EOD

EOD is an abbrevation of End of Day which is qute often used financial company. It means the time when we estimate the profit or loss about products we have. It must be done every day, and it must be of cousre correct. Especially it is very important for financial company, particulary swap houses which deal exotic derivatives. There are some reason for this.
At first, derivatives are not real products. They are not fruits, fishes, sweets, nor oils. They are only the kind of contracts which promise specialized cash flow. So we have to estimate how much the price is every day.
Secondly, Exotic derivatives are difficult to price. Exotic, as you can imagine easily by this word, is not a simple product. So we have to simulate them by using complexity logic. it might be impossible only by using simple formulation.
From this point, EOD are quite related with quants developers. It is not too much to say that quats developers' task are almost to manage that EOD has been done every day correctly.

Plain Vanilla

Plain Vanilla is a technical term about financial products. It means the most basic or standard version of a financial instrument, options, bonds, futures, swaps. In particular, a plain vanilla option is the standard type of option, whose pricing model was published by Fischer Black and Myron Scholes in 1973. This theory is called "Black-Scholes formula", and anyone who engaged with financial markets knows about it. Moreover, Black-Scholes formula is quite related with partial differential equation, more exactly speaking, by supposing some conditions, a solution of some partial differential equation is expressed with the expectation of some random variables.

The most symple case is a Black-Sholes equation. From Black-Sholes equation, we can get the risk value of option products easily. From this equation, we are able to manage the option as much as our risk reducing. If option traders have done the call option, the first they do is almost "Delta" hedging, that is reducing the risk for underlying changing. Even they can hedge the delta perfectully, they remain the risk for time-values, which is called "Theta". But this risk can be cancelled if they do "Gamma" dealing. Black-Sholes equation is certainly explaining these way.

Quantitive Meeting

In Tokyo, there are at least over 30 swap houses, which are included U.S., U.K. and E.U. companys. I had dinner party with quants who work in Otemachi, Marunouchi, Nihonbashi, and Roppongi and so on.
Around many quants, topics are always about the latest model, the latest product.
"What is your new model in your company??" "Has your company already developed XX product ??" "How is YY model calibrated in the market??"
Quants are defined as people who love finance, who love a lot of rewards for ourselves, and who love mathmatics.
Quants are living with an ambitious for developing our original model and our original theory.
The most exciting time for me is of course when I have done them.

Brownian Bridge

Brownian Bridge is defined as the conditional expected distribution of a standard Brownian Motion given the condition that we know values of Winner process at a starting point and some points. We of course know that this expectations and covariances.
As a mathematical instrument, Brownian Bridge is used when we simulate a extotic product pricing. Concretely, interest rate models are simulated at some discrete-fixed times which are often called "simulation grids". Though we sometimes have to price products whose payoffs do not lie in the simulation grids, we only know information of simulation grids from this calculation. But If we use Bronwian Bridge, we can get a good view of the process at not even simulation grids. Thus by using it, there may happen that we can get a better result.

Quasi-Monte Calro

Quasi-Monte Calro is a method for the computation fot the integral.
This method is based on low-discrepancy sequences.
On the other hand, Monte Calro method has a long history, and it derives from the Law of Large numbers.
The most advantage of Quasi-Monte Carlo compared with Monte Carlo is the faster convergence. We need 100 times samples to make the convergence accurate 10 times if we use Monte-Calro method, while we need only 10times samples to get the same result with Monte Calro if we use Quasi-Monte Calro.
But, Quasi-Monte Calro method works well only how integral function is smooth, and how its dimension is small. These are problems for Quasi-Monte Calro.
In finance, we often use the above ways to price some financial products. To price accurately, or to price quickly, Financial developer must know these ways.

Paris suburbs

I have visited one of university in Paris, excalty in Paris suburbs to attend a financial seminar.
One of their topic was about some estimation of correlations. A speaker who is a famous researcher talked in English very fulently, but it was difficult to understand it. The claim was that we can estimate the correlation among company's stocks by using asymptotic expansions even in condition that we only 'observe' them during some discrete-time. He called them 'observation time', and he formulated them by poisson-time.
I think it is very interesting because a correlation is important for finance. Of course we have many ways of its estimation, but implying or hedging the correlation may be impossible by using financial instruments. If this research is more advanced, it will be tradable.

First diary

I am a business man in Tokyo, majoring in Mathematics, using Probability Theorem.
This blog is for mostly purpose that I just want to keep making diary in English,
Of course I am very glad if many peaple will read this.