The Black-Scholes equation

Terry Tao once upon a time on the Balck-Scholes Equation.

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Some time ago, I wrote a short unpublished note (mostly for my own benefit) when I was trying to understand the derivation of the Black-Scholes equation in financial mathematics, which computes the price of various options under some assumptions on the underlying financial model.  In order to avoid issues relating to stochastic calculus, Itō’s formula, etc. I only considered a discrete model rather than a continuous one, which makes the mathematics much more elementary.  I was recently asked about this note, and decided that it would be worthwhile to expand it into a blog article here.  The emphasis here will be on the simplest models rather than the most realistic models, in order to emphasise the beautifully simple basic idea behind the derivation of this formula.

The basic type of problem that the Black-Scholes equation solves (in particular models) is the following.  One has an underlying financial instrument

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10 places where anyone can learn to code

Learning to Code: a mission, a life goal, a cause. A way of Life.

TED Blog


Teens, tweens and kids are often referred to as “digital natives.” Having grown up with the Internet, smartphones and tablets, they’re often extraordinarily adept at interacting with digital technology. But Mitch Resnick, who spoke at TEDxBeaconStreet in November, is skeptical of this descriptor. Sure, young people can text and chat and play games, he says, “but that doesn’t really make you fluent.”

[ted_talkteaser id=1657]Fluency, Resnick proposes in today’s talk, comes not through interacting with new technologies, but through creating them. The former is like reading, while the latter is like writing. He means this figuratively — that creating new technologies, like writing a book, requires creative expression — but also literally: to make new computer programs, you actually must write the code.

The point isn’t to create a generation of programmers, Resnick argues. Rather, it’s that coding is a gateway to broader learning.“When you learn to read, you…

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The perils of valuation

Today I post here what has been to me a rather impostant, if somewhat suprisingly discreet post in FT’s Alphaville about what sometimes happens in companies’s valuations. It follows an event of sudden drop in the share price of Quindell PLC after Gotham City, an equity research house release their valuation report about the company. Alphaville’s Dan McCrum sums it up brilliantly:

”Without attesting to the quality of the research, which goes into great detail about the accounting, two things immediately jump out: Quindell listed via reverse merger in 2011, since when it has had three different auditors.

Other tit-bits include the allegation that the New York office does not exist, and that while the chief executive invested £11.5m into the company between 2001 and 2005, the company spent the same amount building a country club.”

Fair markets deserve fair practices of Research houses, proper checks of conflicts of interests. And a way of accepting the checks and balances of assuring transparent and competitive markets wich is accepted by all involved. Otherwise the point of much of criticism of Market Economics is strong indeed.



Mild und Leise

From No Mundo (2) de Carlos M. Fernandes. A Post about one the most important artists of Western Culture and his death. His opera Tristan and Isolde was a cornerstone achievement of Western Culture.

No Mundo (2)

Foi a 13 de Fevereiro de 1883, há exactamente 129 anos: Richard Wagner morreu em Veneza, a cidade da morte, a cidade que morre, lentamente, afogada pela lagoa. Ali mesmo, quinze anos antes, Wagner escrevia o segundo acto de Tristan und Isolde, a mais bela e completa obra de arte da idade contemporânea. Leonora, a anti-heroína da novela Entre Naranjos de Vicente Blasco Ibañez, que no quería cantar otras óperas que las suyas [de Wagner], viu o mestre nos seus últimos dias, lo vio cuando llegaba a Venecia para morir en el silencio de los canales, en aquella calma unicamente turbada por el golpe de remo, donde muchos años antes había creído perecer mientras escribía su Tristán, el himno a la muerte pura y libertadora. Para morrer em silêncio. Mild und leise.

Granada, 13 de Fevereiro de 2012

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Chaos Theory in Politics (by Santo Banerjee et al.)

See on Scoop.itEdgar Analytics & Complex Systems

The present work investigates global politics and political implications of social science and management with the aid of the latest complexity and chaos theories. Until now, deterministic chaos and nonlinear analysis have not been a focal point in this area of research. This book remedies this deficiency by utilizing these methods in the analysis of the subject matter. The authors provide the reader a detailed analysis on politics and its associated applications with the help of chaos theory, in a single edited volume.

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Unconventional Computation & Natural Computation 2014

See on Scoop.itEdgar Analytics & Complex Systems

The International Conference on Unconventional Computation and Natural Computation has been a forum where scientists with different backgrounds, yet sharing a common interest in novel forms of computation, human-designed computation inspired by nature, and the computational aspects of processes taking place in nature, meet and present their latest results.


Unconventional Computation & Natural Computation 2014
University of Western Ontario, London, Ontario, Canada, July 14-18

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Swarming in Biological and Related Systems

See on Scoop.itEdgar Analytics & Complex Systems

In the last 15 years, the collective motion of large numbers of self-propelled objects has become an increasingly active area of research. The examples of such collective motion abound: flocks of birds, schools of fish, swarms of insects, herds of animals etc. Swarming of living creatures is believed to be critical for the population survival under harsh conditions. The ability of motile microorganisms to communicate and coordinate their motion leads to the remarkably complex self-organized structures found in bacterial biofilms. Active intracellular transport of biological molecules within the cytoskeleton has a profound effect on the cell cycle, signaling and motility. In recent years, significant progress has also been achieved in the design of synthetic self-propelled particles. Their collective motion has many advantages for performing specific robotic tasks, such as collective cargo delivery or harvesting the mechanical energy of chaotic motion.


In this focus issue we have tried to assemble papers from leading experts which we hope will provide a current snapshot of this young and rapidly expanding field of research. They cover both theoretical and experimental investigations of the dynamics of active matter on different spatial and temporal scales.


Focus on Swarming in Biological and Related Systems
Lev Tsimring, Hugues Chate, Igor Aronson

2014 New J. Phys. 16

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Diários de Granada (13-05-2012)

In Granada, Spain. Again with Carlos.

No Mundo (2)

Subi a Ctra. de El Purche, desde Monachil até à altura do parque de campismo. Há um caminho que vai desde o parque até ao merendero, a Este. Na parte final do percurso podemos sentar-nos e olhar para os cumes da Serra Nevada. E vemos o Veleta e o telescópio. E a lagoa de Yeguas, escondida pela perspectiva. E o silêncio, quebrado ocasionalmente pelos moscardos em voo picado. E uma nesga de redenção.

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I have never been in Málaga, Spain. But Carlos M. Fernandes have been there. Not just eating and sleeping I suppose.

No Mundo (2)

Após uma noite de tapas, cañas, pescaíto frito e flamenco, volto para o Hostal la Hispanidad (o quarto tem um número e um nome, Peru), em frente à estação de comboios. Pelo caminho, já perto da estação, passo por um bar irlandês e entro para uma última pinta, e que seja de Guiness. Está uma mulher sozinha numa das mesas. Chora. Escreve uma nota numa folha de papel, levanta-se e sai do bar. Acabo a cerveja tranquilamente, pago, saio, e recolho-me definitivamente no Hostal la Hispanidad e no meu quarto, que tem um número, o 22, e um nome.

Málaga, 12 de Abril de 2012

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