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Probabilistic numerical approximation schemes in finance : learning methods for high-dimensional BSDEs and unbiased Monte Carlo algorithms for stochastic volatility models

Junchao Chen

deep learning / machine learningResource overview

Probabilistic numerical approximation schemes in finance : learning methods for high-dimensional BSDEs and unbiased Monte Carlo algorithms for stochastic volatility models

Paper2022

by Junchao Chen

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Suggested foundations for monte carlo and numerical simulation and volatility models and surfaces. Specialist prerequisites vary by paper.

Before you read

Laws of Large Numbers and the Central Limit Theorem
Understand convergence, sampling error and confidence intervals.
Random Number Generation
Generate reproducible samples and distinguish randomness from model assumptions.
Stochastic Processes, Brownian Motion and Itô's Lemma
Follow diffusion-based models and their assumptions.
ARCH and GARCH
Separate conditional volatility from observed returns.

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Monte Carlo Option Pricing
Turn a discounted payoff into an estimator.
Correlated Randoms and Low-Discrepancy Sequences
Study dependence and alternatives to independent sampling.
Stochastic Volatility and the Heston Model
Study a correlated stochastic-variance model.

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From martingales to option pricing
Start in discrete time, move to Brownian motion, then read the original pricing argument and simulate it.

Probabilistic numerical approximation schemes in finance : learning methods for high-dimensional BSDEs and unbiased Monte Carlo algorithms for stochastic volatility models

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Probabilistic representation of integration by parts formulae for some stochastic volatility models with unbounded drift