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April 2018 CT8 Q6

R

rlsrachaellouisesmith

Ton up Member
Hi,

In (ii) of the question we are asked to prove put call parity using a self financing replication portfolio.
We have also got a proof in Chapter 12 where we say:
assuming no arbitrage, and by the law of one price
whereas for this proof the one from chapter 16/17 we say:
given the portfolios are self financing and arbitrage is not allowed

Are there any further difference between the 2 proofs other than this? If so, I have missed the detail.
What is the difference between these two statements?

Thank you,
Rachael
 
There is no difference. The self-financing condition means that nothing is added externally to the portfolio and nothing is removed from it. This is implied in the argument of Chapter 12 when the values of the portfolios at time T are calculated. It's implied because the notion of self-financing hasn't been introduced by that point. In the exam question it's explicitly stated.
 
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