The paper compares machine learning methods with traditional techniques for pricing and sensitivities of financial products with path-dependent structures.
problem Evaluating financial products with early-termination clauses, especially those with path-dependent structures.
method The paper compares regression methods including randomized recurrent and feed-forward neural networks, and a novel approach using signatures of the underlying price process, with traditional polynomial basis functions for pricing and sensitivities.
result Machine learning algorithms often match the accuracy and efficiency of traditional methods for Asian and look-back options, while randomized neural networks are best for callable certificates.
In this short note, we will strengthen the classic Doob's Lp inequality for sub-martingale processes. Because this inequality is of fundamental importance to the theory of stochastic process, we believe this generalization will find many interesting applications.
The paper uses option theory to estimate corporate bond liquidity spreads.
problem Estimating liquidity spreads for corporate bonds.
method Option-theoretic approach considering risk-free rate volatility and credit risk.
result The model provides a robust tool for pricing illiquid bonds.
In the past 20 years, momentum or trend following strategies have become an established part of the investor toolbox. We introduce a new way of analyzing momentum strategies by looking at the information ratio (IR, average return divided by standard deviation). We calculate the theoretical IR of a momentum strategy, an…
We present a detailed study of the performance of a trading rule that uses moving average of past returns to predict future returns on stock indexes. Our main goal is to link performance and the stochastic process of the traded asset. Our study reports short, medium and long term effects by looking at the Sharpe ratio …
Framework selects optimal historical data windows for non-stationary learning.
problem Learning in environments where conditions change over time.
method Stability principle applied to select look-back windows.
result Regret bounds are minimax optimal for strongly convex or Lipschitz population losses.
This study evaluates a dynamic pairs trading strategy in cryptocurrencies using cointegration tests.
problem Improving profitability and risk management in cryptocurrency trading.
method Engle-Granger, KSS, Johansen tests; optimal look-back window; mean-reversion speed calibration; microstructure limitations consideration.
result The strategy outperforms naive buy-and-hold in Bitmex exchange with low maximum drawdown.
Notes on embedding criteria for smooth manifolds.
problem Conditions for embedding smooth manifolds into Euclidean space.
method Linking recent results to classical criteria and K-theory.
result Recent results connect to classical embedding criteria.
Improved few-shot learning with lower-level neural network embeddings.
problem Limited data scenarios in few-shot learning.
method Graph-based meta-learning framework using hidden layer feature embeddings.
result Utilization of lower-level neural network embeddings improves classifier accuracy.
Before retiring, looking back to forty years of writing and publishing scientific papers, I decided to present to the scientific community a selection of my scientific works. I chose mostly articles published in prestigious journals or Proceedings that made a certain impact in the scientific world. I have selected thir…
This paper concentrates on the time series momentum or contrarian effects in the Chinese stock market. We evaluate the performance of the time series momentum strategy applied to major stock indices in mainland China and explore the relation between the performance of time series momentum strategies and some firm-speci…
StockTime predicts stock prices more accurately using LLMs and time series data.
problem Challenges in integrating time series data and natural language for stock price prediction.
method StockTime is a specialized LLM architecture that integrates textual and time series data to predict stock prices.
result StockTime outperforms recent LLMs in predicting stock prices with more accuracy.
AutoML aims to automate machine learning tasks, reviewed in this chapter.
problem Automating the design of machine learning systems.
method Historical review and description of main paradigms.
result Major achievements in AutoML have been made in recent years.
This thesis investigates belief propagation's performance in graphical models with loops.
problem Belief propagation's performance and convergence guarantees in models with loops are uncertain.
method Investigates how model parameters affect belief propagation's performance, convergence, and approximation quality.
result Model parameters influence the number of fixed points, convergence properties, and approximation quality of belief propagation.
In this paper, we solve the problem of adapting classifiers across domains. We consider the problem of domain adaptation for multi-class classification where we are provided a labeled set of examples in a source dataset and we are provided a target dataset with no supervision. In this setting, we propose an adversarial…
Dynamic econometric models improve trading signals in momentum strategies.
problem Static momentum strategies are inefficient; dynamic models enhance accuracy.
method Dynamic binary classifier model to learn time-varying momentum importance.
result Dynamic classifier outperforms traditional naive time series momentum strategy.
