Happy Equations

I attended the Financial Summit Workshopon Sep 21-22 at National Taiwan University in Taipei. Many speakers provided great tutorial and speeches during the sessions. The most important guest is Dr. Edward Altman from Stern School of Business New York University.

Dr. Altman is the developer of the famous Z-Score method for evaluating credit risk of public-traded firms. Although he developed the very first model in 1967, it is still very useful in today's financial environment. Dr. Altman mentioned about the difficulty of developing such a complex model during ancient punch card age of computers. I was surprised by the accuracy of the model.

Dr. Altman has great humor and talked many jokes in his sessions. He also like default and bankrupcy of major companies. I was impressed and learned  a lot during this workshop.

We finished first release of RightPairs for pair trading last week. We are very happy because it is the most powerful generic calculation agent we ever developed.

First of all, it can run on multiple PCs and multi-threads. We tested the calculation on three 4-CPU servers, each server run calculation agents in 12 threads, without any problem. It takes full advantage of multi-processor and multi-thread. Currently it do only correlations, but it is quite easy to add more calculation features.

Our software is at http://www.rightpairs.com

I have not studied deeply about partial matching. Someone asked about using regular expression for partial matching ACGT-like pattern and strings. I wrote a simple program to test my idea about partial matching using regular expression.

The first effort is on brute force partial matching. I prepared all the possible patterns and match them to the target string. It worked fine if you can only accept 1 tolerrance (1 doesn't match) since the number of patterns to match is equal to the length of original pattern. But if you want more than 1 tolerrance, the number of patterns goes up to C(pattern length, tolerrance), it might drive you crazy if you have a pattern more than 100.

I tried to use another technique "Check Appearance". I don't know whether it has an official or scientific name. First I get a substring which length is the same as pattern from target string. Then I compare the frequency of A, C, G, T in the pattern and the new string. If their differerence are below the tolerrance, than I can do the RegEx matching. I found it is useful especially the pattern is long and tolerrance is low. I should try some other methods if I have time.

I attach my all source code here. Please understand the code is developed for quick testing, not a full functional release. There are many bugs and accuracy of the result must be checked. Please let me know if you find any bugs.

Download link has been moved to JumboGuide.

There are many free data on the net, but nobody collect and use them. I am starting a project to collect various data on the net. Using regular expression provided by .NET, I think it is quite simple to collect web data. I have put related works on http://www.derivativepower.com and http://www.jumboguide.com

After waiting for 2 months for exam result, I finally got a notification from GARP that I passed 2005 FRM Exam.

I thought I might not pass it because I didn't know how to solve most of questions in the exam. I am lucky enough that I got good scores in many section. The exam result shows only in Quartile.

Credit Risk Measure and Management: 1st Quartile
Market Risk Measure and Management: 2nd Quartile
Operational and Integrated Risk Management, Legal, Accounting, and Ethics: 2nd Quartile
Quantitative Analysis: 1st Quartile
Risk Management in Investment Management: 1st Quartile

FpML (Financial product Markup Language) is a good choice to store and to process financial derivatives. Current specification 4.2 Working Draft has defined the following produts:

• Interest Rate Swap (plain vanilla IRS, quanto swap)
• Interest Rate Option (caps/floors/collars)
• Credit Default Swap
• Equity Forward
• Equity Option (European, American, Bermuda, Exotic)
• Equity Swap
• Asset Swap
• Forward Rate Agreement (FRA)
• FX Average Rate Option
• FX Barrier Option
• FX Digital Option
• FX Simple Option
• FX Swap
• Swaption

For more information, you can go to FpML Website.

I spotted the Google Map APIs for a while. In my opinion, as a web developer in Taiwan, I might choose Google Map as my tool. I don't mean Google Map is better than ArcWeb Services. In fact, Google Map offer just basic mapping APIs and can't compare with ESRI ArcWeb. But ESRI ArcWeb Services offers little content outside US. We can't get detailed sattlelite images of Taiwan from ArcWeb. Google Map and Google Earth really have very detailed images of urban areas in Taiwan.

But, Google Map has no road map in Taiwan, although ArcWeb has only outdated large scale road map. The best choice is to have your own ArcGIS Server and purchase your own data, it might cost tens thousands US dollars. If you are looking for free services, there are always trade-offs.

For information about ArcWeb Services, http://www.esri.com/software/arcwebservices/index.html

For information about Google Map API: http://www.google.com/apis/maps/

Taiwan is a beautiful island with many beautiful scenes. It has more than 100 peaks taller than 3000 meters (9000 feet). In 2003, Taiwanese government picked 100 mountains which were accessible in 1 day from urban area. Most of them have roads directly connected to the trails and closed to major cities. The elevations are from 100 meters to more than 2000 meters.

Currently I can't find any information about these trails in English, so I will provide information at my travel website at http://www.jumboguide.com/guide/tt.aspx?forumid=45&lang=English

Although it is Saturday, my wife and me woke up at 5:30am. We were going to find our first geocache. We picked the nearest cache, only 1km away my home, at the top of Hemei Mountain by the Green Lake (BiTan). We arrived the platform on the top of trail. It took us 20 minutes to search the cache. Finally we found it. There are tens have logged it. We took an elephant key ring and put some old Taiwanese stamps in it. We are very happy for success at our first hunt.

