The Stanford MS-FM Times

This blog chronicles my life as a student at the MS in Financial Mathematics at Stanford University

  • About the Author

    Financial Mathematics
    Stanford University

    Fixed Income Research
    DBS Singapore

    Finance
    IIM Ahmedabad

    Chemistry
    IIT Kanpur

Epilogue

Posted by tapishkushwaha on January 30, 2009

Ive been asked in recent months why i have not been writing anymore. The answer to that lies in the horror stories i hear about people getting kicked out of their jobs for posting their veiws publicly. Now this would be the worst of times to be a maverick and test that theory on myself ! So i will take the safe path and abstain. The least i can do though is to make this a smooth transition to oblivion.

I think a fitting end would be for me to give my final thoughts on the Financial Mathematics program at Stanford University and the experiences i had in California.

Academics: I would call the following courses a must do at Stanford.

STAT206 – Applied Multivariate Analysis – Try and take this as early as possible, especially if you are rusty in your linear algebra. It will brush up the basics and prepare you for the sometimes otherwise obscure statistics to follow.

MS&E345 – Advanced topics in Financial Engineering – I absolutely loved this course as this teaches derivative (both equity and fixed income) pricing in as structured a way as possible. I dont think many, if any, will argue with this.

MATH238 – Financial Mathematics – Although not as refined as MSE345, this course will teach you a lot more than basic options theory and will delve into stochastic control as well.

MATH227 – Partial Differential Equations and diffusion processes – For me, this was the best taught class at stanford. Ive heard that the Professor Nolen is leaving Stanford and that would mean a big loss to students, for he really is a stupendous teacher. This course and his teaching makes light of the fears that many people have of PDE’s.

MS&E247s – International Investments – I liked this course as it was all about macroeconomics. I really like the field and it was my main motivation for getting into finance. The best part about it is how it helps me understand how the ‘world works’. ( in some sense!)

Life at Stanford: One has to be a student here to realize how fortunate one is. Its such a fantastic place to live and study that it does seem unreal at times. Ive often been asked how i ever got any studying done in a place like that. Theres just so much going on and so much to see and do that it does get a bit distracting at times.

The Professors are really approachable and inspite of being amongst the best in the world, have a lot of time for you as a student. The staff is incredibly helpful and Amy Duncan in the Statistics dept always seems to have all the answers.

There are a number of activities and events on campus that one should not miss. The primary being the annual GAIETIES, the BIG GAME, FULL MOON AT THE QUAD and events at the International centre.

I would advise people to buy a car though, if they can, as the commute in the bay area is a problem otherwise. At the very least one must get a driving license as soon as possible as then you can rent and drive around. It really would be a shame if one left that place without properly exploring the bay area. I cant claim to have done an excessive amount of travelling but i did not miss out on it completely either.

Advice for future interviewees: Do read the following THOROUGHLY before interviews.

1. Heard on the wall street – Timothy Falcon Crack – Cover to cover. Treat this as a guide for what topics to cover and go back to Hull and read and practise it till you are very comfortable with it.

2. Futures, Options and other Derivatives – John C Hull – Selected

3. The WSJ everyday. Buy the online subscription, its cheap.

Study the GREEKS for all equity focussed and trading interviews. Read Bond math for all Fixed Income interviews. Practise brain teasers. I love them, some people dont, do them regardless.

 

It was three years back that i wrote my autobiography for a course at IIM. I surprised myself by the enjoyment i derived from that exercise. That and some positive feedback on my work encouraged me to start this blog. Its sad that i cannot continue. Can you blame me (given the perils associated with it)?!

All the best and adios.

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The (K)night is darkest before the dawn…

Posted by tapishkushwaha on August 11, 2008

So, the past few months have been hectic, both for me and the people involved directly with the markets. The woes continue and the end seems to be far off at this point. Just today morning, i read this article on bloomberg on how the longest expansionary consumer spending run in the U.S is about to come to an end soon. Inflation, commodity prices (nevermind the recent slight cooling), housing depression and a decrease in payrolls, everything looks bleak.

