/*
** Version 01
** Date : 20/07/2001                                        
** --------------------------------------------------------------------------
** Copyright K.Cuthbertson and D. Nitzsche
** "Financial Engineering:Derivatives and Risk Manangement" - J. Wiley 2001
**
**  HEDGING AND VOLATILITY
**  Graphing a jump diffusion process
**
*/

new ;   cls ;

@ ------------------------ next 2 statements required for GAUSS graphs ---------------------- @
library gauss pgraph ;
graphset ;

format /m1/rdn 16,8 ;  output off ; screen off ;
" -------------------------------------------------------------------------- " ;
"                                                                            " ; 
" Version  20/07/2001                                                        " ; 
" -------------------------------------------------------------------------- " ; 
" Copyright K.Cuthbertson and D. Nitzsche                                    " ; 
"                                                                            " ; 
" Financial Engineering:Derivatives and Risk Manangement - J. Wiley 2001     " ; 
"  HEDGING AND VOLATILITY                                                    " ; 
"  Graphing a jump diffusion process                                         " ; 
"                                                                            " ;
" -------------------------------------------------------------------------- " ;
output off ; screen off ; 

" ------------------------------------------------------------ " ;
"                                                              " ; 
"            Definitions of Variables Used                     " ;
"            -----------------------------                     " ;
"                                                              " ; 
"                                                              " ; 
"   S0 =          Share Price (starting value)                 " ;   
"   D =           Drift parameter                              " ;   
"   sigma =       Volatility of S                              " ;  
"   Intens =      Intensity                                    " ;   
"   Jump =        Jump parameter                               " ;   
"   TT =          Time to maturity                             " ;  
"   dt =          Time step                                    " ;  
"                                                              " ;  
" ------------------------------------------------------------ " ;

/* ------------------------------------- START USER DATA INPUT -------------------------------- */

S0     = 100 ;   
D      = 0.05 ;    
sigma  = 0.1 ; 
Intens = 0.2 ;   
Jump   = 0.4 ;  
TT     = 1 ;       
dt     = 0.01 ;     

/* -------------------------------------- END USER DATA INPUT ------------------------------- */

/* ------------------------------------ STARTING THE CALCULATION ---------------------------- */

Size = (TT/dt)+1 ;

/* rndseed 23456567 ; */        @ Switching this seed 'on', fixes the random variables @ 

ee     = zeros(Size,1) ;
S      = zeros(Size,1) ;
S[1,1] = S0 ;

e      = rndn(Size,1) ;

t = 2 ; 
do until t > Size ;
   if e[t,.] < Intens*Jump ;
        ee[t,1] = 1 ;
        
        else ;
        ee[t,1] = 0 ;
     endif ;
  
   S[t,1] = S[t-1,1]*(1+D*dt+sigma*sqrt(dt)*(e[t,1]-Jump*ee[t,1])) ;
   
t = t + 1 ;
endo ;


xx = zeros(Size,1) ;                            @ Setting up Vector for X-axis @ 

     g = 1 ;
     h = 0 ;
     
     do until g > Size ;
     
  xx[g,1] = h ;
        h = h + dt ;
        g = g + 1 ;
     endo ;

S_Jump = xx~S ;


@ ------------------------------------ Printing Output and the Graph ------------------------- @

output on ; screen on ; 
?; "----------------------------------------------------------------------- " ;
?; "  HEDGING AND VOLATILITY                                                " ; 
?; "  15/06/2001 (Version 1)  K. Cuthbertson / D. Nitzsche                  " ; 
?; "  Graphing a 'share price' which follows a jump diffusion process       " ; 
?; "----------------------------------------------------------------------- " ;
   "                                Parameter Inputs                        " ; 
   "----------------------------------------------------------------------- " ;
?; ftos(S0,       "Starting value of the share price : %*.*lf"  ,10,2) ;
?; ftos(sigma,    "Volatility of     S : %*.*lf"                ,24,2) ;
?; ftos(D,        "Drift parameter : %*.*lf"                    ,28,2) ;
?; ftos(Intens,   "Intensity parameter : %*.*lf"                ,24,2) ;
?; ftos(Jump,     "Jump parameter : %*.*lf"                     ,29,2) ;
  
?; ftos(TT,       "Time period : %*.*lf"                        ,32,2) ;
?; ftos(dt,       "Time steps : %*.*lf"                         ,33,2) ;
?; 

/* 
?; " Printing complete time series of stock price "; S_Jump ;
*/

title("Stock Price : Jump Diffusion Process") ;
xy (xx, S) ;


end ;