Abstract. Multivariate analogues of the put-call symmetry can be expressed as certain symmetry properties of basket options and options on the maximum of several assets with respect to some (or all) permutations of the weights and the strike. The so-called self-dual distributions satisfying these symmetry conditions are completely characterized and their properties explored. It is also shown how to relate some multivariate asymmetric distributions to symmetric ones by a power transformation that is useful to adjust for carrying costs. Particular attention is devoted to the case of asset prices driven by Lévy processes. Based on this, semistatic hedging techniques for multiasset barrier options are suggested.Key words. barrier option, dual market, Lévy process, multiasset option, put-call symmetry, self-dual distribution, semistatic hedging AMS subject classifications. 60E05, 60G51, 91B28, 91B70DOI. 10.1137/0907541941. Introduction. Consider European options on S T = S 0 e rT η being the price of a (say nondividend paying) asset at the maturity time T , where S 0 is the spot price and e rT η is the factor by which the price changes, r is the (constant) risk-free interest rate, and η is an almost surely positive random variable. In arbitrage-free and complete markets, the option price equals the discounted expected payoff, where the expectation can be taken with respect to the unique equivalent martingale measure. In this case Eη = 1 and the discounted price process (S t e −rt ) t∈ [0,T ] becomes a martingale. Unless indicated by a different subscript, all expectations in this paper are understood with respect to the probability measure Q, which is not necessarily a martingale measure. In this paper we do not address the choice of a martingale measure in incomplete markets.One of the most basic relationships between options in arbitrage-free markets is the European call-put parity. This parity can be expressed by
Abstract. The fate of anthropogenic emissions of mercury (Hg) to the atmosphere is influenced by the exchange of elemental Hg with the earth surface. This exchange holds the key to a better understanding of Hg cycling from local to global scales, which has been difficult to quantify. To advance research about land–atmosphere Hg interactions, we developed a dual-inlet, single detector relaxed eddy accumulation (REA) system. REA is an established technique for measuring turbulent fluxes of trace gases and aerosol particles in the atmospheric surface layer. Accurate determination of gaseous elemental mercury (GEM) fluxes has proven difficult due to technical challenges presented by extremely small concentration differences (typically < 0.5 ng m−3) between updrafts and downdrafts. We present an advanced REA design that uses two inlets and two pairs of gold cartridges for continuous monitoring of GEM fluxes. This setup reduces the major uncertainty created by the sequential sampling in many previous designs. Additionally, the instrument is equipped with a GEM reference gas generator that monitors drift and recovery rates. These innovations facilitate continuous, autonomous measurement of GEM flux. To demonstrate the system performance, we present results from field campaigns in two contrasting environments: an urban setting with a heterogeneous fetch and a boreal peatland during snowmelt. The observed average emission rates were 15 and 3 ng m−2 h−1, respectively. We believe that this dual-inlet, single detector approach is a significant improvement of the REA system for ultra-trace gases and can help to advance our understanding of long-term land–atmosphere GEM exchange.
Two integrable random vectors ξ and ξ * in R d are said to be zonoid equivalent if, for each u ∈ R d , the scalar products ξ, u and ξ * , u have the same first absolute moments. The paper analyses stochastic processes whose finite-dimensional distributions are zonoid equivalent with respect to time shift (zonoid stationarity) and permutation of its components (swap invariance). While the first concept is weaker than the stationarity, the second one is a weakening of the exchangeability property. It is shown that nonetheless the ergodic theorem holds for swap-invariant sequences and the limits are characterised.
Eddy covariance (EC) measurements of carbon dioxide (CO2) in urban environments are carried out widely since the late nineties. However, long‐term time series are still rare and little is known about long‐term tendencies, even though cities are major sources of CO2 globally. Here a full decade of EC measurements from Basel, Switzerland, is presented. An approach for the calculation of horizontal averages is presented. It improves the significance and comparability of measured fluxes from heterogeneous environments and emphasizes the need of adequate weighting by horizontal averaging in such heterogeneous urban environments, especially for the derivation of cumulative quantities like the annual net ecosystem exchange. The urban CO2 mole fraction (ρC) is compared with regional background measurements, and good agreement in terms of long‐term trend and seasonal variability is found. Over the last decade an increase of 2 ppm y−1 is observed, both locally and globally. CO2 flux (FC) data are analyzed for diurnal and seasonal cycles as well as interannual variabilities. FC shows a large interannual variability in times of high source activity (e.g., during the day and in winter). In contrast, a relatively constant background flux of 5 µmol m−2 s−1 is found during periods of low source activity. The long‐term trend of FC is mostly superimposed by the large temporal variability and is found to be −5% over the last 10 years.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.