Seminar series
Date
Fri, 10 May 2013
Time
16:00 -
17:00
Location
DH 1st floor SR
Speaker
David Hobson
Organisation
Warwick
Suppose we are given a double continuum (in time and strike) of discounted
option prices, or equivalently a set of measures which is increasing in
convex order. Given sufficient regularity, Dupire showed how to construct
a time-inhomogeneous martingale diffusion which is consistent with those
prices. But are there other martingales with the same 1-marginals? (In the
case of Gaussian marginals this is the fake Brownian motion problem.)
In this talk we show that the answer to the question above is yes.
Amongst the class of martingales with a given set of marginals we
construct the process with smallest possible expected total variation.