I certainly agree with the contention though that this is an exciting time to be in the markets, especially in terms of the learning one gets in tough times. Everything is a lot easier when there is a lot of flow in the business and one is just swept away in the mass of work. Also, buying into a firm/job at the bottom of the trough is something one would ideally like to do.

Right now, the market is witnessing a tussle between contrasting business models. The diversified and well capitalized Citi and JPMorgan Chase vs the focussed shops like Lehman. It remains to be seen who weathers the storm better.

Ive tried to look for other bright spots, but they all seem to fizzle out faster than you can say “credit”. The high point for the world this summer seems to be “The Dark Knight“. Infact, Hollywood collections this year have shown an upward trend, proving that people are still flocking the theatres, recession or no recession.

Amongst other highlights, China showed the world what an opening ceremony should look like, truely spectacular (images).

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Of long breaks and secrets!

Posted by tapishkushwaha on April 17, 2008

Well its been a long time since i wrote last and a busy time at that. I guess so much is being said about the economy or the job scenario at all these FE programs that theres not much left for bloggers like me! Add to that, ive just got done with a qtr with 5 courses, and let me tell you, it wasn’t pretty. It makes me wonder that being in such a hurry sometimes is not a good thing!

Well a lot of people have asked me about the result of my job hunt and where i’l be heading. Problem is, a lot of people in important places have been kind enough to have a look at this blog and hence i do not think i can be very clear on that here. Suffice to say that im happy with the progress thus far and that i will be associated with a bank in a few months time.

As for the internship offers for my class at Stanford, almost all the people have offers by now. One observation though is that a lot people have got positions outside the US, which is very understandable given the pessimism here. I mean if the 5th largest I-bank gets sold for a song, common sense tells us things are far from rosy.

Amongst other things, I recently had the pleasure of attending a panel discussion on the Credit Crisis and the possible effects of public policy on it. The panelists were 3 eminent economists, John Taylor (former Under secy of Treasury), John Williams (SF Fed) and John Shoven (Stanford Econ dept). While they were quite confident that the economy as a whole would hold up quite well and the recession will be a very mild one, unfortunately they were much more pessimistic about the Financial Sector. They saw Wall St compensation coming down quite bit given the Bonus heavy packages. They were also  of the opinion that Wall St banks in general had hired too many people in the recent years and they would have to get rid of the extra flab.

All bad news for fresh grads!

All the negativity aside, i wish all the fresh new FE students all the very best for the coming yr and a half.

p.s thinking of headings is really not as easy as it would seem.

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Drilling it In

Posted by tapishkushwaha on January 26, 2008

It is the begining of the winter term at Stanford and i am buried under a mountain of coursework and assignments. I can find solace in the fact that there was no escaping the deluge and i had to go for 15 units at some time or the other. This turns out to be the time when i bite the bullet.

 PARTIAL DIFFERENTIAL EQUATIONS AND DIFFUSION PROCESSES

This course talks about the basics of partial differential equations (starting with The Heat eq.) and Boundary Value Porblems and then goes on to SDE’s. Having covered the basics in the first half of the course, the second half then applies the concepts to the Black-Scholes eq, Barrier Options, Digital options, American options, Volatility estimation and Interest Rate Models. With some luck we might be able to squeeze in some Stochastic control.

{\partial u\over \partial t} = k \left({\partial^2 u\over \partial x^2 } + {\partial^2 u\over \partial y^2 } + {\partial^2 u\over \partial z^2 }\right)  = k ( u_{xx} + u_{yy} + u_{zz} ) \quad  

ADVANCED TOPICS IN FINANCIAL ENGG

 This is a great overview course that provides a unified framework for pricing derivatives. Having concentrated so much on Brownian Motion (and i really mean a lot!), this course dives into Poisson Processes as well and shows how that is as easy to work with.

MATHEMATICAL FINANCE

 My favorite course for the term and its an extension of the introductory course i did in the summer. It starts off with the binomial tree model, moving onto Black Scholes, Implied Volatility, Short rate models and Convertible Bonds.

