Talk on "Financial Alchemy" by Thorsten Rheinländer, to be held in room 251 at 1 p.m. on Wednesday 13-Feb
The following is the title and abstract of the talk to be given by Thorsten Rheinländer:
Title: Financial Alchemy
Abstract: While the holy grail of medieval alchemists was to transmute common metals into more precious ones, modern dual market theory attempts to turn rather complicated derivatives into simpler ones by a change of numeraire technique where the underlying price process (given it is a martingale) acts as price deflator.
We first review the classical put-call parities as well as symmetries and provide a link due to Molchanov and Schmutz via random convex sets. One of the most spectacular applications of dual markets techniques is related to the pricing of the Russian option which in its most basic form is a perpetual lookback option. According to Peskir and Shiryaev, a dual market transform allows one to evaluate the pricing expectation via a univariate rather than a bivariate distribution in the original market.
However, as in the medieval counterpart, to achieve these transformations there is some magic involved, namely in the form of rather stringent assumptions on the dynamics of the price process which need not always be satisfied in practice. We will discuss these in detail, and provide a general duality result which allows to achieve more general transmutations involving additional volatility linked hedging instruments.
The original parts of this presentation are jointly with Elisa Alos; Zhanyu Chen; Michael Schmutz; and Jenny Sexton.