NNT's Blog

My Technical Appendix

Thu, 16 Apr 2009 14:40:00 --0100

This update: http://www.fooledbyrandomness.com/blackswan-technical.htm Some people make technical comments on a literary book (TBS was presented as a literary-philosophical essay), but do not go after my technical work that present analytical discussions and empirical evidence. I find it flattering (if unchallenging) to only be attacked in the wrong places, but it is more honest and more helpful to scientific progress to comment on technical works AND NOT DISSEMINATE A WRONG PRESENTATION ABOUT MY IDEAS (Fama, Scholes, Engle, etc.), or by some other extremely idiotic or extremely jealous persons. Actually, no: this is VERY dishonest. I will consider it bad faith to attack the statistical statements in my literary work without looking at the technical documents and WILL NOT SPARE any shady academic who does so.

David Freedman's Farewell Gift

Sun, 02 Nov 2008 10:35:00 --0100

David Freedman's Farewell Gift Very sad news: David Freedman, Berkeley statistician and a critic of pseudoscience using statistics, died of cancer. He was my ONLY supporter in the statistical community, and, reading some of the critics of The Black Swan, he suggested this excerpt from his book as a moving farewell gift:

Many of You Will be Sued

Wed, 01 Oct 2008 10:44:00 --0100

MALPRACTICE I am about to prove the "nonneutrality of representation". It means that risk measures CAUSE a disproportionate increase in risk taking on the part of the unsuspecting user. The consequence is that many risk quants (& authors of VAR books, consultants, & members of the International Association of Financial Engineers promoting modern finance) will be sued (by the victims) for providing faulty Value-at-Risk measures because it led to an INCREASE in risks. Even if you tell the person"you need to supplement this method with that method such as stress testing", it is not sufficient --he will rely on the measure. All I needed to show is the illusion of safety. Yes, many of you (providers of risk measures) will be sued by the innocent people who lost their savings --like tobacco companies who were sued by the innocent smokers. You will be held accountable. I will make sure it happens. I said in 1996 ( & 1997 in my debate with that ... Jorion) that I will be on the witness stand -and I will be. I will be. PS- This is called malpractice. I got interested in iatrogenics a few years ago.

Prediction Markets

Sun, 14 Sep 2008 00:04:00 --0100

This picture is what I am seeing about bets on the US elections. It has been there for 24 hours. People talk a lot about election markets. This is plain hogwash. Too small to be worth a trade. How you can get information "from the market" when such market is under straight Dutch book violations (here prob >1). Maybe I should reduce my web visits even more. Bye

Too many emails as if I didn't know that I was right

Thu, 16 Aug 2007 13:53:00 --0100

I am at the Edinburgh literary festival and the last thing I care about is you finance people. I've been swamped by emails telling me that I was right (forwarding stories about "25 sigmas" by the Goldman Sachs CEO --who needs to be replaced or banned from speaking to the press -- or the Rothman guy in the wsj on 1 in 10,000 year events). I don't understand these emails. It is as if I didn't know that I was right. Tell me what I don't know.

Quiz 7 Answer (Marcos Carreira got it right)

Sat, 17 Mar 2007 12:54:00 --0100

Marcos Carreira got it right. No wonder he gave me a Brazilian address to send him a copy of TBS. People in Braziou know about high interest rates. The idea of follows: something that is supposed to drift BUT DOES NOT DRIFT is volatile. Consequence: when a currency has a high interest rate, spot volatility is totally irrelevant. Using HVT on Bloomberg is not an intelligent idea. The problem with the question: 100% interest rates can be ambiguous when translating into daily rates. I meant the daily equivalent of 100% interest rates. So where r is the daily rate, the answer is : STD= [Sqrt[ Sum [i=1, i=22] [ (0 - r)^2]/22] Sqrt[256] (annualized) MAD= Sum[i=1,i=22][Abs[0-r]/22] (daily there will be another post on annualization of MAD) If you use daily r of .4, the answer is 6%. Marcos used a lower daily r but I assumed that he was right and that the interest rate I used in my question was ambiguous. I got an intelligent answer from Leon Pollard, that monthly volatility should be about 4% (if you measure volatility monthly) --but Marcos beat him to it. I have another 92 Quizzes --I am in Budapest and I saw a bunch of post Empire men playing chess in a Belle Epoque style spa, standing in a pool of warm spring water. I realized that I find option quizzes far more fun than chess.