STOCHASTIC DIFFERENTIAL EQUATIONS

I guess theres no easy way to say this. It is SDE! Its as rigorous as any course on Stochastic Calculus is and uses the concepts we did last qtr.

\mathrm{d} X_t = \mu X_t \, \mathrm{d} t +  \sigma X_t \, \mathrm{d} B_t. 

ONE BIG CODING CLASS!

I needed to practise coding, and im getting enough of it now!

The good part about these courses is that the first 4 all seem to be drilling in the same concepts from different perspectives. In that sense this has become my own little string theory unification problem! Seriously speaking though, its a lot of fun and learning the theory and its application simultaneously just seems more useful than having them separated over a period. What is not fun though is having 5 assignment submissions simultaneously.

 I think i should clarify one aspect of my earlier posts either here or on GD. When i talk about the employment scenario, ive been generally talking about the ‘Banking’ jobs and not the ones in hedge funds or prop trading firms. I must say that the slowdown in banks have been a boon for some of the smaller firms as they have been able to lay their hands on some good talent this year. And i have seen a lot more job opportunities in that sector. The fact that a lot of them bet on oil and other commodities and haven’t had the breadth to be burnt by the big ‘S’ mess has helped them.

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Rough Times

Posted by tapishkushwaha on November 25, 2007

The past few months have made me acutely aware of the fact that the financial industry (especially the banks) is in bad shape. Be it the scarce numbers (of banks) that turned up on campus for recruiting or the small numbers that were called in for interviewing, everything points towards a gloomy picture. It was only last year when there seemed to be opportunities aplenty, but things have changed pretty quickly.

 In the course of my interviews over the past few months, ive had almost every interviewer asking me what i think of the current state of the economy (almost as much as ive been asked volatility smiles!). And ive had a multitude of reactions to my answer to this question. The responses have ranged from “Its not that bad, look at the strong fundamentals” to “The fed needs to cut another 100 bps and the crisis is much deeper than people are thinking” to “This is the worst since the great depression!”. The thing that strikes me about this is the amount of uncertainty that prevails. Nobody seems to have a definite answer. I think THAT is most worrying.

The tragedy for students graduating now has been the fact that most of the investment banking jobs after a Financial engineering degree have typically been on the Fixed Income side. And it is Fixed Income divisions that are the hardest hit, thus making it impossible for them to hire right now. I have seen a number of extremely smart people not getting offers simply because the firms do not have a clear idea of what kind of a headcount they will need in the coming year.

The bright side is that there have also been efforts rectify the situation. A lot has been said and written about the M-LEC (Master – liquidity enhancing conduit) being funded by Citigroup, Bank of America and JPMorgan Chase, along with several other financial institutions, who have been meeting to come up with a plan to create a fund that could prevent a sharp sell-off in securities owned by bank-affiliated investment vehicles. Another course of action seems to be a freeze on interest rates on ARM’s (Adjustable Rate Mortgages) in a bid to keep delinquencies under control.

Given the volatile markets, It is expected that this coming January might see a lot of turnover. For the sake of many many students who are here on big loans and have worked hard in getting their degrees over the past two years, i hope and wish that the New Year brings better opportunities for everyone.

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Back to Business

Posted by tapishkushwaha on September 23, 2007

The nice 5 week break is over and its back to the serious business of classes, assignments and examinations starting tomorrow (Sept 24th).

I really have multiple reasons to be really excited this term.

1. Its the Recruiting season!! All the major banks and financial institutions are going to be on campus strutting their stuff, trying to lure the best of the best and looking for people with the best ‘fit’ with their teams. The Sub-prime mess which has created recessionary expectations has added another dimension to the whole process and i have a feeling the going will be tough. All the major banks have shown an interest in recruitment in the Stanford career fair (Oct 9th) but im not really sure how many slots theyl be looking to fill. For all one knows this might just end up being a PR run for many of them. (Keeping relationships going with top schools in bad times is really important for recruiters).

Someone important recently said on a forum how there will always be spots for good, qualified people and that gives me hope (shameless i know!). But seriously speaking one has to be confident of oneself, especially in times like these.

