/*
** Version 01
** Date : 20/07/2001                                        
** --------------------------------------------------------------------------
** Copyright K.Cuthbertson and D. Nitzsche
** "Financial Engineering:Derivatives and Risk Manangement" - J. Wiley 2001
**
**   VALUE AT RISK: FORWARD RATE AGREEMENT (FRA)
**
**   VaR for FRA in Table 23.7
**
*/


new ; cls ;  outwidth 250 ;
format /m1/rd 12,4;  output on ;  screen on ;

/*
** output file=c:\docs\arun\out.out reset;                      @ ----- USER TO CHECK FILEPATH ----- @   
*/

/*
?; " --------------------------------------------------------------------------------------------" ;
                                   Mapping 6m x 12m FRA
   " --------------------------------------------------------------------------------------------" ;
?; "  VaR of 6 x 12m FRA (lend at 6m and receive at 12m)                              ";
?; " Cash outflow for selling 6m x12m FRA is equivalent to borrowing at t=0           ";
   " at the 6m-rate and lending at t=0 at the 12m rate                                ";
    
?; " Days in 1st and 2nd leg of FRA (days01~days12)  	                              ";
?; " Interest Rate (simple,propn) for 1st and 2nd leg of FRA (r1 and r2)	 	      ";
?; " Standard Deviation of Asset 'Return' at 1st and 2nd leg (sigma1,sigma2)          ";
?; " R =  Correlation between 'return' on Asset-1 and Asset-2                         ";
?;
?; " $-Notional principal in the FRA (Q)                     		                  "; 
?; " Present Value of synthetic spot cash flows (pv1~pv2)                             ";          
?; " VaR = Value-at-Risk                   						                      "; 
?; " --------------------------------------------------------------------------------------------" ;
*/

@ ------------------------------------------- USER INPUT HERE ------------------------------------ @

days01  = 182;                   
days12  = 183 ;                   

Q       =  -1000000;                @ notional principal, lend at 6m @          
r1      =   0.0639;                 @ spot rate, p.a. - simple, propn @
r2      =   0.0696;                 @ spot rate, p.a. - simple, propn @
sigma1  =   0.130121 ;              @ sigma (Daily, %) @
sigma2  =   0.291600 ;              @ sigma (Daily, %) @

R={  1    0.7,  0.7   1  } ;              @ correlation matrix (2x2) @  

@ ------------------------------------------END OF USER INPUT  ------------------------------------ @ 


@ ------------------------------------------- PV of 1st leg --------------------------------------- @

t1   = days01./365;
pv1  = Q./(1+t1.*r1);

@ ------------------------------------------- PV of 2nd leg ---------------------------------------- @

days02 = days01+days12 ;

t2     = days02/365;
val2   = -Q.*( (1+r2.*t2) ./ (1+r1.*t1) );          @ value of sythetic at t=2 @
pv2    = - pv1;

@ ------------------------------------------ VaR Calculations --------------------------------------- @

t12    = t2-t1 ;
f12    = (1/t12).*( ( (1+r2*t2)./(1+r1.*t1) ) - 1 ) ;           @ forward rate @

Z      = zeros(2,1);

Z[1,1] = 1.65*(sigma1/100)*pv1;
Z[2,1] = 1.65*(sigma2/100)*pv2;

VaR    = sqrt( Z'*R* Z );

@ ------------------------------------- Print the output ------------------------------------------------------ @

?; " -----------------------------------------------------------------------------------------------------------" ;
   "                                Mapping 6m x 12m FRA                                                        " ;   
   " -----------------------------------------------------------------------------------------------------------" ;
?; " VaR of 6 x 12m FRA (lend at 6m and receive at 12m)                               " ;
   " Cash outflow for selling 6m x12m FRA is equivalent to borrowing at t=0           " ;
   " at the 6m-rate and lending at t=0 at the 12m rate                                " ;
   " ------------------------------------------------------------------------------------------------------------" ;
?; " Days in 1st and 2nd leg of FRA (days01~days12)  	                              " days01~days12 ;
?; " Interest Rate (simple,propn) for 1st and 2nd leg of FRA (r1 and r2)	 	      " r1~r2 ;
?; " Standard Deviation of Asset 'Return' at 1st and 2nd leg (%, per day)             " sigma1~sigma2 ;
?; " R =  Correlation between return on Leg-1 and Leg-2                               " R ;
?;
?; " $-Notional Principal (Q)                                            		      " Q ;
?; " Cash flows at t1 and t2 in the actual (and synthetic) FRA (Q~val2)               " Q~val2 ;
?; " Forward rate over 6 months (1+ f12.*t12): should equal val2./Q                   " (1+f12.*t12) ;  
?; " Present Value of leg-1 and leg-2 of synthetic                                    " pv1~pv2 ;  
?; " Individual VaR's of 1st and 2nd legs of FRA                                      " abs(Z') ;
?; " VaR = Value-at-Risk                   						                      " VaR ;
?; " Worse Case VaR	 		                                                          " sumc(abs(Z));   
?; " -------------------------------------------------------------------------------------------------------------" ;

end;