Diffusion Probabilistic Model for Implied Volatility Surface Generation and Completion
X. Ma (TU Delft - Electrical Engineering, Mathematics and Computer Science)
S. Liu – Mentor (TU Delft - Numerical Analysis)
K. Vuik – Mentor (TU Delft - Delft Institute of Applied Mathematics)
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Abstract
Implied volatility surfaces are integral to option pricing and risk management but often display missing data. Prior research has typically engaged mathematical models or data-driven methods for generating or completing these surfaces. Given the similarity between implied volatility surfaces and images, our paper introduces the Denoising Diffusion Probabilistic Model (DDPM), a novel deep learning image generation model, for this task. A distinctive aspect of DDPM's training involves progressively adding noise to the surfaces until they resemble pure noise, and then learning to denoise back to the original surfaces. We employ the Heston model to simulate implied volatility surfaces, then train the DDPM using this synthetic data. Additionally, a Variational Autoencoder model (VAE) is implemented as a comparative benchmark for assessing DDPM's efficacy. Our experiments demonstrate that DDPM excels in generating and reconstructing missing areas in implied volatility surfaces, highlighting its potential in this field. Looking to the future, combining DDPM with VAE could provide more interpretable results, enhancing the model's utility and applicability in financial analysis.