Corpus ID: 235125912

Option Valuation through Deep Learning of Transition Probability Density

@article{Su2021OptionVT,
  title={Option Valuation through Deep Learning of Transition Probability Density},
  author={Haozhe Su and M. V. Tretyakov and D. Newton},
  journal={ArXiv},
  year={2021},
  volume={abs/2105.10467}
}
Transition probability densities are fundamental to option pricing. Advancing recent work in deep learning, we develop novel transition density function generators through solving backward Kolmogorov equations in parametric space for cumulative probability functions, using neural networks to obtain accurate approximations of transition probability densities, creating ultra-fast transition density function generators offline that can be trained for any underlying. These are “single solve”, so… Expand

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References

SHOWING 1-10 OF 54 REFERENCES
Option Pricing via QUAD: From Black–Scholes–Merton to Heston with Jumps
The Black–Scholes model is the rare closed-form formula for pricing options, but its shortcomings are well known. Adding stochastic volatility, American or Bermudan early exercise, non-diffusiveExpand
Option Valuation under Stochastic Volatility II: With Mathematica Code
In his second volume on stochastic volatility and option pricing, Alan Lewis extends his previous work with a particular focus on jump modelling. The Heston or Feller 3/2 models are frequentlyExpand
Estimating the Implied Risk Neutral Density
The market's risk neutral probability distribution for the value of an asset on a future date can be extracted from the prices of a set of options that mature on that date, but two key technicalExpand
Arbitrage‐Free SABR
Smile risk is often managed using the explicit implied volatility formulas developed for the SABR model [1]. These asymptotic formulas are not exact, and this can lead to arbitrage for low strikeExpand
Path Dependant Option Pricing Under Levy Processes
A model is developed that can price path dependent options when the underlying process is an exponential Levy process with closed form conditional characteristic function. The model is an extensionExpand
Density Approximations for Multivariate Affine Jump-Diffusion Processes
We introduce closed-form transition density expansions for multivariate affine jump-diffusion processes. The expansions rely on a general approximation theory which we develop in weighted HilbertExpand
Advancing the Universality of Quadrature Methods to Any Underlying Process for Option Pricing
Exceptional accuracy and speed for option pricing are available via quadrature (Andricopoulos, Widdicks, Duck, and Newton, 2003), extending into multiple dimensions with complex path-dependency andExpand
Time Dependent Heston Model
TLDR
Using a small volatility of volatility expansion and Malliavin calculus techniques, an accurate analytical formula is derived for the price of vanilla options for any time dependent Heston model (the accuracy is less than a few bps for various strikes and maturities). Expand
A Fast and Accurate FFT-Based Method for Pricing Early-Exercise Options Under Levy Processes
A fast and accurate method for pricing early exercise and certain exotic options in computational finance is presented. The method is based on a quadrature technique and relies heavily on FourierExpand
Option pricing when underlying stock returns are discontinuous
Abstract The validity of the classic Black-Scholes option pricing formula depends on the capability of investors to follow a dynamic portfolio strategy in the stock that replicates the payoffExpand
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