Prices of tradables can only be expressed relative to one another at any instant of time. This fundamental fact should therefore also hold for contingent claims, i.e. tradable instruments, whose prices depend on the prices of other tradables. We show that this property induces a local scale invariance in the problem of pricing contingent claims.Due to this symmetry we do not require any martingale techniques to arrive at the price of a claim. If the tradables are driven by Brownian motion, we find, in a natural way, that this price satisfies a PDE. Both possess a manifest gauge invariance. A unique solution can only be given when we impose restrictions on the drifts and volatilities of the tradables, i.e. the underlying market structure. We give some examples of the application of this PDE to the pricing of claims. In the Black-Scholes world we show the equivalence of our formulation with the standard approach. It is stressed that the formulation in terms of tradables leads to a significant conceptual simplification of the pricing-problem.
This article is the second one in a series on the use of local scale invariance in finance. In the first [6], we introduced a new formalism for the pricing of derivative securities, which focuses on tradable objects only, and which completely avoids the use of martingale techniques. In this article we show the use of the formalism in the context of path-dependent options. We derive compact and intuitive formulae for the prices of a whole range of well-known options such as arithmetic and geometric average options, barriers, rebates and lookback options. Some of these have not appeared in the literature before. For example, we find rather elegant formulae for double barrier options with exponentially moving barriers, continuous dividends and all possible configurations of the barriers. The strength of the formalism reveals itself in the ease with which these prices can be derived. This allowed us to pinpoint some mistakes regarding geometric mean options, which frequently appear in the literature. Furthermore, symmetries such as put-call transformations appear in a natural way within the framework.
Electricity market design varies across countries throughout Europe. Thereby the provision and remuneration of flexibility always takes place in short-term market segments. Taking into consideration the fundamental changes of the power system, this paper discusses options for the future short-term market design. We develop a conceptual basis for a possible integration of currently separated short-term market segments. Market segment integration (MSI) is defined as the interaction between and possible combination of market segments, i.e. intraday market (ID), congestion management (CM) and balancing market (BA). The paper especially focusses on two options, namely an integrated BA and CM market and an integrated ID and CM market. For these options we determine the basic design features. We propose a criteria catalogue which allows the evaluation of the market design options. Based on several criteria we discuss possible positive and negative consequences as well as potential solutions
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