. What struck me as interesting is how interest rates are so low you can almost ignore them, hence setting r = 0 makes good sense. Doing so, you get a simpler equation:


This isn't a piece of cake to solve either, but it turns out an approximate 'at the money' solution is rather simple, such that

with tau being the time until the strike price is carried out (in years). And this works quite well for real stocks. Re-arranging, you can find the implied volatility (IV) sigma is


I then modified this formula slightly to account for the actual price of calls and puts themselves. For instance, you pay for something, being 'at the money' isn't quite good enough; you must be ATM minus the price of the call:

Conversely, a put needs to add the call price into the formula:

I wanted to see how this looked for two actual stocks: Tesla (TSLA) and Google (GOOGL) for call/puts as of April 10th for Sept 16, 2016 (that's 159 days from now, hence tau = 159/365). Also for reference today's actual stock price for TSLA is $250, while for GOOGL it is $760.

Again, the volatility equations are only true for at the money values, which should be when these two formulas match like so:


Hence I plotted real-world calls and puts for each stock. The point of intersection should be the best-estimate of a call/put balanced volatility according to the market.



I compare my IV estimate with that reported by the 'Greeks' table, averaged over all values (that's what the C/P average is in the tables), and it seems this estimate is very close to the 'correct' volatility. Tesla has a volatility of 46% for one year moving forward, and Google is doing better at only 24%. Also both points of intersection are centred about 1% ahead of the real price. Perhaps that implicitly accounts for the transaction fees associated with the stocks?

What is interesting is that I used nothing more than an intersection of two scatter plots via some easy-to-find data and a single-line formula. Thanks to low interest rates, something that began as a complex partial differential equation boiled down to borderline mental arithmetic. This is good, because none of these numbers are all that accurate to begin with, so nice not having to jump through extra hoops.

Of course now knowing all of this, I have no idea what I'm going to use this information for.

No comments:

Post a Comment