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 ○ △ ○ △ ○ △ ○ △ ○ △ ○ △ ○ △ ○ △ ○ △ ○ △ . . . . . . 5/31. □ . . . □ . . . □ . . . □ . . . □ . . . □ . . . □ . . . □ . . . □ . . . □ 5/1 5/2 → → . . → . . . . (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