291 research outputs found
Improved Frechet bounds and model-free pricing of multi-asset options
Improved bounds on the copula of a bivariate random vector are computed when
partial information is available, such as the values of the copula on a given
subset of , or the value of a functional of the copula, monotone with
respect to the concordance order. These results are then used to compute
model-free bounds on the prices of two-asset options which make use of extra
information about the dependence structure, such as the price of another
two-asset option.Comment: Replaced with revised versio
Asymptotically optimal discretization of hedging strategies with jumps
In this work, we consider the hedging error due to discrete trading in models
with jumps. Extending an approach developed by Fukasawa [In Stochastic Analysis
with Financial Applications (2011) 331-346 Birkh\"{a}user/Springer Basel AG]
for continuous processes, we propose a framework enabling us to
(asymptotically) optimize the discretization times. More precisely, a
discretization rule is said to be optimal if for a given cost function, no
strategy has (asymptotically, for large cost) a lower mean square
discretization error for a smaller cost. We focus on discretization rules based
on hitting times and give explicit expressions for the optimal rules within
this class.Comment: Published in at http://dx.doi.org/10.1214/13-AAP940 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Market models with optimal arbitrage
We construct and study market models admitting optimal arbitrage. We say that
a model admits optimal arbitrage if it is possible, in a zero-interest rate
setting, starting with an initial wealth of 1 and using only positive
portfolios, to superreplicate a constant c>1. The optimal arbitrage strategy is
the strategy for which this constant has the highest possible value. Our
definition of optimal arbitrage is similar to the one in Fernholz and Karatzas
(2010), where optimal relative arbitrage with respect to the market portfolio
is studied. In this work we present a systematic method to construct market
models where the optimal arbitrage strategy exists and is known explicitly. We
then develop several new examples of market models with arbitrage, which are
based on economic agents' views concerning the impossibility of certain events
rather than ad hoc constructions. We also explore the concept of fragility of
arbitrage introduced in Guasoni and Rasonyi (2012), and provide new examples of
arbitrage models which are not fragile in this sense
Constant Proportion Portfolio Insurance in presence of Jumps in Asset Prices
Constant proportion portfolio insurance (CPPI) allows an investor to limit downside risk while retaining some upside potential by maintaining an exposure to risky assets equal to a constant multiple m>1 of the 'cushion', the difference between the current portfolio value and the guaranteed amount. In diffusion models with continuous trading, this strategy has no downside risk, whereas in real markets this risk is non-negligible and grows with the multiplier value. We study the behavior of CPPI strategies in models where the price of the underlying portfolio may experience downward jumps. This allows to quantify the 'gap risk' of the portfolio while maintaining the analytical tractability of the continuous--time framework. We establish a direct relation between the value of the multiplier m and the risk of the insured portfolio, which allows to choose the multiplier based on the risk tolerance of the investor, and provide a Fourier transform method for computing the distribution of losses and various risk measures (VaR, expected loss, probability of loss) over a given time horizon. The results are applied to a jump-diffusion model with parameters estimated from market data.Portfolio insurance; CPPI; Lévy process; Value at Risk; expected loss
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