#C11.txt, Feb. 26, 2015, starting Finance
Help:=proc(): print(`Arbi(S0,K,r,Sd,Su,T,P,x1,x2)`): end:



#Arbi(S0,K,r,Sd,Su,T,P,x1,x2): Inputs 
#S0: the current price of the stock
#K the strike price, the buyer has the OPTION
#to by the stock at time T, paying K dollars, Sd<K<Su
#r=interest rate yielded from saving account
#Sd, Su the two possibilities for the price of the stock at time T
#Unless you hate money if if it was Sd you don't excercise the option
#T is the time after 0 when you may excercise the option
#P is the price of option
#x1,x2:the strategy, buy x1 Goverment bonds (with interest r) and
#x2 units of stock (whose price is x2*S0)
#It outputs true (if the portfolio [x1,x2] allows, with the price P, gives the seller
#of the option riskless guarantee of profit (aka <em>arbitrage</em>),
#nd false otherwise. It also returns, in the former case, the amount of
#profit in each case (Sd and Su respecticely, where the option was not and was excercised respectively)

Arbi:=proc(S0,K,r,Sd,Su,T,P,x1,x2) local CV,FVd,FVu,Gd,Gu:

CV:=x1+x2*S0:

if CV>P then
 print(`Shame on you, you should not exceed your budget`):
 RETURN(FAIL):
fi:

FVd:=x1*exp(r*T)+x2*Sd:

FVu:=x1*exp(r*T)+x2*Su:

#if the price of the stock is Sd, then the option is not excercised
Gd:=FVd:
#if the price of the stock is Su, then the option execrcised
Gu:=FVu+K-Su:

if (Gd>0 and Gu>=0) or (Gd>=0 and Gu>0) then

true,[Gd,Gu]: 
else
false:
fi:

end:


#Eco(S0,K,r,Sd,Su,T,P): Inputs 
#S0: the current price of the stock
#K the strike price, the buyer has the OPTION
#to by the stock at time T, paying K dollars, Sd<K<Su
#r=interest rate yielded from saving account
#Sd, Su the two possibilities for the price of the stock at time T
#Unless you hate money if if it was Sd you don't excercise the option
#T is the time after 0 when you may excercise the option
#P is the price of option
#output, the cut-off price where the seller can't have
#arbitrage, assuming he or she uses all the P dollars to
#invest
Eco:=proc(S0,K,r,Sd,Su,T) local x1,x2,i:



end: