Refine
Year of publication
- 2009 (2) (remove)
Language
- English (2)
Project
- E9 (2) (remove)
Application Area
- E (2) (remove)
Good-deal bounds have been introduced as a way to obtain valuation bounds
for derivative assets which are tighter than the arbitrage bounds. This is achieved by ruling out not only those prices that violate no-arbitrage restrictions but also
trading opportunities that are `too good'.
We study dynamic good-deal valuation bounds that are derived from bounds on optimal
expected growth rates. This leads naturally to restrictions on the set of pricing measure which are local in time, thereby inducing good dynamic properties for the good-deal valuation bounds.
We study good-deal bounds by duality arguments in a general semimartingale setting.
In a Wiener space setting where asset prices evolve as It\^o-processes,
good-deal bounds are then conveniently described by backward SDEs.
We show how the good-deal bounds arise as the value function for an
optimal control problem, where a dynamic coherent a priori risk measure is minimized by the choice of a suitable hedging strategy.
This demonstrates how the theory of no-good-deal valuations can be associated to an established concept of dynamic hedging in continuous time.
We develop a generic method for constructing a weak static minimum
variance hedge for a wide range of derivatives that may involve optimal exercise features or contingent cash flow streams, to provide a hedge along a
sequence of future hedging dates. The optimal hedge is constructed using
a portfolio of preselected hedge instruments which could be derivatives
with different maturities. The hedge portfolio is weakly static in that
it is initiated at time zero, does not involve intermediate re-balancing,
but hedges may be gradually unwound over time. We study the static
hedging of a convertible bond to demonstrate the method by an example
that involves equity and credit risk. We investigate the robustness of the
hedge performance with respect to parameter and model risk by numerical
experiments.