August 2008


It is 4:00 am on saturday morning and it is raining outside. Wonderful setting to write something. So, here I go.

BlackScholesandbeyond

This book was referred by Prof Stefanica, the director of Baruch MFE program . I stacked this book in my inventory under the assumption that I will read it at some point of time soon. Few backs , I had to go to Boston to visit Anoop, my childhood friend. I love long journey for it gives me a chance to be away from comp and just read, reflect and think about various things….I managed to go over this book in the journey. Let me attempt to summarize this book :

My first take on this book : This is probably one of the best books where almost every equation is replaced by an intuitive argument. The analogy of hedging with that of bet maker which spans about 4-5 pages is so beautiful that those pages alone make this book worth buying !! Ok , I will summarize in a random order and not in the order the book is organized.

Volatility Smile:

smile logo2

Constant volatility input in BS model is only for discussion purpose. In market , one sees that Lower strikes have high implied vol than higher strikes. A smile , as it is advertised in the finance literature, is when the volatility Vs Strike shows a behavior where OTM puts are expensive than BS Put value and ITM calls are cheaper than BS Call value.
How to incorporate volatility model in to BS world ? Well, there are three types of vol- Historical, model and combination of the the two. It is widely accepted that historical vol is a mean reverting process , meaning, it reverts to a mean, with a specific turn around time, with a specific volatility (yup, this is volatility of volatility – call it meta volatility ). Now how does one go about defining this model and calibrating the model . One way is to look at models like heston model which are mean reverting vol models , the other options is look at the universe of GARCH models like GARCH/AGARCH/EGARCH/GJR-GARCH/TGARCH, well..there is no end to this GARCH life that you can live. So, once you get a hold on mean reversion process, then you can think of pricing , hedging, calibrating and trading on that volatility.

If the correlation between stock prices and vol is +, then returns distribution is generally fat right tailed
If the correlation between stock prices and vol is -, then returns distribution is generally fat left tailed

Another little takeaway from this chapter is the stoppage time for bisection and newton raphson methods. log(sigma/power(2,k))< tolerance , it is pretty self explanatory why the stoppage condition is set up in that manner.

Trees & Basic Option Pricing with Binomial Trees:

bintree

Binomial tree is best described in Joshi – Chap 4. Having read such nice explanation ,it will be difficult to find a book which gives such a clear explanation. It was not a surprise that Option pricing on trees was an okish explanation. What does one need to know in Trees

The whole idea of trees is to build u,d,p in such a way that these prices at each discretization step matches the local volatility Sigma. Well there are a couple of ways to do it, eitherbyassumingp=q=0.5 or by assuming ud=1. The former is robust as forward price always falls between up and down move. A math-fin student should have all the formulae of local vol, u, d on his finger tips !!

  • Bond + Delta shares can replicate an option – Pricing by replication
  • Pricing by Hedging
  • Risk Neutral valuation
  • One comes across Quantization error and Option Specification error while working on trees
  • Best thing about trees is that american option can be easily priced by asking a simple question – Which is greater, the cost of hedging or cost of paying for immediate exercise?
  • Early exercise barrier for American options
  • Tree pricing with continous dividends
  • Tree pricing with discrete lumpy dividends
  • ARROW – DEBREU Price of a node is Value of a security that pays a dollar if the price reaches that node and 0 otherwise
  • Connection between butterfly and arrow-debreu price

Black Scholes World:

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Chapters 1 through 5 talks about BS world, their implications , assumptions, delta hedging , greeks. For a person familiar with the subject , this book is light a good bedtime read with nice intuitive explanations for delta hedging, greeks behavior etc.

In every book , there are things when one needs to carefully understand what the author is trying to say and get the best out of the book. In this book too, there are sections on Implied volatility trees that make an amateur math fin student stretch his thinking. Hence I would carefully summarize my learnings of implied volatility trees now.

volatility poster

What if I were to completely trust the markets and then want to hedge an option that is written. That’s where implied vol trees come in to focus. Thinking is this :

For a given (option price ,strike) points , lets build a price tree , so that for every price point, I know the option price. What do I get from this ? I can calculate all the hedge parameters and hence I am safe after writing an option.