2. CS106X – Computer Science courses at Stanford are known to be some of the most rigorous in the country, and rightly so, it is after all, the Silicon Valley! The second reason im excited is that i get to sample one very soon. This is an intensive C++ programming class everyone has ‘warned’ me about. I debated and agonized about doing it in a term where im going to be very busy with interviews, and then decided on taking it. Bring it on Stanford!! Well and then theres the benefit of getting a solid grip of coding and using C++ which i really want to be good at.

Ive seen a lot of MBAs and even fin-math people for that matter trying to get away from full time jobs that require any amount of coding, but i dont want to do that. Irrespective of whether i use it later or not, i feel its a skill every financial engineer ought to have and in good measure. (Reading Emanuel Derman’s “My life as a Quant” has really inspired me in this regard).

That brings me to my proposed course list for the Fall Term

STAT 240 – Statistical Methods in Finance – Regression analysis and applications to the Capital Asset Pricing Model and multifactor pricing models. Principal components and multivariate analysis. Smoothing techniques and estimation of yield curves. Statistical methods for financial time series; value at risk. Term structure models and fixed income research. Estimation and modeling of volatilities. Hands-on experience with financial data.
MS&E242H – Investment Science Honors – The course starts with developing the basic concepts under certainty. This includes arbitrage, term structure of interest rates and bond portfolio immunization. We then extend to a situation of uncertainty in one period. Topics: arbitrage; fundamental theorems of asset pricing; pricing measures; derivative securities; financial risk measures: basic theory, applications and estimation; mean-variance portfolio analysis, equilibrium and the capital asset pricing model. Group projects involving financial market data.

STAT 219 – Stochastic Processes – Main topics are introduction to measurable, Lp and Hilbert spaces, random variables and (conditional) expectation, uniform integrability and modes of convergence, stationarity and sample path continuity of stochastic processes, examples such as Markov chains, Branching, Gaussian and Poisson Processes, Martingales and basic properties of Brownian motion.

CS106X – Programming Abstractions – How programming concepts are expressed in C++. Abstraction and its relation to programming. Software engineering principles of data abstraction and modularity. Object-oriented programming, fundamental data structures (such as stacks, queues, sets) and data-directed design. Recursion and recursive data structures (linked lists, trees). Introduction to time and space complexity analysis.

3. The Beauty of the Fall colors – Yes, do I have an appreciation for beauty of a non-financial mathematical nature !!

So you see, theres much to look forward to and much to learn this qtr. I just think its going to be a lot of fun, and hopefully not at my expense😉 (Can someone get me a Bernanke ‘put’ please)

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Term 1!!

Posted by tapishkushwaha on August 11, 2007

First of all i owe everyone an apology for not writing in for so long. Infact i did start to write a post a couple of weeks back, but was frustrated by my inability to get a simple ‘plot’ into the post! Still havent figured out wordpress fully!

Lets talk about my experience in the courses ive gone through these past few months,

Introduction to Mathematical Finance: The biggest takeaway from this course has been an introduction to Stochastic Calculus and Ito Calculus. Somehow, i always equated financial math to martingales, numeraires and Brownian motion. It was great to finally learn some of this and actually apply it to derivative pricing. Although this was just a begining, a humble begining and greater things are afoot (Well i can get a little poetic at times).  The basic idea is this, If x(t) is an Ito process, meaning

 dx(t) = a(x,t)\,dt + b(x,t)\,dW_t  

then,

 df(x(t),t) = \left(\frac{\partial f}{\partial t} + a(x,t)\frac{\partial f}{\partial x} + \frac{1}{2}b(x,t)^2\frac{\partial^2 f}{\partial x^2}\right)dt + b(x,t)\frac{\partial f}{\partial x}\,dW_t.  

This innocuous looking application combined with a change of measure turns out to be the basis for risk-neutral derivative pricing theory.

Time series Modeling: This was a topic close to my heart. My 6 months as a quant at DBS were spent trying to predict currency movements based on technical indicators. So, it was great to finally get a chance to read up time series theory formally. The language we used to do the models was R (a freely availible cousin of S). The most exciting part of the course has been that we’re working with real data and so get to see what goes on real time.

