Derman's Lecture in Fields Institute

Similar to his book, his lecture was very fascinating. Emanuel Derman; the former GS quant, the present professor in IE&OR Department of Columbia  University in NY, and the writer of  the fabulous book My Life as a Quant : Reflections on Physics and Finance; gave a lecture in Fields institute entitled “Metaphors, Models & Theories in Science and Finance”.

He started to discriminate between models and theory with the emphasis on finance. According to Derman, metaphor is just like what Arthur Schopenhauer mentioned “Sleep is the interest we have to pay on the capital which is called in at death; and the higher the rate of interest and the more regularly it is paid, the further the date of redemption is postponed.”

Models are metaphoric insights. However, theories are the truth. So, we have to consider the limitations of the models. Best way to say; “by building models, we sweep the dust under the rug. But, in practice, we need to aware our customers about that.”, he urged. He remembered the audience the joke-wise word of Andrew lo: “In physics it takes three laws to explain 99% of the data; in finance it takes more than 99 laws to explain about 3%.” But, “there is one law in finance.” he mentioned, “The law of one price.”

P.S.1: Soon, you will find his beautiful slides with his audio in Fields Institute website.

P.S.2:  I'm going to pay me interest for tonight.

Monte Carlo Methods in Finance

Monte Carlo (MC) methods are vastly used to approximate the price of financial derivatives and the reasons which make them so popular are:

1. the curse of dimensionality when the derivative is on a bunch of assets which makes the deterministic numerical methods for PDEs useless,
2. the existence of non-Markovian exotic derivatives which makes the above technique in applicable.

The beginning of the MC in finance was the 1977 paper of Phelim Boyle:

Phelim Boyle, Options: A Monte Carlo Approach, Journal of Financial Economics (1977) 323-338

which has not any thing new in MC but the contribution is the application to derivative pricing. I suggest you to read the above paper and then follow the history of MC up to know. It is very interesting to see that from  the early work of Phelim up to present, some pure theories from stochastic process are born and maturated to cover financial demands to faster and more accurate methods e.g. backward stochastic differential equations or Malliavin approximation of conditional expectation. Does it at all excite you?

If you need a reference for MC, use the book of Paul Glasserman and if you need a faster and less detailed but complete enough text, use the Lecture Notes of Bruno Bouchard; of course with enough French proficiency.

Meet By Chance in Starbucks

You can not be more lucky if in a lonely day, you meet your favorite man in your favorite place. Yes, I met one of my favorite guys in one of my favorite places. Feeling to lonely from long vacation of my wife and tired from the long weekend (thanksgiving), I decided to go to Starbucks to have a fresh coffee and to review the slides of my talk in October 19. 

You can't imagine what happened. Phelim Boyle, the famous finance professor, entered and ordered a coffee. I couldn't help showing myself to him. I stood up waving hands. He saw me and came to my table. We shook hands. He picked up his coffee and we started talking about finance.

Not only my loneliness disappears, but also I got more impression to work the rest of the day. Consequently, it's always good to have an affectionate famous professor in the the small town like Waterloo who you can meet him almost surely , like a Brownian motion.

Meeting the pioneer of Monte Carlo methods

I never mentioned in this blog my expertise in Monte Carlo method and the title of my thesis; "A probabilistic numerical method for fully nonlinear parabolic partial differential equations". If you are confused with the title, just read it as "Monte Carlo method for some nonlinear partial differential equations". The fact that these equations appears in Merton model for dynamic portfolio selection, relates my work to finance.

The pioneer of Monte Carlo methods in finance is Phelim Boyle which is now at the same university as mine, but in the business school not mathematics. It would be a pity if I never met him. But, fortunately I met him today and we agreed on regular visits.We are going to have launch together and it may bring me some new research opportunities.

Confidence interval for pricing

Last week, some one reminds me an statement made by Chris Rogers during the Thematic program in quantitative finance in Fields institute (Toronto, 2010) about giving an confidence interval for the price of a derivatives, instead of just one number.

I can add that the idea could be applied not only in finance but also anywhere a probabilistic model is taken into account.

First words

Finematics is a blog to share my experiences in Financial Mathematics. This blog may be helpful for those who want to know about the subject; from students who are to decide to take some courses or attend a program, to researchers from other areas. Also, I intend to provide some basic of probability which play an important role in Financial Mathematics.

I do not want to teach Financial Mathematics in this blog, but here you can find diverse ideas and tips in the subject. The difficulty of the posts could vary from the basic definitions in finance to some easy basic mathematical knowledges. Therefore, here we do not intend to provide research level Mathematics.