There are a lot of wrinkles that one need to work on , like false probabilities etc. I don’t think I will have time to code up an implied vol tree considering my schedule. Implied Binomial trees are slightly different from implied vol trees where investor preferences are taken as input and all the options for a specific fixed expiration date is taken as input.

Even though I understand the basic concept behind implied vol trees and implied binomial trees, I will not be able to appreciate until I code these pricing techniques.!!! Hmm…Need to somehow find time.

Overall , my takeaway from this book :

A great book which explains intuitively a lot of things from BS world and extends the BS world by looking at its limitations and work arounds.

demon of our design

This is the second post on this book which will try to summarize the chapters on Hedge funds from this book.

Brave new world of Hedge Funds

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Hedge funds exploded in to the financial world in the recent years. There are various types of hedge funds, classic one being top down. A few nice take aways from this chapter is the discussion of tulip mania where the author reasons that the existence and flourishing of futures market was the reason for speculative mania. Also a discussion of the importance of float in the market is discussed in the context of Internet bubble.
The biggest takeaway from this chapter is the answer to the following : Why does the price move ? It moves because of liquidity. Unlike the MBA crap that information moves price, this explanation is nifty . Broker dealers provide liquidity to the clients and they trade in suck liquidity. Elegant view to look at intra day price movements.
The author talks about the rise of pairs trading technique, relative value trades, LTCM and the recent evolution of long/short portfolios . I never knew that Bamberger from Morgan Stanley was the actual brain child between Pairs trading and Tartaglia stole it and scaled it .

Cockroaches and Hedge Funds

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Well, this item of the book gained a lot of popularity.This chapter rocks for the author discusses examples from evolutionary biology and discusses about its relation to financial markets. Cockroaches, over centuries of evolution have developed response mechanisms that carry responses from sensory hairs to its legs. They are not filtered by the brain. This is a coarse decision rules in action. In another example, crayfish, also has developed a stimuli triggers a set of stimuli and then one set of action is taken up amongst all the alternative actions.

Another contrasting example is Furu, which is a specific type of fish which has developed a very specialized kind of response behavior, however, it just could not sustain sudden changes in the environment. Thus the author says that a coarse ruled based system is better for evolutionary systems. In that sense, a better risk management need not mean, more reporting, more metrics ..In fact, the more specialized the risk management becomes, the more it carries a risk of being ineffective. This chapter resonates with black swan where the conclusion is more or less similar to black swan. Risk management needs one to be prepared to deal with black swans, the unobservable. Sometimes, the danger to the system is the system itself . A beautiful description and comparison between evolutionary behavior and financial markets. JUST THIS CHAPTER MAKES THE BOOK WORTH BUYING

Hedge Fund Existential

Hedge-Fund-Investing-11

Talks about hedge funds in general and talks about the difficulties in classifying Hedge funds. The author manages to give his own classification with the attributes being Asset Class, Direction, Investment Type, Geographic region and Liquidity. Author ends the chapter with a prediction that ultimately hedge funds will become standardized investment vehicles. Reasoning: Hedge funds cannot be classified. As many investment strategies there are in the world, there can be that many hedge funds. Whats the advantage with a hedge fund ? An short term opportunity which is passed up established regulated funds will be lapped up by hedge funds..So, it is clear that over a period of time, hedge funds will dominate

To conclude

What's the answer to the paradox that this book seeks to answer ?

"Simpler financial instruments and less leverage make up a painfully obvious prescription for fixing the design of our markets. These modifications will lead to a financial marketplace that will be apparently less finely tuned and less responsive to investor needs. But, like the coarse response mechanism of the cockroach, when faced with the inevitable march of the events that we cant even contemplate, simpler financial instruments and less leverage will create a market that is more robust and survivable"

Overall fantastic book and a wonderfully spent 24 hours.