各國政府不會把 Capital Cost 算入太空計畫的成本當中,
所以 Marginal Cost, 邊際成本才是考量重點.
Dr. Edwards 預估在第一部太空電梯完成後.
每公斤運輸的實際變動成本是220美元.

太空電梯的建造成本大概與太空梭差不多,
但是單位運輸成本可以降低.
第一座太空電梯的成本估計約一百億美元,
主要任務應該是建立第二座太空電梯,
第二座的成本估計是三十億美元,
一旦越來越多太空電梯建造完成,
太空貨運可自給自足不需政府補助,
未來可望降到每公斤10美元以下.

如果建造成本完全要由民間自付,
估計含建造和維護成本要四百億美元,
每公斤的價格要到3000美元.
相較於目前運於在地球同步軌道每公斤20000美元來說,
還是便宜多了.

太空電梯地面的錨站 (anchor station) 有固定式和移動式,
移動式的大概都是規劃在海上,
可以視情況移動位置躲避惡劣天氣.

也有規劃在高樓頂端, 這樣子可以有便宜的電力,
雖然只是幾百公尺的高度, 但可以讓最底部的纜線寛度大幅降低.

Dr Edwards 目前提案是在東太洋赤道附近的 Galapagos 群島西邊建立浮動錨站,
利用現有的鑽油平台技術就可以了.
據他說這個地點距離最近的海上和空中航線有650公里,
可以降低意外和恐怖攻擊的機會.

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I studied FRM materials and got an indea last night. It is hard to define the operational risk of financial institutes, in fact, any institutes. But a multi-agent system might be a good choice to simulate operational risk. Blow is a rough idea:

To simulate operational risk in Department A, which has
1 department head, 10 traders, 2 risk managers, 5 back office

defined communication lines:
deapertment head to everyone: 17
traders cross: 10x9=90
traders to risk managers: 10x2=20
traders to back office have no full route: 15
risk managers to back office: 2x5=10

defined probability of error of each person and each lines
defined potential loss of each person when he/she failed to perform unintentionally

defined probability of intentional error of each person
defined potential loss of each person when he/she failed to perform intentionally

We can now start to simulate. This model is too simple for any existing environment. We can have the PCs, telecomm lines, and any equipments into the model. Also external events and entities. If we got 500 persons and 10000 entities, we still can do it use MAS.

Let it be my next project.

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I was asked about VaR of a 20 years fixed-income or fund. VaR is an estimate about potential profit or loss in a short term, says 1, 5, or 10 days. How about VaR for a 20 years maturity government bond? Or for someone want to evaluate his long-term investment?

We know VaR is getting larger as the term longer:

n days VaR = 1 day VaR * sqrt(n)

if 1 day VaR is v
5 days VaR is v * sqrt(5) = 2.236v
10 days VaR is v * sqrt(10) = 3.162v

if you evaluate longer term
365 days VaR is 19.105v
3650 days VaR is 60.415v
7300 days VaR is 85.440v

Wow, the potential profit or loss might be very high.

By definition is true, of course, but we know it is not in practice. Why?

Because long term volatility is hard to estimate and the rule of square n is not a good way to calculate even short term VaR.

I clawed the webs and found only one paper about long term VaR model.
See Long-Term Value at Risk. By. Kevin Dowd, David Blake, and Andrew Cairns

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Date 12/11/2004

After passing the custom, a beautiful Polyneasian girl present wreaths for us. Because our cruise will start embarking next day, we take a bus to the hotel IntercContinental BeachComber Tahiti. 30 odd people are probably all westerners on the bus, only another pair of Oriental's face. We knew later that they are Chinese lived in San Francisco. All the travellers on the cruise, as we knew, only we come from Asia. All others are very surprised we come from so far a place. In fact, it is only a little farer compare with European visitors. The Europeans all take plane from Paris to Los Angeles to transfer to Tahiti. Travel by cruise is familiar by westerners but not for orientals, that's why there are only few orientals onboard.

Arriving the hotel ten minutes later, again we waited for a long time too of check-in, It seems the people here are not in a hurry.  A beautiful girl at the other side of counter answered every questions slowing. A group of travellers carried the luggage and wait behind of us. Wait until our check-in When the check-in is finished, all of us are nailed black and blue by the mosquito.

Because we are only one night in transit here, so has not lived in the "over the water bungalow". Our room is rich of south asian style, coconut trees outside the balcony hide most of our view of sea. TVs are mostly French programs, two or three English movie channels and ESPN, but we do not want to watch TV. We put down our baggages and go to the first floor to see tonight's performance.

We sat on a good place in the restaurant and paid the first bill in Tahiti. The price on the menu is franc CFP of Pacific Ocean of local currency, we are not still very familiar with the exchange rate, two cups of fruit juice, unexpectedly it is nearly 17 euro. Fortunately the meal will be served free on the cruise from tomorrow. Otherwise it can really called very good weight-reducing journey.

The show is traditional Polyneasian dance. If you have ever been to Guam or Hawaii must see the similar performance. Strong rhythm and wild movementare the characteristics of the Oceania dance. The dancers invited audienced to show on the stage and perform together. We have a lot of fun.

The poolside after the performance was very quiet, and the scene of hotel is very beautiful too. When I was planning the honeymoon, my wife said it was very regrettable that we are in Tahiti but not lived in the on the water bungalow. I think it is not a issue after this night on the ground.