4,170 research outputs found
Robust pricing and hedging under trading restrictions and the emergence of local martingale models
We consider the pricing of derivatives in a setting with trading
restrictions, but without any probabilistic assumptions on the underlying
model, in discrete and continuous time. In particular, we assume that European
put or call options are traded at certain maturities, and the forward price
implied by these option prices may be strictly decreasing in time. In discrete
time, when call options are traded, the short-selling restrictions ensure no
arbitrage, and we show that classical duality holds between the smallest
super-replication price and the supremum over expectations of the payoff over
all supermartingale measures. More surprisingly in the case where the only
vanilla options are put options, we show that there is a duality gap. Embedding
the discrete time model into a continuous time setup, we make a connection with
(strict) local-martingale models, and derive framework and results often seen
in the literature on financial bubbles. This connection suggests a certain
natural interpretation of many existing results in the literature on financial
bubbles
Growth Optimal Investment and Pricing of Derivatives
We introduce a criterion how to price derivatives in incomplete markets,
based on the theory of growth optimal strategy in repeated multiplicative
games. We present reasons why these growth-optimal strategies should be
particularly relevant to the problem of pricing derivatives. We compare our
result with other alternative pricing procedures in the literature, and discuss
the limits of validity of the lognormal approximation. We also generalize the
pricing method to a market with correlated stocks. The expected estimation
error of the optimal investment fraction is derived in a closed form, and its
validity is checked with a small-scale empirical test.Comment: 21 pages, 5 figure
A fundamental theorem of asset pricing for continuous time large financial markets in a two filtration setting
We present a version of the fundamental theorem of asset pricing (FTAP) for
continuous time large financial markets with two filtrations in an
-setting for . This extends the results of Yuri
Kabanov and Christophe Stricker \cite{KS:06} to continuous time and to a large
financial market setting, however, still preserving the simplicity of the
discrete time setting. On the other hand it generalizes Stricker's
-version of FTAP \cite{S:90} towards a setting with two filtrations. We do
neither assume that price processes are semi-martigales, (and it does not
follow due to trading with respect to the \emph{smaller} filtration) nor that
price processes have any path properties, neither any other particular property
of the two filtrations in question, nor admissibility of portfolio wealth
processes, but we rather go for a completely general (and realistic) result,
where trading strategies are just predictable with respect to a smaller
filtration than the one generated by the price processes. Applications range
from modeling trading with delayed information, trading on different time
grids, dealing with inaccurate price information, and randomization approaches
to uncertainty
Infinitely many securities and the fundamental theorem of asset pricing
Several authors have pointed out the possible absence of martingale measures for static arbitrage-free markets with an infinite number of available securities. This paper addresses this caveat by drawing on projective systems of probability measures. Firstly, it is shown that there are two distinct sorts of models whose treatment is necessarily different. Secondly, and more important, we analyze those situations for which one can provide a projective system of ó .additive measures whose projective limit may be interpreted as a risk-neutral probability. Hence, the Fundamental Theorem of Asset Pricing is extended so that it can apply for models with infinitely many assets
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