Link : A Demon Of Our Own Design : Summary -Part I

demon of our design

If one looks around, there are a tons of innovations happening in the financial sector.

  • From the instruments side, the world has graduated from simple plain vanilla options to exotic derivatives, CDO's on CDO , an alphabet soup of all mortgage derivative products. Ideally all these should help in better management in risk, right ?
  • There are more players in the markets, different types of players, hedgers, arbitrageurs, speculators, market makers, hedge fund managers, prop desk traders etc. These players should be smart enough in making the market more stable ???
  • Tons of legality around stock markets and asset trading, new rules to shorting etc,
  • Infrastructure to support trading has grown by leaps and bounds. On your vacation to hawai, lying on a beach, you can execute a complex derivatives trade with a click ,
  • Price transparency wise , again a big yes
  • More crisis, More boom bust cycles.

All the above should have made the investors more wise and made the markets efficient, less volatile. However we are seeing the markets becoming more volatile, more manias , more structurally inefficient products being traded,..Does it sound like an irony ? Well, this book sets out to explain WHY ? The author has been a trader in MorganStanley , Smith Barney, LTCM, and has worked on a host of significant roles that his view can be understood not from a passive spectator narration of somebody but from a perspective of a player in the market. This means that it will be more – matter of fact – rather than color it from journalist flavor.

Today morning, for some reason I could not concentrate on my work at all . Spoke to Kiran for sometime and it helped me a bit to get over my mood, and then figured out that I need to get DRUNK to restore my sanity. In my case, getting drunk is equivalent to reading a superb book from my inventory . I had this book in my inventory for quite some time and felt that the best way to get over my bad mood was to read this wonderful account of " Demons of our own design". Let me try to give a summary of the book , chapter by chapter. Each chapter is a gem.

DEMONS OF 87:

crash

This chapter took me through the 1987 oct 19 S&P Crash by 20%. There are some unique reasons which the author quotes for explaining the crash. One word that is synonymous with the crash is "Portfolio Insurance". This was a strategy to hedge against a market crash by shorting S&P Futures. All was rosy until the markets actually begins to take a beating. Ideally since the portfolio is hedged, people shouldn't have lost money. However this strategy is a lame strategy if every portfolio manager has the same game plan to bail out . Yes that's what happened .Market became ILLIQUID. Well, this part I was anyway aware. However new stuff that I leant from this chapter is the role of Cash Futures Arbitrageurs. When there was a huge sell of S&P Futures, and combined with a fall of stock market, there was a great spread between cash market and stock futures market. Thus a different breed of players started to take the market in a precipice. Traders longed stock futures and shorted the stocks thus aggravating the already free fall of S&P, free fall of S&P Futures and the immense amount of hedging that happens for portfolio insurance products at the money. Note that gamma for at the money option is max. This means the more market putters around the floor of the portfolio loss set, the more managers with delta hedge and it becomes more expensive to delta hedge than have a losing trade..Yes, that's what happened according to the book. It was expensive to delta hedge and cheaper to hold on to losing position…WOW!! What sort of market that would have been ?

Biggest take away from this chapter is the fact that – Time frame in which futures market operates is VERY different from time frame in which spot markets operate. Hence the crisis in the futures markets will take time to get communicated in the stock markets and this time delay aggravates the crisis even more as other arbitrageurs, buy side folks, market makers try to have their own strategies and at the end , manage to screw up the entire market.

New Sheriff in the Town

sheriff-c2

This chapter talks about the rise of fixed income trading and instruments in 1980's. Cites a few major disasters that occurred in the fixed income world. Orange Country, Citron Fund which went long on short term interest rates and long on long term interest rates:) . But inverted yield curve killed the fund and it was saddled with 1.7 Billion Loss .
The next account in this chapter is about Nick Leeson who single handedly brought Barings bank down , by entering in to a straddle on Nikkei 225. Straddle is great if the market stays put. However it is a loss making position if the market moves a lot. Essentially it has negative gamma. And yes Nikkei moved like crazy and Leeson who was showing abnormal profits from account 88888 went bust.
Another trader who brought Kidder (of Kidder Peabody) down was a harvard grad , Joe Jett who used an accounting loop hole in STRIPS sales and showed profit until Kidder couldn't digest the losses.
The author also mentions the rise of index-amortizing swaps, use of APL language in Morgan stanley and its limitations about not being able to perform fast Montecarlo valuations, make a good read. The chapter ends with the most important question –