We Don?t Quite Know What We Are Talking About When We Talk About Volatility

Thu, 15 Mar 2007 00:59:00 --0100

We Don?t Quite Know What We Are Talking About When We Talk About Volatility paper http://ssrn.com/abstract=970480

Quiz 7 - The problem with "drift" (The 1st who gets it wins a copy of The Black Swan )

Tue, 13 Mar 2007 12:48:00 --0100

When you ask someone the following question: A currency has 5% interest rates (can be generalized to any security). The base currency (costs of funds) is 5%. The underlying moves up 1% a day for 22 days in a row. How do you compute volatility (Standard Deviation) for the PURPOSE of decision-making (option pricing)? Almost everyone I've quizzed throughout my career answers: 0% volatility. Their spreadsheet functions using series of log returns also erroneously provide: 0% volatility. Nonsense. The real answer is 16% annualized. Why? STD = Sqrt[(E[X-E[x])^2] MAD =E[|X-E[x]|] When you are facing an uncertain outcome you do not expect the mean return to be 1% a day. You simply expect 0% drift. Therefore you should not center volatility around the ex post drift but the ex ante one. In other words, the options would produce the P/L of 0 volatility if and only if the drift is expected to be 1% The classical anticipating-nonanticipating strategy. AN OPTION BREAKS EVEN AT 16% VOL (+- some adjustment) NOT 0. Corrollary A currency has 100% annual interest rates [paid daily]. Base currency is 5%. The exchange rate does not move for a month. What is volatility (monthly, annualized)? Easy... please send answers to gamma [at] fooledbyrandomness [dot] com The winner gets a copy of The Black Swan . I will not offer to sign the copy (I hate to offer to sign my book ... my signature has nothing special ... )

Quiz 6 (answer)

Tue, 13 Mar 2007 12:17:00 --0100

Simply raise vol twice this time by increment DV. Compare the following Portfolio values (hence PV) PV[V] - PV [V+DV] and PV[V+DV]-PV[V+2DV] . If the second value is smaller (larger) than the first and one is long volatility, then he is short (long) the tails. Is the second value is smaller (larger) and he is short volatility, he is long (short) the tails. Model Risk Effectively this exercise reveals more than fat tails --sensitivity to model errors, sensitivity to problems of distribution. In a way, everything starts and ends with NonGaussianism.

Quiz 6

Fri, 09 Mar 2007 01:55:00 --0100

How can you figure out if an option book is short the tails? Move ONE single parameter, but twice. Hint: not complicated at all. Please send answer to gamma [at] fooledbyrandomness [dot] com

Quiz 5 Answer

Thu, 08 Mar 2007 19:48:00 --0100

Simple: Just raise implied volatility and look at the delta. If the delta rises, then the book is look OTM calls and shorter OTM puts, i.e. long skewness --you want Expectation of the cubic returns E[DS^3] to be >0. In other words look at the sign of the DDelta-Dsigma. The problem is that the analytical derivative is not sufficient since the effect might flip if you have way out of the money options that might "wake up" at higher volatility. So you should make sure that the reaction is monotonic. In other words you might have exposures to higher ODD moments of the distribution.

Quiz 5 (very simple)- Ferreting Out Asymmetries

Wed, 07 Mar 2007 13:11:00 --0100

How can you figure out by MOVING A SINGLE PARAMETER if a collection of options has an exposure to the third moment of the distribution (i.e. short or long skewness)? Please send replies to gamma [at] fooledbyrandomness [dot] com I mean ONE SINGLE parameter.

Marks-to-Market, Risk, Fraud, Accounting Opacity, & Black Swans

Sun, 04 Mar 2007 22:00:00 --0100

I recall in my past life as a trader working for financial institutions that some desks, mostly bank units, did not want to deal with the volatility of the marks-to-market on a daily or monthly basis and ran "accrual" books. An accrual book is gradually marked throughout its life --so the trader knew pretty much, baring a "black Swan", what his P/L was going to be. Some also tried to escape the marks-to-market when they engaged in some arbitrages that should "converge" at expiration. They claimed to know what the value of the trade would be at expiration time T, so there was no need to mark immediately and deal with the vagaries of the marketplace. In their mind letting the market value these trades did not reflect the economic value of their books. The argument offered was "I will only unwind at expiration, not before". They were certain about it. They were as certain about it as people tying the know are certain that they are united forever. I am writing this note because one day, in 2005, at a panel discussion, a board member of FNMA and an advocate of "modern finance" got emotional about the bad press related to some accounting irregularities that was supposed to have taken place at that firm. The panel discussion had nothing directly to do with FNMA or with accounting policies. It was about risk management. I thought of the argument proposed and realized that by not marking to market every single item in one's book one fell prey to model risk. It was the same type of epistemic arrogance that was behind the central planner: you set an equality between A and B by fiat. [It is not just some unpleasant member of the board of FNMA that falls prey to epistemic arrogance. Merton Miller took similar arguments when he defended the Metalgesselschaft traders who went bust trading short term futures against long term forwards. His argument was that "long term" things should be OK and that we should not have paid attention to the "short term" differences in market values]. Why Model Risk? The simplest of securities embeds model risks: the way the contract is described in your system may be missing a minor component. Minor, except... Say that I have the simplest of trades deemed fungible on my books: I am long a forward with Bank A and short the exact same one with Bank B. I may be hedged, but I have at least a credit risk there. Sometimes the smallest variations in the contracts can be significant. No two contracts will ever be exactly fungible unless they are legally offsetting. Now the market knows that these contracts are not as identical as they are thought to be. Markets discover things faster than some slow-thinking regulator or overmathematized risk manager. When Russian options traded at 5 implied when supplied by a Russian bank and at 11 with a nonRussian institution, you had a marks-to-market risk not accounted for by models. The market knew it, not the banks. Another sucker's problem is the classical forward-future "mispricing". The forward IS NOT a future, be it only because a future has cash-flow elements throughout its life, something the models miss severely. Many blew up on this. A Safer System Many corporations do the following arbitrage. They buy plenty of companies, say n units. Say half the companies do well, the other half do poorly. All of them will be marked at cost on your books. You have a bad quarter: no problem. Just sell those that fetch a price higher than acquisition (i.e. books) and you will show a profit. GE does that routinely (Jack Welsh admits it in his memoirs). The same with traders. When you let them "accrue" you end up having the books doing worse than market. If the trader has a profit, he takes it. A loss becomes accrued. It is like traders becoming "long term investors" when their positions are under water. A system without opacity will be like Japanese institutions: seemingly less volatile, but exposed to large losses. (I compare this in The Black Swan to a dictatorship that shows political stability but incurs the risk of revolution compared to a country like Italy with a smaller risk of reolution but more fluctuations. Fluctuat nec mergitur.) One good thing about hedge funds: unlike FNMA they mark to market. They have such bad press that they are forced to do so. Unlike banks and corporations they cannot play nasty games and fool their shareholders. Recall what Enron did with its "contracts". They may have other problems, but, at least, they are transparent. Reduction and Platonicity This problem resembles the more general one of the creation of categories and mental representations that simplify and reduce --it is necessary to simplify. Except that we forget that they aqre just simplifications.

