Past exam of the mathematics course of the University of Cambridge / 2005 / ii / Paper 4 / 28J / b

Table of contents
- Solution b

Solution

At zero interest, interchanging spot and strike gives

d_{1} (K, S_{0}) = - d_{2} (S_{0}, K)

and

d_{2} (K, S_{0}) = - d_{1} (S_{0}, K)

. Substitution into the put formula therefore gives

C (S_{0}, K) = P (K, S_{0}) .

Scaling both positive arguments by

α

lo g (S_{0} / K)

and both

d

values unchanged, while multiplying every price prefactor by

α

. Thus

C (α S_{0}, α K) = α C (S_{0}, K) .

These are Put-call symmetry in the Black-Scholes model and degree-one homogeneity.

 Ancestors (10)

 View article source

 Discussion (0) New discussion

There are no discussions about this article yet.

 Articles by others on the same topic (0)

There are currently no matching articles.

  See all articles in the same topic Create my own version