Completion of an incomplete market by quadratic variation assets.
Loading...
Date
2011
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
It is well known that the general geometric L´evy market models are
incomplete, except for the geometric Brownian and the geometric Poissonian,
but such a market can be completed by enlarging it with power-jump
assets as Corcuera and Nualart [12] did on their paper. With the knowledge
that an incomplete market due to jumps can be completed, we look
at other cases of incompleteness. We will consider incompleteness due to
more sources of randomness than tradable assets, transactions costs and
stochastic volatility. We will show that such markets are incomplete and
propose a way to complete them. By doing this we show that such markets
can be completed.
In the case of incompleteness due to more randomness than tradable assets,
we will enlarge the market using the market’s underlying quadratic
variation assets. By doing this we show that the market can be completed.
Looking at a market paying transactional costs, which is also an incomplete
market model due to indifference between the buyers and sellers price, we
will show that a market paying transactional costs as the one given by, Cvitanic
and Karatzas [13] can be completed.
Empirical findings have shown that the Black and Scholes assumption of
constant volatility is inaccurate (see Tompkins [40] for empirical evidence).
Volatility is in some sense stochastic, and is divided into two broad classes.
The first class being single-factor models, which have only one source of
randomness, and are complete markets models. The other class being the
multi-factor models in which other random elements are introduced, hence
are an incomplete markets models. In this project we look at some commonly
used multi-factor models and attempt to complete one of them.
Description
Thesis (M.Sc.)-University of KwaZulu-Natal, Durban, 2011.
Keywords
Financial risk management., Stochastic analysis., Stochastic processes., Theses--Statistics and actuarial science.