On the control of the difference between two Brownian motions: an application to energy markets modeling. (English) Zbl 1350.60084
Summary: We derive a model based on the structure of dependence between a Brownian motion and its reflection according to a barrier. The structure of dependence presents two states of correlation: one of comonotonicity with a positive correlation and one of countermonotonicity with a negative correlation. This model of dependence between two Brownian motions \(B^1\) and \(B^2\) allows for the value of \(\mathbb{P}(B^1_t-B^2_t\geq x)\) to be higher than \(1/2\) when \(x\) is close to \(0\), which is not the case when the dependence is modeled by a constant correlation. It can be used for risk management and option pricing in commodity energy markets. In particular, it allows to capture the asymmetry in the distribution of the difference between electricity prices and its combustible prices.
MSC:
| 60J65 | Brownian motion |
| 60J70 | Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) |
| 60J25 | Continuous-time Markov processes on general state spaces |
| 60J60 | Diffusion processes |
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 91B70 | Stochastic models in economics |
| 62H99 | Multivariate analysis |
Keywords:
Brownian motion; copula; asymmetry; coupling; barrier; local correlation; energy markets; commodities; riskReferences:
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