Finance Experimental IEOR Spring 2012
Mike Lipkin, Pankaj Mody
Lecture 1F
The Market (Reality)
What is experimental finance? A better term might be empirical finance. In this course we will not take for granted any equilibrium result from standard option theory. We will look for departures from standard no-arbitrage conditions, see how long they last, and decide whether they are tradeable.
Experimental Finance
Mike Lipkin, Alexander Stanton
Page 2
Lecture 1F
The Market (Reality)
An aside:
We are exploring many things which are new to the traditional thinking in mathematical finance. Often there are NO KNOWN ANSWERS. Problem Sets will often ask you to make your own choices for products to look at. This should not disappoint you, since that means there is plenty of room for personal discovery.
That is why this is a laboratory course; it is also why my lectures will ask a lot of questions in green!
Experimental Finance
Mike Lipkin, Alexander Stanton
Page 3
Lecture 1F
Some preliminaries.
The Market (Reality)
Coursework consists of seven problem sets (individual work for the first PS, groups are OK afterwards; you need to gain facility with SQL and IVY and the best way is to just plow ahead) and one project (groups of three). The problem sets take variable amounts of time, either because you must think carefully about the organization of your queries and formatting, or because your (well-formulated) SQL queries will take much time. Since the time needed will be so uncertain, make sure to begin work early in the week. You can plan to do other things (even sleeping) while the longer queries are crunching. The problem sets can be turned in as soon as you wish, but no later than the scheduled date set in the course outline. The reason you might work through any of them early is because you might want to think about a project in an area discussed later in the course (such as take-overs or hardto-borrows).
Experimental Finance
Mike Lipkin, Alexander Stanton
Page 4
Lecture 1F
The Market (Reality)
You should be aware that the problem sets may be in reverse
order of difficulty. The reason is that most of you will start the
course with limited experience with both IVY and SQL and you will need to spend a good amount of time developing facility with them. The subject matter will start with routine stuff to let you explore IVY. Later we will get to interesting things but in a very superficial way. The project is intended to get you to look more deeply at an area of interest to you. Since I am an options trader and IVY is an options database, we will be restricted in what we look at. However the skills you develop will serve you well when you explore other databases with different securities information.
Experimental Finance
Mike Lipkin, Alexander Stanton
Page 5
Lecture 1F
The Market (Reality)
The preliminary project proposal must be made, no later than, by the Wednesday class of the sixth week. The degree of difficulty should be about the same as that of a combined two to three problem sets. Pankaj and I will consider the proposal for novelty, merit and difficulty and give you the goahead with, or without, emendation. Throughout the first few weeks, there will be plenty of references to unknown problems. Feel free to try and tackle any of these. You can choose your own groups of 3, but if there are people here with existing knowledge of SQL it would be helpful to spread yourselves around.
The final three weeks will consist of PowerpointTM presentations by the groups of the results of their projects. The length of the presentations should be about 25 minutes each. Which groups go on which week will be assigned at random. [You can ask us about previous projects: some very successful, some less so] Throughout the course and also in a dedicated lecture Pankaj will present and comment on some of these.
Experimental Finance
Mike Lipkin, Alexander Stanton
Page 6
Lecture 1F
The Market (Reality)
Homework should be e-mailed to Pankaj and Thiam in the format Pankaj sets out. ML: [e-mail] PM: [e-mail] Marco Santoli(TA/grader): [e-mail] See Mr. Santoli to arrange SQL help. The lecture period will be divided into two 70 minute halves with a ten minute break in between (some of Pankaj's talks may be in the computer room). This lecture will be slightly shorter so that Pankaj can cover more introductory material. Pankaj is a database expert; I am a floor trader/market-maker. What we are attempting to do has not been done elsewhere to my knowledge. That is to develop in you the capability of thinking out new ideas and proposals in option theory and attacking them via experiment in the fashion of a geologist- searching the fossil record. The work you will engage in is new enough that you can use what you find here for (job) talks** (and potentially even a journal paper)!!
