Good day , Sir
Thank you to set aside a little time out of a tight schedule to read this letter.
My name is Kenith. I’m a graduate student of industrial organization and economics
department of Tamkang university in Taiwan. I’ve got some problems about TSP
operations and programs establishments, and sincerely wish to obtain your assistance.
I feel sorry. I'm causing you much trouble.
The follows six programs are my questions：
1stQ：
I met first problem is: I use Gamma distribution to estimate daily average
precipitation,
Gamma distribution model is:
 -1
X
f (X；  、  )＝  
 

 -X  
 exp   
  

     




，
X  0 ；  、 > 0
, where X is cumulative precipitation
 is shape parameter
 is scale parameter
However, precipitation samples confine so that setting a critical point as C, C=0.1mm;
0mm<X j <0.1mm  N c
, so precipitation style is equal to
If X = 
 Xi >0.1mm  N w
N
c
+
N
w
For example,
5/1 5/2
Daily cumulative precipitation(mm)
0 0
Date
5/3 5/4 5/5 5/6 5/7 5/8 5/9 5/10
0 0 12.5 2.5 0.5 0.2
0
0
Getting Nc = 6 and Nw = 4
Then M.L.E (Maximum Likelihood Estimation)
L(X；  、  )＝
Nc
Nw
j=1
i=1
 F(C;  .  ) f(Xi ;  . )
 -1
＝  F  C;  .   
，where F is CDF
Nc
Nw

 Xi 
 
  
i=1
 -X 
exp  i 
  
   
c
F ( C ;  .＝ ) f(X j ;  . ) dx = Pr (X j  C)
；
0
Take Natural log,


Nw
1 Nw
(X ;  . ) = Nc ln F  C ;  .  - N w  ln    + ln    +  -1  ln  Xi  -  Xi
 i=1
i=1
This main equation I’ve been unable to establish is my first problem.
2nd Q:
How do I establish to simulate program that daily average precipitation of
30 days duration by Monte Carlo Simulation (M.C.S)
For example：
1995 1996 1997 1998 1999 2000 2001 2002 2003 2004
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5/1
5/2


→
→
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→
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(2-1)

as CPD index
3rd Q: Count maturity value of Call option
Establish CAP (i.e. premium upper bound)
(3-1) Min[$ unit price * Max(CPD index －K , 0) ， $upper bound ]
No establish CAP
(3-2) $ unit price * Max(CPD index －K , 0)
, where K is strike value (K=CPD  1/2 standard dev.)
My 3rd question is how do I establish (3-1)、(3-2) programs , respectively.
4th Q: Maturity value discount
(4-1) →
payoff =
1
rt
 3-1 
1
[ 3-2 ]
,where r = 1+ Treasury Bill rate of 30 days during
rt
As the same as 3rd question, I need (4-1)、(4-2) programs , respectively.
(4-2) →
payoff=
5th Q: Repeat 10,000 times for programs of 2nd to 4th questions
(5-1) → repeat (2-1)、(3-1)、(4-1) by 10,000 times
(5-2) → repeat (2-1)、(3-2)、(4-2) by 10,000 times
As the same as above , I need (5-1)、(5-2) programs , respectively
6thQ:
Call price ＝
(6-1) →
(6-2) →
1
 payoff(1) + payoff(2) + payoff(3) +
10000
1
10000
10,000
1
10000
10,000
+ payoff(10000) 
 ( 5-1 )
n=1
 ( 5-2 )
n=1
Finally I need (6-1)、(6-2) programs , respectively
Please point out the above mistakes for correction to me.
response to my questions as soon as you can.
very much.
I deeply appreciated your
At last, Thank you to do me a favor
Yours truly,
Kenith Huang
22nd Oct. 2004