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Fast calibration of two-factor models for energy option pricing
The document discusses the fast calibration of two-factor models for energy options pricing, particularly in relation to virtual power plants. It covers model choice, calibration methodologies, and evaluates models using historical data from the German electricity market and the Dutch gas market. Additionally, it highlights achievements in computational efficiency and suggests future developments such as testing new models and incorporating stochastic volatility.
Fast calibration of two-factor models for energy option pricing
- 1. Fast calibration oftwo-factor models for energy options pricing EmanueleFabbiani Andrea Marziali Giuseppe De Nicolao
- 2. A motivating example: VirtualPower Plant2 Virtual Power Plant price Calibrated models for the underlyings Monte Carlo simulations
- 3. A motivating example: VirtualPower Plant3 Virtual Power Plant price Calibrated models for the underlyings Monte Carlo simulations
- 4. A motivating example: VirtualPower Plant4 Two issues: ➢ Model choice ➢ Model calibration
- 5. Outline ➢ Pricing options:Black formulae ➢ Models for Energy commodities ➢ Deriving the variance of linear stochastic systems ➢ Market calibration ➢ Test cases: EEX and TTF 5
- 6. The Black formulae Supposethe underlying future behaves like a martingale – a zero-drift GBM. 6
- 7. The Black formulae Supposethe underlying future behaves like a martingale – a zero-drift GBM. The values of call and put European options are: 7
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- 10. The Black formulae Choosea different model. Let p(t) be the variance of the underlying. 10
- 11. The Lyapunov equation Givena linear stochastic system 11 The variance of the state x is the matrix P such that:
- 12. 12 From Lyapunov to Black NUMERICAL SOLUTIONANALYTICAL SOLUTION
- 13. 13 Numerical and analytical solutions Numerical SolutionAnalytical Solution
- 14. Numerical vs Analytical solutions COMPUTATIONTIME – Linear Scale COMPUTATION TIME – Log Scale 14
- 15. 15 Model calibration Kalman filter TWO-FACTOR MODEL HistoricalCalibration Market Calibration
- 16. 16 Model evaluation Two-factor model 57 tradingdays German Electricity market (EEX) and Dutch gas market (TTF) European options on futures Ornstein-UhlenbeckGeometric Brownian Motion Calibration (~70% of listed options) Test (~30% of listed options) Mean Absolute Error
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- 21. 21 Case study (2017-11-28, TTF). Predicted vs actualprices. Test set.
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- 27. Achievements ➢ By applyingLyapunov equation, provided a computationally efficient procedure to derive the variance of several models ➢ Compared computational efficiency of numerical and analytical solutions of the Lyapunov equation ➢ Assessed the performances of different models in pricing listed vanilla options 27
- 28. Future developments ➢ Testdifferent models ➢ Include stochastic volatility ➢ Calibrate model parameters directly against market volatility 28
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