Experimental Finance Mike Lipkin, Alexander Stanton Page 7
Lecture 1F
The Market (Reality)
For this objective, our most important tool will be the IVY database. The technical details for its exploration will be studied with Pankaj. Here, we just point out, that it is a compendium of closing prices, implied volatilities, interest rates, open interests, etc. for every stock, index and etf in the market!!! Unlike a physicist, we cannot generally prepare an experiment (short of losing large amounts of $$) to perform in the market. However, if we are ignorant of the market specifics, such as which way a stock moved on July 22, 2003, then we can perform statistical experiments on past data without bias. These are important methods for learning about non-classical market behavior. What are non-classical behaviors? Anything which can make you profit. Let's start with a somewhat unusual, but not unheard of example:
Experimental Finance
Mike Lipkin, Alexander Stanton
Page 8
Lecture 1F
The Market (Reality)
Suppose you are working at a desk and running a variant of BlackScholes, as sophisticated as you care to make it, and a hedge fund shows you 15000 contracts $0.15 through your theoretical value: "I can sell you 15000 VMW Apr 85 calls for $7.46."
Experimental Finance
Mike Lipkin, Alexander Stanton
Page 9
Lecture 1F
The Market (Reality)
Here is another page of VMW quotes:
Experimental Finance
Mike Lipkin, Alexander Stanton
Page 10
Lecture 1F
The Market (Reality)
EMC to maintain 80% VMware stake
EMC Corp., which specializes in high-end computer storage systems, is based in Hopkinton. (Neal Hamberg/ Bloomberg News/ File 2004) Bloomberg News / March 3, 2010
Experimental Finance
Mike Lipkin, Alexander Stanton
Page 11
Lecture 1F
The Market (Reality)
Do you buy them? What considerations do we need make? What if the hedge fund wanted to sell 500 options only? Volatility/Vega Risk The above is an example of a volatility depression (spike). After the trade there will be a new volatility profile. What will that profile look like? Would it surprise you to know that there is no existing, theory accepted of the dynamics of pricing?
Later in the course (Problem Set V) we will start to tackle the nature of volatility discontinuities. What we are interested in is not a static (or thermodynamic) model which allows stochastic volatility, but a way of learning about the "response function" of a real market. In a sophisticated theory, the following kind of mathematical object would be calculable: <(K1,t1)(K2,t2)>. (Some of you may want to investigate this object in a project.)
Mike Lipkin, Alexander Stanton Page 12
Experimental Finance
Lecture 1F
The Market (Reality)
As you can imagine. If we do decide to buy the Apr 85 calls we will have greatly increased our Vega. From the discussion it is clear that in any case, prices will decline in other strikes and series.
By how much? No one knows. There is (almost) a complete absence of theory.
If the Apr 85 calls decline by 1.5 (implied) vol points,
how many points will the Apr 90 calls come in by?
The market there is $5.40-$5.60.
Does it make sense to hit the bid? (What does hit mean?)
The July 85 calls are $10.40-$10.60.
Should you sell the calls at $10.40 as a hedge? Is this better than the $5.40 sale? What if there are earnings between April and July? (In Problem Set V we will examine earnings periods.)
Experimental Finance
Mike Lipkin, Alexander Stanton
Page 13
Lecture 1F
The Market (Reality)
Should you sell EMC volatility instead?!? Suppose that the hedge fund "informs" you that the calls will trade.
Should you be leaning short? What does this say about the assumption that the stock process is independent of option trading? Is there a flaw in the Martingale assumption?
Later (Problem Set IV) we will see that option volume can affect stock prices. Here are some Real World examples:
Experimental Finance
Mike Lipkin, Alexander Stanton
Page 14
Lecture 1F
The Market (Reality)
On September 16, 2005, a BA customer sold 150,000 FDC Jan 40 calls to market-makers, mostly within a two-hour window. The implied volatility went from 23 to 19 in January and from 28 to 20 in November.* * at-the-money options
On Tuesday, May 23, 2006, market-makers were told "133,000 RAD Jan '08 2 calls will trade at 2.35 vs. 4.38 stock. How much would you like to sell?"
