Université Paris 1

In this talk, I consider the problem of pricing and (statically)
hedging short-term contingent claims written on illiquid or
non-tradable assets.
In a first part, I show how to find the best European payoff written
on a given set of underlying assets for hedging (under several
metrics) a given European payoff written on another set of underlying
assets -- some of them being illiquid or non-tradable. In particular,
I present new results in the case of the Expected Shortfall risk
measure. I also address the associated pricing problem by using
indifference pricing and its link with entropy.
In a second part, I consider the more classic case of hedging with a
finite set of simple payoffs/instruments and I address the associated
pricing problem. In particular, I show how entropic methods (Davis
pricing and indifference pricing à la Rouge-El Karoui) can be used in
conjunction with recent results of extreme value theory (in dimension
higher than 1) for pricing and hedging short-term out-of-the-money
options such as those involved in the definition of Daily Cliquet
Crash Puts.