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This is the forecast of Lumber production based on an ARIMA(1,0,0) model (Autoregressive Model). Having done some lengthy (and i mean really lengthy) assignments for this course means that i have a fair grasp of the modeling procedure now. Learning R has been a plus and its something thats going to be really relevant in my future workplace.

International Investments: Having worked in Fixed income research where macroeconomics was the bread and butter of fund managers, this course has been a relaxant/enjoyable experience. Ive revised the concepts that i studied in B-school and ive also been able to stay uptodate with happenings around the globe, thanks to this course.

That, in a nutshell is what ive been doing with my time in my first term at Stanford University. The next week is the final week before we’re off for a 5 week break. Im looking forward to meeting the rest of my classmates, all of whom arrive in mid-september. A lot of the fin-math guys from last year should be around too, making it quite a crowd in the fall!!

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Term 1: Summer 2006-07

Posted by tapishkushwaha on July 3, 2007

So its sunny California(via a 5 day stopover in NYC) finally after a 19 hour long flight over the North pole, no less!

I arrived on the Stanford University campus on the 19th of June and was immediately struck by the beauty of the architecture here. Its definitely the most beautiful university campus i have seen.  The marvels on campus are complemented perfectly by the hills in the background and the lovely Bay area (its a little chilly for me sometimes!) weather.

So, after the initial formalities of getting an ID, a bank account and a bike, it was down to ‘shopping’ for courses. I had decided to attend a lot of lectures in the 1st week and choose 9 of the most interesting units thereafter. I finally settled on the following study list,

Summer 2006-07

Introduction to Mathematical Finance

Time Series Modelling and Forecasting

International Investments

Audit: Theory of Probability

I have soon realized that International Investments not being a purely mathematical course provides the ideal relaxation that i will need. Its also great for me to keep in touch with macroeconomics and the developments in the world of business. (Readings of ‘The Economist’ and the ‘WSJ’ are mandatory….. well almost)

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Thinking Machines: AI in IBs

Posted by tapishkushwaha on June 22, 2007

“Way up in a New York skyscraper, inside the headquarters of Lehman Brothers Holdings Inc., Michael Kearns is trying to teach a computer to do something other machines can’t: think like a Wall Street trader. In his cubicle overlooking the trading floor, Kearns, 44, consults with Lehman Brothers traders as Ph.D.s tap away at secret software. The programs they’re writing are designed to sift through billions of trades and spot subtle patterns in world markets.

Kearns, a computer scientist who has a doctorate from Harvard University, says the code is part of a dream he’s been chasing for more than two decades: to imbue computers with artificial intelligence, or AI.

His vision of Wall Street conjures up science fiction fantasies of HAL 9000, the sentient computer in “2001: A Space Odyssey.” Instead of mindlessly crunching numbers, AI-powered circuitry one day will mimic our brains and understand our emotions — and outsmart human stock pickers, he says.

“This is going to change the world, and it’s going to change Wall Street,” says Kearns ” – Bloomberg, May2007

This is an extract from an article that appeared in the Bloomberg Markets magazine in the month of May. Its amazing how closely science is now intertwined with business and quant finance more specifically. This article reminded me of Roger Lowenstein remarking in his masterpiece, “When genius failed” about how the bigwigs of the science world at LTCM would regularly run to physics libraries and journals, hoping to find models and theories to fit their money making schemes.

 Next: Arrival at Stanford!

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The Visa Interrogation

Posted by tapishkushwaha on May 22, 2007

I finally got my F-1 visa done yesterday, laying to rest fears that i might have to fly back to India just for this.

Visa Officer: Who is funding your program?

Me: My father and a friend of his.

VO: A friend! Why is he doing that?

Me: He is a good friend!

VO: I have plenty of good friends, nobody ever gave me so much money!

Me: errrr…

Anyhow, all is well that ends well and after my tickets are done im looking forward to getting down to the serious business of studying.

By the way, books are dirt cheap in India (1/10 the price in US). So all Indians and others who know someone in India, you would do well to purchase the cheap paperback asian editions of the books u need for the course.

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