Jul 15, 2023
Reliability Option Pricing
Pricing Reliability Options under jump-diffusion dynamics with theoretical and numerical methods
Conducted as part of my graduation project at the University of Padova - Department of Mathematics "Tullio Levi-Civita" (Padova, Italy), supported by the Marco Garuti Scholarship. The project focused on the pricing of Reliability Options under stochastic models with jumps, combining closed-form results and numerical approaches.
Market Data Analysis
Extracted statistical features from Italian energy market price time series
Analytical Contribution
Developed a closed formula for pricing the Reliability Option under Merton’s Jump Diffusion
Numerical Techniques
Applied Monte Carlo simulations and Fourier-based methods to Reliability Options under Merton’s Jump Dynamics and Vasicek with Jumps
Key contributions
- Analytical formula: Derived closed-form formula for Reliability Option pricing under Merton's Jump Diffusion model, previously unavailable for this contract type.
- Market data analysis: Analyzed IPEX market data (2017-2023) covering 24 hourly electricity price time series and daily gas prices, performing 15+ statistical tests identifying mean reversion, heavy-tailed distributions, and jump processes.
- Benchmarking: Benchmarked 3 pricing methods (Analytical Formula, Monte Carlo up to 1M paths, Lewis-Fourier) across 2 stochastic models with sensitivity analysis across 8+ parameters—Fourier method achieved 10^-13 precision and 99.8% faster execution (0.03-1.76s vs 65-700s).