Pricing Longevity Bonds Makes Live Shorter

The final exam required us to price longevity bonds and incorporated long-run risks into pricing. It is said no paper does this very successfully so far.  One of the biggest problems is that there are many uncertainties should be considered.
To simplify the analysis and make the pricing tractable, I consider only two uncertain sources: interest rates and life expectancy. Since the coupon payment will not be realized until a period of time after the holder purchases the bonds, it is no doubt we need a stochastic discount factor to calculate its price today. This is the same for the mortality rate which is expected to be declined with time. Mimicking the idea of forward rate, I create something called forward mortality rate. Then assume both of them follow Ito process.
Assigning an arbitrary life length, T, I can calculate the present value of coupon for each period starting from the day of realization to T. The price of longevity bonds is just the sum of present values.
Of course it is impossible to get the closed-form present value or price unless we know the exact form of Ito process and T.
The take-home exam is as hard as hell, but it's indeed a good practice for modeling.



Snow Day

The last day of dead week is a snowy day.
Always I don't read weather forecasts, so it is an enjoyable surprise to see snow flakes flying around in the air. Sitting in front of the window and taking a sip of hot coffee, it seems reading a finance paper is not so annoying.

                       To memorize the first big snow day at Raleigh in winter 2010

Thanksgiving

I missed the beauty of fall again.
When I gain something, I lose something.
But is the tradeoff fair?

Shin Megami Tensei: Strange Journey

At the peak of the FPS era, old-fashioned, especially turn-based, RPGs had faded. Wizardry, Might & Magic and Ultima retires or target a small group of audience by another forms. A few confront the trend and survive. Shin Megami Tensei (SMT) is one of them. By including sensitive religious issues and modern world into its essences, SMT series stands apart from numerous RPGs with medieval styles.

The first few titles I had played were Megami Tensei Gaiden: Last Bible I & II on GB. and SMT I on SFC. I didn't think them were bad, but their styles are not type. Due to its appealing trailer, the latest title Strange Journey on NDS catches my eyes. It doesn't disappoint me. The absorbing plot, challenging boss battles and powerful orchestral music all tell why the series lives so long.

For 20 plus years of gaming experiences,  I had been learning to be more open-minded to any kind of games. Maybe I should apply the same mind to any aspect in my life.

 

 Shin Megami Tensei (真 女神轉生): Strange Journey. The box art is strange enough. This game is rated M for mature because of blood, violence, and sexuel themes. I guess religious sensitivity is the reason behind this, however. 

在黑夜相會

       連續幾晚都做夢。前兩三日醒來後，仍依稀記得夢到同一個人，然後就呆坐床上。幾分鐘後才回過神來。

       昨夜，則是身在一個非常不同的夢境中。那裡的天色也是黑暗的，異常的黑暗。一座有蓋的大型甲板從陸地延伸到漆黑的海面上。甲板上點了幾盞燈火，這裡將有一場比武。約有十來個左右的人觀戰。我背對著陸地，對方則是背對著大海。夢中的我，未見對方長像，但知道他是段數在我之上，而我也頗有自信自己能獲勝。身穿白色武道服，我拿了一條咖啡色腰帶，準備繫上。這時卻發現，這條腰帶太短又太細。試了幾次，又經旁人協助，仍無法成功繫在腰間。慌張之下，突然醒來。

       前幾夜的夢境尚能理解，而昨夜之夢頗為奇異。如要說有相同之處，那可能是兩者都反映過去的遺憾。

萬中選一/萬分之一

在書店待了許久，晃了幾圈，最後還是一本書都沒買。選擇太多反而讓人不知從何下手。在這個人人可以寫書，出版爆炸的時代，要挑中適合自己的課外讀物實在不容易。

除了一些由名人掛名，卻由他人代筆的書外，我最討厭的就是小書了。就體積而言，小書大部份都不小，但是內容卻乏善可陳。通常都是由許多小故事，加上看似頗負寓意的結語組成。這類書經常不是一頁沒幾個大字，就是行距過寬。根本不需要買，站著看完整本腿都還不覺酸。因為缺乏明顯主題，連帶使整體架構非常鬆散。走出書店立刻忘了所有內容。可惜當今有不少著名作家專寫這類書籍，某位旅美作家更是箇中高手。

論純粹娛樂，小說可能最好。只是我寧可買片有不錯劇情的RPG，自己融入故事更具娛樂性；財經類書籍雜誌一樣缺乏興趣。一年至少有300天都與相關的教科書為伍，再看這些實在是種折磨。而且，多數內容過於直覺，難有新鮮感，自然興趣缺缺。

從前對政治思想有些射獵，家裡書櫃還擺了幾本相關書籍。但或許是因為式微，潛在讀者稀少，所以書店也不進這類思考嚴謹的書籍了。現在即使架上有幾本有關政治的讀物，常是從標題或封面文字就開始強調其聳動性，我連翻都不想翻。。我認為，在自由社會接受過高等教育又經過社會化者，已經有獨立思考能力可分析現實政治，不需要這些書來傳達"真相"或“預言”給我們。

即便扣除以上類別書籍，剩餘也是數以千萬計。每次走出書店，手上拿著的那本書，看似經過精挑細選，實則和閉著眼亂抓相差無幾。

回秀孟對孤島2009年元旦賀詞

秀孟:
"雖然2008年沒什麼值得紀念的事
雖然今年101煙火很遜
雖然今年賠了很多錢
雖然老了一歲還是沒什麼成就
但是
至少我們又平安的度過一年
送大家一段Cheers!! "話
節錄至[婚禮之後]這部電影
他是這樣講的
"每個在妳們心中佔有一個位置的人"
"花時間跟她們相處"
"才是真正有意義的事情"
祝各位

小弟已經放棄對新的一年的期許，新年的大環境是根據前一年的大環境來走，或是前前一年的大環境，或是前前前一年，so on and so forth。正所謂種瓜得瓜，種豆得豆。以致於不能理解為何眾多人要聚在廣場慶祝。

多年前，美國人在時代廣場迎接新的一年，心中充滿期許，當年卻來了911。接著的新年，大家又上街希望世界會更好，然後反恐戰爭揭開序幕，持續多年…。去年的這天早上醒來，有假可放路上空氣又清新，多少人覺得今年會更美好，然後金融海嘯翻騰而來…。所以對新的一年，已經不感覺興奮，也不再期望，因為局勢不可能有跳躍性的好轉。

我將期許拉回自己身上，把時距縮短只希望自己的前途能漸漸上軌道。

祝各位有決心實現以往的目標
乾杯