Time and Space Bounds for Reversible Simulation

We prove a general upper bound on the tradeoff between time and space that suffices for the reversible simulation of irreversible computation. Previously, only simulations using exponential time or quadratic space were known. The tradeoff shows for the first time that we can simultaneously achieve subexponential time and subquadratic space. The boundary values are the exponential time with hardly any extra space required by the Lange-McKenzie-Tapp method and the ($\log 3$)th power time with square space required by the Bennett method. We also give the first general lower bound on the extra storage space required by general reversible simulation. This lower bound is optimal in that it is achieved by some reversible simulations.Comment: 11 pages LaTeX, Proc ICALP 2001, Lecture Notes in Computer Science, Vol xxx Springer-Verlag, Berlin, 200

Competition among Alternative Option Market Structures: Evidence from Eurex vs. Euwax

We study option market design by providing a theoretical motivation and comprehensive empirical analysis of two fundamentally different option market structures, the Eurex derivatives exchange and Euwax, the world’s largest market for bank-issued options. These markets exist side-by- side, offering many options with identical or similar characteristics. We motivate the two market structures based on option investor clienteles which differ with respect to the probability of selling the option back to the dealer/issuer before maturity, which in turn affects the investors expected transaction costs. As suggested by the clientele argument, the most important empirical finding is that Euwax ask prices and bid prices are consistently higher than comparable Eurex ask prices and bid prices. The difference of the bid prices is larger, resulting in smaller Euwax bid-ask spreads, which makes Euwax preferable for investors with a high probability of early liquidation. We find that competition from one market reduces bid-ask spreads in the other market.Options, Market Design, Microstructure, Bid-Ask Spreads

Quantum state discrimination bounds for finite sample size

In the problem of quantum state discrimination, one has to determine by measurements the state of a quantum system, based on the a priori side information that the true state is one of two given and completely known states, rho or sigma. In general, it is not possible to decide the identity of the true state with certainty, and the optimal measurement strategy depends on whether the two possible errors (mistaking rho for sigma, or the other way around) are treated as of equal importance or not. Results on the quantum Chernoff and Hoeffding bounds and the quantum Stein's lemma show that, if several copies of the system are available then the optimal error probabilities decay exponentially in the number of copies, and the decay rate is given by a certain statistical distance between rho and sigma (the Chernoff distance, the Hoeffding distances, and the relative entropy, respectively). While these results provide a complete solution to the asymptotic problem, they are not completely satisfying from a practical point of view. Indeed, in realistic scenarios one has access only to finitely many copies of a system, and therefore it is desirable to have bounds on the error probabilities for finite sample size. In this paper we provide finite-size bounds on the so-called Stein errors, the Chernoff errors, the Hoeffding errors and the mixed error probabilities related to the Chernoff and the Hoeffding errors.Comment: 31 pages. v4: A few typos corrected. To appear in J.Math.Phy

CP Violating Asymmetry in Stop Decay into Bottom and Chargino

In the MSSM with complex parameters, loop corrections to the decay of a stop into a bottom quark and a chargino can lead to a CP violating decay rate asymmetry. We calculate this asymmetry at full one-loop level and perform a detailed numerical study, analyzing the dependence on the parameters and complex phases involved. In addition, we take the Yukawa couplings of the top and bottom quark running. We account for the constraints on the parameters coming from several experimental limits. Asymmetries of several percent are obtained. We also comment on the feasibility of measuring this asymmetry at the LHC.Comment: Contributed talk given by Sebastian Frank in June 2009 at SUSY09 - 17th International Conference on Supersymmetry and the Unification of Fundamental Interactions, Northeastern University, Boston, USA. To appear in the AIP conference proceedings, 4 pages, 7 figures (fixed links in references

Alternative Market Structures for Derivatives

In this paper, we compare option contracts from a traditional derivatives exchange to bank-issued options, also referred to as covered warrants, whose markets have grown rapidly around the world in recent years. While bank-issued option markets and traditional derivatives exchanges exhibit significant structural differences such as the absence of a central counterparty for bank-issued options, they frequently exist side-by-side, and the empirical evidence shows that there is significant overlap in their product offerings. We examine trading costs and liquidity in both markets and find that bank-issued options have smaller quoted percentage bid-ask spreads than traditional option contracts by an average of 4.3%. The bid-ask spread difference manifests itself in a highly regular fashion in that ask (bid) prices for bank-issued options are consistently higher than comparable ask (bid) prices for traditional option contracts. The difference of the bid prices is larger than the difference of the ask prices resulting in smaller bid-ask spreads for bank-issued options. The empirical analysis also indicates that bid-ask spreads in either market are lowered by competition from the other market. We present a potential explanation for the co-existence of the two market structures which suggests that the bank-issued option market caters more towards retail investors with predominantly speculative motives while traditional derivatives exchanges may cater more towards institutional investors with predominantly hedging motives.Options, Market Design, Microstructure, Bid-Ask Spreads