2
$\begingroup$

I am a newbie. Please help me understand how to resolve the exercise 2.2 from the book "The concept and practice of Mathematical Finance". The solution from the book says that our super-replicating portfolio will be $\alpha$ shares and $\beta$ bonds. It must dominate at zero. This implies that $\beta$ >= 0. First of all, what does it mean "it must dominate at zero". Secondly, why if it dominates at zero, then $\beta$ >= 0? Thanks so much for your help!

Problem

enter image description here

Solution

enter image description here enter image description here

$\endgroup$
2
  • $\begingroup$ Hi Jack, could you please post the question as well? Not every user has easy access to the book. $\endgroup$
    – jaamor
    Commented Feb 28, 2015 at 18:12
  • $\begingroup$ Here is the question, Each of the following products pays a function of spot price, S, of a non-dividen-paying stock one year from now. If there is no interest rates and spot is 100, give the optimal upper and lower bounds on their prices today. (i) The pay-off is 1 between 110 and 130 and zero otherwise. $\endgroup$
    – dullboy
    Commented Feb 28, 2015 at 21:25

2 Answers 2

1
$\begingroup$

"It must dominate at zero" means that when the final spot level is zero, the value of the super-replicating portfolio must be greater than or equal to the value of the payoff, which is zero. Since the super-replicating portfolio consists of some stock (which has zero value when the spot price is zero) and some bonds (which have value one), there must be a non-negative number of bonds.

$\endgroup$
1
$\begingroup$

"Dominating at zero" is what it sounds like: It means that the value of the portfolio has a >0 value when the spot price (and α) is at 0.

So if α = 0 then β must be a positive (non zero) value in order to "dominate" or be >= 0.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.