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.
2008年4月10日木曜日
2008年4月7日月曜日
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.
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.
2008年4月4日金曜日
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.
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.
2008年4月2日水曜日
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.
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.
2008年4月1日火曜日
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.
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.
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