16 research outputs found
Sticky processes, local and true martingales
We prove that for a so-called sticky process there exists an equivalent
probability and a -martingale that is arbitrarily close to
in norm. For continuous , can be chosen arbitrarily
close to in supremum norm. In the case where is a local martingale we
may choose arbitrarily close to the original probability in the total
variation norm. We provide examples to illustrate the power of our results and
present applications in mathematical finance
Sticky continuous processes have consistent price systems
Under proportional transaction costs, a price process is said to have a
consistent price system, if there is a semimartingale with an equivalent
martingale measure that evolves within the bid-ask spread. We show that a
continuous, multi-asset price process has a consistent price system, under
arbitrarily small proportional transaction costs, if it satisfies a natural
multi-dimensional generalization of the stickiness condition introduced by
Guasoni [Math. Finance 16(3), 569-582 (2006)].Comment: 10 pages, v3: incorporates minor corrections and the proof of the
main result has been clarified, to appear in Journal of Applied Probabilit
On the Existence of Consistent Price Systems
We formulate a sufficient condition for the existence of a consistent price
system (CPS), which is weaker than the conditional full support condition (CFS)
introduced by Guasoni, Rasonyi, and Schachermayer [Ann. Appl. Probab.,
18(2008), pp. 491-520] . We use the new condition to show the existence of CPSs
for certain processes that fail to have the CFS property. In particular this
condition gives sufficient conditions, under which a continuous function of a
process with CFS admits a CPS, while the CFS property might be lost.Comment: To appear in "Stochastic Analysis and Applications". Keywords:
Consistent pricing systems, No-arbitrage, Transaction costs, Full support,
Conditional Full Support, Stability under Composition with Continuous
Function
No arbitrage without semimartingales
We show that with suitable restrictions on allowable trading strategies, one
has no arbitrage in settings where the traditional theory would admit arbitrage
possibilities. In particular, price processes that are not semimartingales are
possible in our setting, for example, fractional Brownian motion.Comment: Published in at http://dx.doi.org/10.1214/08-AAP554 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
A note on closed-form spread option valuation under log-normal models
In the papers Carmona and Durrleman [7] and Bjerksund and Stensland [1],
closed form approximations for spread call option prices were studied under the
log normal models. In this paper, we give an alternative closed form formula
for the price of spread call options under the log-normal models also. Our
formula can be seen as a generalization of the closed-form formula presented in
Bjerksund and Stensland [1] as their formula can be obtained by selecting
special parameter values to our formula. Numerical tests show that our formula
performs better for certain range of model parameters than the closed-form
formula presented in Bjerksund and Stensland [1].Comment: 37 Pages, 3 table
A discussion of stochastic dominance and mean-CVaR optimal portfolio problems based on mean-variance-mixture models
The classical Markowitz mean-variance model uses variance as a risk measure
and calculates frontier portfolios in closed form by using standard
optimization techniques. For general mean-risk models such closed form optimal
portfolios are difficult to obtain. In this note, we obtain closed form
expressions for frontier portfolios under mean-CVaR criteria when return
vectors have normal mean-variance mixture (NMVM) distributions. To achieve this
goal, we first present necessary conditions for stochastic dominance within the
class of one dimensional NMVM models and then we apply them to portfolio
optimization problems. Our main result in this paper states that when return
vectors follow NMVM distributions the associated mean- CVaR frontier portfolios
can be obtained by optimizing a Markowitz mean-variance model with an
appropriately adjusted return vectorComment: 19page
On the Stickiness Property
In [2] the notion of stickiness for stochastic processes was introduced. It was also shown that stickiness implies absense of arbitrage in a market with proportional transaction costs. In this paper, we investigate the notion of stickiness further. In particular, we give examples of processes that are not semimartingales but are sticky.
No Arbitrage Conditions For Simple Trading Strategies
Strict local martingales may admit arbitrage opportunities with respect to the class of simple trading strategies. (Since there is no possibility of using doubling strategies in this framework, the losses are not assumed to be bounded from below.) We show that for a class of non-negative strict local martingales, the strong Markov property implies the no arbitrage property with respect to the class of simple trading strategies. This result can be seen as a generalization of a similar result on three dimensional Bessel process in [3]. We also pro- vide no arbitrage conditions for stochastic processes within the class of simple trading strategies with shortsale restriction.