MATH4090/7049: Computation in financial mathematics Practical 2

Notation: “Lx.y”refers to [Lecture x, Slide y]

1. Recall Algorithm 1 for European options in L1.

(a) Modify this algorithm to price a continuously monitored up-and-out barrier put option with the barrier H > S(0).

(b) Modify this algorithm to price an American put option.

2. In this question, you are asked to modify the code you developed in Practical 1 (for European options) to price a continuously monitored up-and-out barrier options with the barrier H > S(0).

You can choose either tree slow .m or tree fast .m from Practical 1, then save the file under the name barrier tree .m.

Download the file test barrier tree .m from Blackboard into the same directory.

Then modify the code in barrier tree .m to enforce the barrier constraint at each tn , n  =  1, . . . ,N (note continuous monitoring), which will be called by the code in test barrier tree .m, such that test barrier tree .m runs properly and outputs“barrier tree.m passed”.

In modifying barrier tree .m, use the following steps

(a) Modify barrier tree .m to accept the barrier H as the last input argument.            (b) Identify in the code where you need to enforce the barrier constraints (only two places).

(c) Modify and insert the following piece of code into these places:

%compute  the  option  prices  at  time  t_n;

%loop  over  all  possible  S  levels

%at  time  t_n

%instruction:  replace  xxx  with  the  correct  number for  j=0:xxx

%instruction:  compute  the  level- j

%  stock  value  at  time  t_n

S  =  ;

%instruction:  complete  the  barrier  constraint  and

%  the  expectation  formula

if(S  >=  )

W(j)  =  ;

else

W(j)  =  ;

end

end