Index tracking is a popular form of asset management. Typically, a quadratic function is used to define the tracking error of a portfolio and the look back approach is applied to solve the index tracking problem. We argue that a forward looking approach is more suitable, whereby the tracking error is expressed as expec…
Study bounds for prices of European and American options with optional termination.
problem Bounding prices of options with potential termination.
method Duality results linking upper prices of vulnerable options to American options with constrained exercise times.
result Linking upper prices of vulnerable options to American options and game options.
New option pricing formulas for American and Bermudan options.
problem Traditional option pricing models assume constant volatility and interest rate.
method Relaxing assumptions, using square root of Brownian motion, providing closed-form formulas.
result Simple, closed-form pricing formulas for American and Bermudan options.
Path integral method calculates barrier option prices.
problem Barrier option pricing in finance.
method Path integral method applied to trapezoid and square potential barriers.
result Analytical expressions for option pricing derived.
New framework identifies hidden risks and optionality in American options.
problem Underestimation of flexibility and convexity in early-exercise features.
method Introducing stochasticity into underlying determinants to quantify hidden risks and optionality.
result Remedies conventional pricing systems that underestimate optionality.
Syllabuses for curriculum learning have been developed on an ad-hoc, per task basis and little is known about the relative performance of different syllabuses. We identify a number of syllabuses used in the literature. We compare the identified syllabuses based on their effect on the speed of learning and generalizatio…
There exist several methods how more general options can be priced with call prices. In this article, we extend these results to cover a wider class of options and market models. In particular, we introduce a new pricing formula which can be used to price more general options if prices for call options and digital opti…
Path integral method calculates PDBS option prices with time-dependent parameters.
problem Pricing proportional double-barrier step options with time-dependent interest rates and volatilities.
method Path integral method applied to a quantum mechanical analogy of barrier options.
result Derivation of pricing kernel for PDBS options with time-dependent parameters.
New method for pricing SOFR futures options, solving both American and Asian exercise styles.
problem Lack of pricing models for SOFR futures options post-LIBOR transition.
method Developed a new version of the GIT method to solve semi-analytically.
result Obtained option prices, exercise boundaries, and Greeks for American and Asian options.
Hamiltonian method applied to floating barrier options pricing.
problem Pricing of floating barrier options.
method Hamiltonian approach in quantum mechanics applied to barrier options.
result Analytical expressions for pricing kernel and option price derived.
Neural network learns to solve Black-Scholes for stock options.
problem Stock option pricing using the Black-Scholes Equation.
method Neural Networks applied to solve the Black-Scholes Equation.
result Neural network can accurately forecast stock option prices.
Optimal hedging strategies for exotic options using vanilla options.
problem Hedging exotic options with illiquid vanilla options.
method Simple approximations and variational techniques in a market model and stochastic volatility model framework.
result Optimal Delta and Vega hedging strategies can be computed easily.
ANNs solve financial option valuation problems without numerical methods.
problem Valuation of European and American financial options.
method Unsupervised learning with artificial neural networks (ANNs) for solving PDEs.
result ANNs accurately compute option values for various stock scenarios.
Fast probabilistic option price predictions using modular Bayesian inference.
problem Accurate probabilistic predictions of future option prices.
method Modular approximate Bayesian inference framework that combines multiple data sources.
result Accurate probabilistic option-price predictions in realistic scenarios.
New formulas for pricing Asian and basket options using stochastic expansion.
problem Pricing Asian and basket options under time-dependent parameters.
method Stochastic Taylor expansion around a log-normal proxy model.
result Highly accurate approximations for Asian options and vanilla options with discrete dividends.
Develops a new MCMC-based Wishart prior for Gaussian Process covariance matrix.
problem Difficult inference for multivariate Gaussian Processes with multiple lengthscale parameters.
method Introduces a self-assembled Wishart prior and uses MCMC for Bayesian inference on kernel hyperparameters.
result Demonstrates the effectiveness of the new prior in GP-based learning with empirical results.
