Trinomial option pricing in the maximum of two stocks

function [price] = TwoStatesAmericanCallTrinKamradRitchken(strike,S01,S02,irate,TTM,sigma1,sigma2,rho,lamda,N)
% N: how much equal piece Ι divide the time TTM  
% S01 & S02 are the initial stock prices
deltaT=TTM/N; 
u1=sigma1*lamda*sqrt(deltaT); 
u2=sigma2*lamda*sqrt(deltaT);
d1=1/u1;
d2=1/u2;
miu1=irate-((sigma1^2)/2);
miu2=irate-((sigma2^2)/2);
p1=(1/4)*((1/lamda^2)+(sqrt(deltaT)/lamda)*((miu1/sigma1)+(miu2/sigma2))+(rho/lamda^2));
p2=(1/4)*((1/lamda^2)+(sqrt(deltaT)/lamda)*((miu1/sigma1)+(miu2/sigma2))-(rho/lamda^2));
p3=(1/4)*((1/lamda^2)+(sqrt(deltaT)/lamda)*((-miu1/sigma1)+(-miu2/sigma2))+(rho/lamda^2));
p4=(1/4)*((1/lamda^2)+(sqrt(deltaT)/lamda)*((-miu1/sigma1)+(miu2/sigma2))+(rho/lamda^2));
p5=1-(1/lamda^2);
S1Vals=zeros(3*N+4,1); % the values of stock1
S2Vals=zeros(3*N+4,1); % the values of stock2
S1Vals(1)=S01*exp(-N*u1);
S2Vals(1)=S02*exp(-N*u2);
for i=2:3*N+4
S1Vals(i)=exp(u1)*S1Vals(i-1);
S2Vals(i)=exp(u2)*S2Vals(i-1);
end
CVals=zeros(3*N+4,3*N+4); % the value of option
for i=1:2:3*N+4
    for j=1:2:3*N+4
        CVals(i,j)=max(max(S1Vals(i),S2Vals(i))-strike);
    end
end
for tau=0:N
    for i=(tau+1):2:(3*N+4-tau)
        for j=(tau+1):2:(3*N+4-tau)
            CVals(i,j)=exp(-irate*deltaT)*(p1*CVals(i+1,j+1)+p2*CVals(i+1,j-1)+p3*CVals(i-1,j+1)+p4*CVals(i-1,j-i)+p5*CVals(i,j));
        end
    end
end
price=CVals(N+1,N+1);

Hi everyone. I'm trying to build a code for pricing options with trinomial model, in the maximum of two assets, in our case it's about 2 stocks.

The 2 stocks can go: up-up with probability p1, up-down with probability p2, down-up with probability p3, down-down with probability p4 and stay at the same price with probability p5. Also i have to say that the price of the stock in each node is given as: S01*exp((i-N)*u1 and S02*exp((i-N)*u2.

Then if i try to run: TwoStatesAmericanCallTrinKamradRitchken(35,40,40,0.05,7/12,0.2,0.3,0.5,1.4,10) the price must be approximately 9.420

The problem might be with how i define the matrixes and the dimension.

Any help and advice is acceptable :)

Answer 1

[Raunak Gupta]

Hi,

From the code I can see that two max are not required in

CVals(i,j)=max(max(S1Vals(i),S2Vals(i))-strike); 

as S1Vals and S2Vals are only vector and not matrices.

Also, in

CVals(i,j)=exp(-irate*deltaT)*(p1*CVals(i+1,j+1)+p2*CVals(i+1,j-1)+p3*CVals(i-1,j+1)+p4*CVals(i-1,j-i)+p5*CVals(i,j));  

the looping variables can create a problem as (i-1,j-i) will try to access 0 index in CVals array whenever i = j. Try changing the looping variables range for code to run at-least. So, I suggest going through the algorithm again for Trinomial option Pricing for two stocks that you may have referenced while writing above code.

[Violeta Oikonomou]

Thanks Raunak for your comment. I 'll try to fix the the looping variables firstly!!