Path Dependence and Volatility

Sat, 03 Mar 2007 00:00:00 --0100

Introduction: A Garlic-Oriented Meeting The first time I met Emanuel Derman, it was in the summer of 1996, at Uncle Nick's on 48th street and 9th Avenue. Stan Jonas paid, I remember (it is sometimes easier to remember who paid than the exact conversation). Derman and Dupire had come up with the local volatility model and I was burning to talk to Emanuel about it. I was writing Dynamic Hedging and in the middle of an intense intellectual period (I only experienced the same intellectual intensity in 2005-2006 as I was writing The Black Swan). I was tortured with one aspect to the notion of volatility surface. I could not explain it then. I will try now. First, note the following. Local volatility does not mean what you expect volatility to be along a stochastic sample path that delivers a future price-time pair. It is not necessarily the mean square variation along a sample path. Nor is it the expected mean-square variation along a sample path that allows you to break-even on a dynamic hedge. It is the process that would provide a break even P/L for a strategy. The resulting subtelty will take more than one post to explain (or I may expand in Dynamic Hedging 2). But I will try to explain as much as I can right here. The first problem is that options are not priced off a mean-square variation in the underlying, but off a mean variation in the underlying. I cover the point elsewhere --the use of L2 norm is not adequate. Skip this for now. The second problem is that options have a vega variation ALONG THE PATH so the PL for a strategy is decomposed as PL from variation in S (asset price), and P/L from changes in "volatility" (or expected mean deviation) --what the option is reflecting about future additional variations in the price of S between that point of evaluation and some terminal expiration. The P/L from changes in both implied and delivered volatility is path dependent. Severely path dependent. Look at the graph. Take S an equity index. Assume that you Start at S0, at time t0. At time t2 you are at S2. Fine. But you can get there by two ways. The first way, path 1, is through S1a. The second one, path 2, is through S1b. Note that path 2 is more volatile than sample path 1 (mean square or mean absolute deviations). Consider an option valued at time to and at time t2 (it expires sometimes in the future, say t3). Now take the standard "implied volatility" (what we call implied volatility by inverting the commonly used Bachelier-Thorp model, what I used to formerly & mistakenly call "Black Scholes" and is still called so by those who have not spoken to Espen Haug). Paradoxically, path 2 will lead to a lower terminal implied volatility at time t2, although that sample path was more volatile. The "retracement" brought a lower volatility. It is not just implied volatility that is lower at S2b (2nd path), but the future variations in the underlying S are expected to be dampened. You can check it empirically by taking volatility at new lows (say with S at the min three months window) and comparing it to situations in which you recover from new lows. In my discussion of barrier options I talk about prices in areas with stops and a high density of barriers that have not been knocked out. This is far worse. So we see a path dependence, a strong memory for the route taken by a price, etc. Mathematically, it means that you cannot easily work with a process --transition probabilities are not unconditional. But the equation is fine and useable; it is the naive interpretation that is often wrong. I initially thought that if we had sigma0 at (S0,t0) and sigma 2 at (S2, t2), the local volatility should be ON AVERAGE approximately (sigma0 +sigma 2)/2. That is very rough approximation. It will be lower, much lower for large deviations, higher for smaller ones. Forward volatility is what it takes to break even in a strategy along the average of all routes followed by the underlying security; there is a stochastic element in it and nonlinearities in option reactions to these variations. Because of such stochastic element, it will be HIGHER than the average sample paths for out of the money options, and lower for at the money ones. Why lower for the at the money ones? Because the collection of paths that will end unchanged are far less troublesome than the ones that stray.

"successful" models & simple backtests

Fri, 02 Mar 2007 01:58:00 --0100

Seven Years Later I was reading (for the new edition Dynamic Hedging) an article by Leland and Rubinstein on portfolio insurance when I stumbled upon the following footnote: M. Rubinstein and H. Leland, "Replicating Options with Positions in Stocks and Cash," Financial Analysts Journal 37, No. 4 (July-August 1981), pp. 63-72. [Added Note: This article was reprinted in the 50th Anniversary Issue of the Financial Analysts Journal (January/February 1995), having been selected as one of the 22 best articles out of the 3,200 published in the Journal during its 50 year history.] I went to the paper and it was, of course, proposing their dangerously misleading method. But it was selected in 1995, after the crash of 1987, as one of the best articles. Further a journalist tried to argue with the great Benoit M. about the "success" of Markowitz "successful" formula ( it is its 50th anniversary). Using success in being used --not in empirical tests --as a criterion is a fraud. Astrology has been so successful (much more than 50 years, perhaps 3300 years!).Should we use such popularity as a criterion for election. "Successful". Now How Do We BackTest? Simply you take the model by professor Rubinstein and the other idiot and run them through history. Further assume the nontrivial fact that people will not produce bids to be good citizens, but will back-off when you supply them with SP500 futures. ("Sunshine trading" has never worked, it is some normative economist's contraptionl; if you don't know what it means, no problem, it is something neclassical economists came up with to save their theories and you do not need to lknow anything about it). Even without feedback effects, will the revision policy reduce risk? Of course not: you don't have a clue about the value of that option that you think that you have and did not buy because of fat tails. By fat tails I mean real fat tails, scalable fat tails. See the graph in an earlier post about the payoff of option contracts and how "smooth" it gets. In other words, a soft option (a dynamic strategy) will NEVER replace a hard option (a real contract) in the real world because the production costs are severely stochastic.