Experimental Finance
Mike Lipkin, Alexander Stanton
Page 15
Lecture 1F
The Market (Reality)
Experimental Finance
Mike Lipkin, Alexander Stanton
Page 16
Lecture 1F
The Market (Reality)
Experimental Finance
Mike Lipkin, Alexander Stanton
Page 17
Lecture 1F
The Market (Reality)
Experimental Finance
Mike Lipkin, Alexander Stanton
Page 18
Lecture 1F
The Market (Reality)
Let's take the previous slide of VMW as a template. The standard approach to market pricing is calibration. All market models take input data from the actual prices out there. Suppose that the resultant model now "fits" the market, in the sense that no theoretical prices lie outside the bid-offer spreads.
Does this mean that the market is correctly priced?
Suppose that over the next week, buyers show up for all the MOT 87.5 line options (previous slide S0=83.77). As a result,
what will happen to the normal skew?
If the skew "inverts", does this mean that the prices are wrong? We will see, (Problem Set VII), that under certain circumstances such as take-overs the skew can take a strange but characteristic shape.
Experimental Finance
Mike Lipkin, Alexander Stanton
Page 19
Lecture 1F
The Market (Reality)
Let's try to summarize some of the ideas we have discussed. The size of a trade matters. The time scale for the relaxation of the market subsequent to a trade matters. A quant analyzing the thermodynamics of the market will not see many of the time scales needed to understand market dynamics. Nor will we using IVY. It is important to pay strict attention to time scales.
What is the shortest time scale we will see with IVY?
This time scale suffices to look at earnings, drug announcements, take-overs and mini-crashes (PSs V and VII). It does not allow us to look at the response to size trades.
What kind of database do you need for that? Would such a database be useful for a trading house? Do you think the elasticity of the response is a function of the individual stock? the open interest? the illiquidity of the stock? Anything else?
Experimental Finance
Mike Lipkin, Alexander Stanton
Page 20
Lecture 1F
The Market (Reality)
Let's conclude this introductory talk by considering a typical problem about which there is a lack of theoretical understanding. The objective will be to abstract the nature of the problem, consider the time scales involved, and finally to propose a database experiment to search for market behavior. Let's take the VMW, EMC example. These are two related companies. Suppose we run a book with positions in VMW and EMC. When we are offered a large trade in VMW, we would like to know if we need to be hedging in EMC. Notice that this is not asking if stock prices are correlated (although they may be), but rather if volatility surfaces are correlated. For example, suppose that we are short 5000 Vega in VMW and long 5000 Vega in EMC. If we buy VMW premium we will become flat, say.
Do we need to sell some amount of NOK volatility? If that is true, what would that tell us and how would we quantify it? What time scale would the vol changes occur on?
Experimental Finance
Mike Lipkin, Alexander Stanton
Page 21
Lecture 1F
The Market (Reality)
To begin with we need to locate significant volatility changes in the histories of MOT and NOK. We need these changes to occur over a characteristic time scale, say one or two days, and then we need to see if there is a subsequent change in the volatility of the partner stock. The following quantities may be relevant: <VMW(t,K1)EMC(t+,K1)> (1)
What is this object? is the change in vol, is the lag time (unknown but possibly very short) between the change in VMW vol and the subsequent change in EMC vol, > 0 assumed. K1 is the strike corresponding to similar deltas in both products. (Notice how the assumptions are multiplying!!) From the physics of dynamical systems, this quantity is called a response function for obvious reasons.
Experimental Finance
Mike Lipkin, Alexander Stanton
Page 22
Lecture 1F
The Market (Reality)
Of course we might start in a simpler way, not looking at significant changes and not worrying about time scales shorter than a day:
<(VMW(t)-EMC(t))> <(VMW(t)-EMC(t))2>
(2) (3)
As you can see, we need to play with a number of averages and see if anything significant pops up. In the absence of theory there is no way to simply locate the significant features. This course encourages you to find them! (You will be happy to note that none of the problem sets involve a question as sophisticated as the previous one, although your projects may.) Your questions for me???
Experimental Finance
Mike Lipkin, Alexander Stanton
Page 23