If WallStreet is swarmed with so many risk managers, why is there a crisis ? The problem is risk managers look for what is already present and measure it like crazy..However risk management is about what one cannot see. It is about BlackSwans …Alas!! World like to believe in " What I see is What I believe" philosophy .

Salomon Rolls Dice
dice-4

This chapter takes the reader through the build up of bond trading infra in Salomon. The only takeaway from this chapter is the MCI/BT merger trade which Salomon lost. In any merger obviously prices converge. If I hold a long short portfolio then if the merger happens, I make money. The only thing that matters is the probability of the merger. In Salomon's case, it got this bet hugely wrong. In the end Traveler's group and Salomon merged in 1997 and the next chapter in this book talks about how Salomon was killed after the purchase

They bought Salomon, then they Killed it

kill-chap5

The highlight of this chapter is the way it describes the tracking error on yield curve trades which killed the US arb division in the merged entity. Thus Salomon props teams operations were shut down and the traders were politely asked to leave. One of the great takeaways from this chapter is the mention of liquidity and its associated problems. The essential trait of investment portfolio- ability to liquidate is the very root of crisis most of the times. How do models take care of Liquidity risk ? I have no clue. By putting in a friction rate, is the liquidity risk captured ?

LTCM – Lesson in Leverage

seesaw leverage small

Well, lot of folks know about LTCM. I know a little bit about it from my previous readings. What does this book offer me new ? That was approach I took before reading this chapter.Well, at the end of it, I didn't get anything new from this narration

Complexity, Tight Coupling and Normal Accidents

complexity-710641

This chapter is about complexity and the way finance with all the myriad interactions, is made ineffective by more controls. More controls need not necessary make the markets less prone to disasters.2 classic examples from the engineering world are discussed, Three Mile Island case and ValueJet case which are tight coupled systems where myriad controls did not help avert the disaster. A great analogy in this chapter is that of postal system where the system is tightly coupled but not interactively complex. This means that a single failure in communication is not catastrophic. It is a fairly less interactive system, meaning , the failure or errors are not fed in to the system and they don't aggregate over time. University with department is another example of system with less interactive complexity.However , it is not the case with Financial markets. We are dealing with interactively complex , tight coupled systems where errors, crisis effects the markets in a non linear way. Extra controls are going to add more variables to the system and make it more error prone than less.

I will summarize the next part of the book which is based on Hedge funds in another post.

muor

I have a problem with Ruby. It is a great language , extremely good for fast prototyping. However this is not the language I use it daily. However, there are times when I have to use ruby where the effort of doing something in a different language is not worth it.

My problem stems from the fact that I forget the syntax as I don't use it regularly. In the last 1 year , I would have probably worked on 4 RoR mini-projects and in every instance I had to pain stakingly go through and review the syntax . This time again I have to develop a diagnostic tool, very very fast and I don't have time to go through the syntax at leisure. I did something different. Picked up this book "Making use of Ruby" and put myself a time limit of 30 minutes for reviewing the relevant syntax..All I can say, is that, the result is pretty good…In 1/2 hr time, one can review the syntax of loops, classes, namespaces, mixins, file operations , instantiations, arrays, hash etc and I must say this book is pretty well organized in that sense. First 120 pages is that would be needed for quick prototyping.

My next task is Rails recap. I just want a quick way to look at price-s score-long/short position data all in one web page and the data is in postgres.The only thing left to figure out is : How to dump the data from postgres in to a chart ? I just hope I figure this out quickly so that I can investigate the results. Sometimes I guess one needs to have patience and develop a diagnostic tool for simple excel based charts are of no help in understanding what's going on…