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This paper introduces a new modelling framework for energy spot prices based on Lévy semistationary processes. Lévy semistationary processes are special cases of the general class of ambit processes. We provide a detailed analysis of the probabilistic properties of such models and we show how...
Persistent link: https://www.econbiz.de/10013144201
Ambit processes are general stochastic processes based on stochastic integrals with respect to Lévy bases. Due to their flexible structure, they have great potential for providing realistic models for various applications such as in turbulence and finance. This papers studies the connection...
Persistent link: https://www.econbiz.de/10013144202
This paper introduces the class of volatility modulated Lévy-driven Volterra (VMLV) processes and their important subclass of Lévy semistationary (LSS) processes as a new framework for modelling energy spot prices. The main modelling idea consists of four principles: First, deseasonalised spot...
Persistent link: https://www.econbiz.de/10013086175
This is the first paper to provide a simple, explicit formula (that doesn’t requirenumerical/computational methods) under stochastic volatility. The formulais as simple as the classical Black-Scholes pricing formula. Furthermore,this paper modifies the Black-Scholes model to make it consistent...
Persistent link: https://www.econbiz.de/10013247571
We introduce a three-factor model of electricity spot prices, consisting of a deterministic seasonality and trend function as well as short- and long-term stochastic components, and derive a formula for futures prices. The long-term component is modelled as a Lévy process with increments...
Persistent link: https://www.econbiz.de/10012929149
We overcome a long-standing obstacle in statistics. In doing so, we show that the distribution of the sum of log-normal variables is log-normal. Furthermore, we offer a breakthrough result in finance. In doing so, we introduce a simple, exact and explicit formula for pricing the arithmetic Asian...
Persistent link: https://www.econbiz.de/10012847738
We introduce a simple, explicit formula for pricing the Bermudan options. Furthermore, the formula does not require any additional parameter (relative to the European option formula). Moreover, we provide an upper bound for the price
Persistent link: https://www.econbiz.de/10012848338
In this paper, we show that the influential Merton jump diffusion model and formula are needlessly cumbersome. In doing so, we provide a simple, explicit formula that doesn't require a computational method. Furthermore, we introduce a new, simple method for solving partial...
Persistent link: https://www.econbiz.de/10012848753
We show that, in practice, the standard unit root tests, cointegration tests, and similar tests are unreliable. This conclusion is more generally applicable to other regression-based tests. In particular, these tests attempt to solve a problem by creating another problem
Persistent link: https://www.econbiz.de/10012835782
Value-at-Risk (VaR) has been widely promoted by the Bank for International Settlement (BIS) as well as central banks of all countries as a way of monitoring and managing market risk and as a basis for setting regulatory minimum capital standards. The revised Basle Accord, implemented in January...
Persistent link: https://www.econbiz.de/10012739261