We consider in this article the arbitrage free pricing of double knock-out barrier options with payoffs that are arbitrary functions of the underlying asset, where we allow exponentially time-varying barrier levels in an otherwise standard Black-Scholes model. Our approach, reminiscent of the method of images of electromagnetics, considerably simplifies the derivation of analytical formulae for this class of exotics by reducing the pricing of any double-barrier problem to that of pricing a related European option. We illustrate the method by reproducing the well-known formulae of Kunitomo and Ikeda (1992) for the standard knock-out double-barrier call and put options. We give an explanation for the rapid rate of convergence of the doubly infinite sums for affine payoffs in the stock price, as encountered in the pricing of double-barrier call and put options first observed by Kunitomo and Ikeda (1992).Exotic options, double-barrier options, method of images, parity relations of double-barrier options,

The local-global map hypothesis states that locally organized response properties--such as orientation preference--result from visuotopically organized local maps of non-retinotopic response properties. In the tree shrew, the lateral extent of horizontal patchy connections is as much as 80-100% of V1 and is consistent with the length summation property. We argue that neural signals can be transmitted across the entire extent of V1 and this allows the formation of maps at the local scale that are visuotopically organized. We describe mechanisms relevant to the formation of local maps and report modeling results showing the same patterns of horizontal connectivity, and relationships to orientation preference, seen in vivo. The structure of the connectivity that emerges in the simulations reveals a 'hub and spoke' organization. Singularities form the centers of local maps, and linear zones and saddle-points arise as smooth border transitions between maps. These findings are used to present the case for the local-global map hypothesis for tree shrew V1.

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Australia's National Electricity Market (NEM) is experiencing one of the world's fastest and marked transitions toward variable renewable energy generation. This transformation poses challenges to system security and reliability and has triggered increased variability and uncertainty in electricity prices. By employing an exponential generalized autoregressive conditional heteroskedasticity (eGARCH) model, we gauge the effects of wind power generation on the dynamics of electricity prices in the NEM. We find that a 1 GWh increase in wind generation decreases daily prices up to 1.3 AUD/MWh and typically increases price volatility up to 2%. Beyond consumption and gas prices, hydro generation also contributes to an increase in electricity prices and their volatility. The cross-border interconnectors play a significant role in determining price levels and volatility dynamics. This underscores the important role of strategic provisions and investment in the connectivity within the NEM to ensure the reliable and effective delivery of renewable energy generation. Regulatory interventions, such as the carbon pricing mechanism and nationwide lockdown restrictions due to COVID-19 pandemic, also had a measurable impact on electricity price dynamics.