Martin Tegner, Stephen Roberts
arXiv 7 Dec 2021 · Finance — Mathematical Finance
arXiv:2112.03718 · PDF · DOI · OpenAlex · Extracted main text
Local volatility is a versatile option pricing model due to its state dependent diffusion coefficient. Calibration is, however, non-trivial as it involves both proposing a hypothesis model of the latent function and a method for fitting it to data. In this paper we present novel Bayesian inference with Gaussian process priors. We obtain a rich representation of the local volatility function with a probabilistic notion of uncertainty attached to the calibrate. We propose an inference algorithm and apply our approach to S&P 500 market data.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | B. S. Hamida and R. Cont (2005) Recovering volatility from option prices by evolutionary optimization | 0.928 | 4 | 3 | 100% |
| 2 | A. Gupta and C. Reisinger (2014) Robust calibration of financial models using Bayesian estimators | 0.737 | 3 | 2 | 100% |
| 3 | N. Jackson, E. Süli, and S. Howison (1999) Computation of deterministic volatility surfaces | 0.737 | 3 | 2 | 100% |
| 4 | B. Dupire (1994) Pricing with a smile | 0.511 | 2 | 1 | 100% |
| 5 | I. Murray and R. P. Adams (2010) Slice sampling covariance hyperparameters of latent Gaussian models | 0.511 | 2 | 1 | 100% |
| 6 | C. E. Rasmussen and C. K. Williams (2006) Gaussian processes for machine learning, volume 1 | 0.511 | 2 | 1 | 100% |
| 7 | R. Trangucci, M. Betancourt, and A. Vehtari (2016) Prior formulation for Gaussian process hyperparameters | 0.405 | 1 | 1 | 100% |
| 8 | T. Björk (2009) Arbitrage Theory in Continuous Time | 0.405 | 1 | 1 | 100% |
| 9 | G. Brunick and S. Shreve (2013) Mimicking an Itô process by a solution of a stochastic differential equation | 0.405 | 1 | 1 | 100% |
| 10 | P. Carr and D. B. Madan (2005) A note on sufficient conditions for no arbitrage | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 26 scored citations.