New FX option interpolations impact implied volatilities.
problem Different interpolations of FX option quotes lead to varying implied volatilities.
method Analysis of various exact interpolations of broker quotes.
result Different interpolations result in different implied volatilities.
This article presents fast lower and upper estimates for a large class of options: the class of constrained multiple exercise American options. Typical options in this class are swing options with volume and timing constraints, and passport options with multiple lookback rights. The lower estimate algorithm uses the ar…
Efficient method for pricing European and American options using Markov switching stochastic volatility model.
problem Modeling and pricing options under varying volatility and mean-reversion speeds.
method Discrete-time Markov switching stochastic volatility with co-jump model, computationally efficient approach for European options, and conversion to European option pricing for American options.
result Efficient and accurate methods for pricing options, including variance swap analysis.
Panoptic trades options without oracles on Ethereum.
problem Trading options without relying on oracles.
method Perpetual, trustless, instant-settlement protocol on Ethereum.
result Trustless, permissionless trading of options on Uniswap v3.
Paper proposes method for generating paths of stochastic volatility CGMY process for option pricing.
problem Generating accurate sample paths for stochastic volatility models for option pricing.
method Monte-Carlo method for European and American options, least square regression for calibration.
result Calibrated model parameters to S\&P 100 index options market using path-dependent options.
This study compares SPX and VIX options and quantifies their relationship.
problem Understanding the relationship between SPX and VIX options markets.
method Uses moment formulas in a model-free approach to compare implied volatilities.
result SPX options reflect the extreme-strike asymptotics of VIX options and vice versa.
Quantum method prices options by evolving a state in imaginary time.
problem Pricing options in a quantum setting.
method Prepares an initial state, evolves it using imaginary time algorithms, and maps to quantum state.
result Numerical verification for European options; extension to path-dependent options.
Study on pricing American Exchange options using Lévy processes.
problem Pricing American Exchange options driven by Lévy processes.
method Represented American Exchange options as European options plus early exercise premium; studied properties of free boundary and provided an approximative formula.
result Developed an approximative formula for American Exchange options.
In this paper we extend Buchen's method to develop a new technique for pricing of some exotic options with several expiry dates(more than 3 expiry dates) using a concept of higher order binary option. At first we introduce the concept of higher order binary option and then provide the pricing formulae of n-th order b…
In reinforcement learning (RL), temporal abstraction still remains as an important and unsolved problem. The options framework provided clues to temporal abstraction in the RL, and the option-critic architecture elegantly solved the two problems of finding options and learning RL agents in an end-to-end manner. However…
Tensor trains speed up option pricing for multi-asset options.
problem Speeding up option pricing for multi-asset options.
method Tensor train learning algorithms to compress functions with parameter dependence.
result The proposed method outperforms Monte Carlo-based pricing in computational complexity.
The study finds no evidence of stochastic arbitrage opportunities in S&P 500 index options.
problem Identifying arbitrage opportunities in S&P 500 index options.
method Developed linear and mixed-integer linear programs to compute the maximum option premium.
result No evidence of systematic stochastic arbitrage opportunities in S&P 500 index options.
The study compares on-chain option prices with a model and finds significant differences.
problem Measuring and comparing on-chain option prices with a model-based benchmark.
method Used a two-regime MS-AR-(GJR)-GARCH model to estimate volatility and GLS to compare prices.
result On-chain option prices are significantly higher than model-based benchmarks, especially for call options.
This paper sets out to provide a general framework for the pricing of average-type options via lower and upper bounds. This class of options includes Asian, basket and options on the volume-weighted average price. We demonstrate that in cases under discussion lower bounds allow for the dimensionality of the problem to …
Paper cleans option price datasets by removing outliers.
problem Unusual option prices in datasets.
method Statistical techniques to identify and remove outliers.
result Removes option prices violating no arbitrage assumption.
Using spectral decomposition techniques and singular perturbation theory, we develop a systematic method to approximate the prices of a variety of options in a fast mean-reverting stochastic volatility setting. Four examples are provided in order to demonstrate the versatility of our method. These include: European opt…