What changes should I apply to this code?

Let S(t) be the price of one share of a particular company at time t. The price S(t+1) at time t+1 can either take the value of uS(t) with probability p1 (where u>1), remain the same with probability p2 or go down to dS(t) with probability 1-p1-p2 (where 0<d<1). I have to create a function which stimulates S(t) for t from 0 up to 20.

The following is the code I have written, but in this code each S(t) depends on the Value S0 which I input at the beginning. How can I change this in such a way that the value S(t+1) depends on the value S(t)? i.e for example S(5) depending on S(4)

function S=question5(u,d,p1,p2)
S0=input('Enter price of share: ') % price of share at time 0
u=input('Enter a number greater than 1: ')
d=input('Enter a number between 0 and 1: ' )
p1=input('Enter probability p1: ') % p1 is the probability of price of share increasing
p2=input('Enter probability p2: ')% p2 is the probability of price of share decreasing
for t=0:1:20
g=rand(1) % random number whose exact value is not important
 if g>0 && g<p1
 S=u*S0
 elseif g>p1 && g<p1+p2
 S=S0
 elseif g>p1+p2
 S=d*S0
 end
end

Thanks in advance.

Answer 1

[Stephan M. H.]

Hi,

if I got it right, the introduction of a auxiliary variable should be all you need:

s_t = S0

for ...

    if ...
      S = u*s_t
    elseif ...
      S = s_t
    elseif ...
      S = d*s_t
    end

    s_t = S 

end

best, Stephan

[veru]

Thank you! :)