A model-free framework extracts risk-neutral densities from short-dated options.
problem Arbitrage and bid-ask spread issues in short-dated options.
method Develops ARIES for filtering static arbitrage and SEDEx for density extraction.
result Robust density extraction across various market conditions and volatility smiles construction.
Paper offers a simpler solution for managing complex financial options.
problem Managing a large number of financial assets with diverse dynamics.
method Developed a simple analytical approximation for market making.
result Shows significant flexibility over existing market making strategies.
Study evaluates three position sizing methods for put-writing on S&P 500 Index options.
problem Underdeveloped practical implementation of short-dated volatility-selling strategies.
method Kelly criterion, VIX-based volatility scaling, hybrid method.
result Ultra-short-dated, out-of-the-money options deliver superior risk-adjusted returns.
New method analyzes volatility models for option prices, especially in rough volatility.
problem Analyzing option prices in rough volatility models.
method Introducing a new methodology to analyze stochastic volatility models, focusing on asymptotics and numerics.
result Detailed expansion and numerical evidence for implied volatility in rough volatility models.
First, we give an asymptotic expansion of short-dated at-the-money implied volatility that refines the preceding works and proves in particular that non-rough volatility models are inconsistent to a power law of volatility skew. Second, we show that given a power law of volatility skew in an option market, a continuous…
Estimates volatility of volatility and leverage effect using high-frequency options data.
problem Estimating volatility of volatility and leverage effect from high-frequency options data.
method Model-free estimators using characteristic function of price increments and spot volatility.
result Developed feasible inference methods for estimating volatility of volatility and leverage effect.
Study the hedging of cryptocurrency options in a volatile market.
problem Hedging options in a volatile, non-stationary cryptocurrency market.
method Calibrated to SVI-implied volatility surfaces, Monte Carlo price paths generated using SVCJ, GARCH, and historical data. Delta, Delta-Gamma, Delta-Vega, and Minimum Variance strategies applied. Wide range of market models tested.
result Calibration results indicate stochastic volatility, low jump frequency, and infinite activity. Short-dated options less sensitive to volatility or Gamma hedges; longer-dated options benefit from multiple-instrument hedges.
Non-spanning identification of scheduled event risk in option pricing.
problem Separating continuous surface from scheduled jump in option pricing.
method Modeling FOMC decisions, CPI releases, and NFP reports as deterministic-time jumps in risk-neutral option pricing.
result Improves held-out event-spanning pricing with Gaussian and two-component mixture jumps.
We derive a higher-order expansion for rough volatility models.
problem Characterizing and estimating rough volatility models.
method Higher-order asymptotic expansion of characteristic functions.
result Distinct roles of rough and jump dynamics in volatility.
This paper explores the harmonic mean of implied volatility and its relation to local volatility.
problem Understanding the relationship between implied volatility and local volatility.
method Investigates the harmonic mean of a positive function for any fixed maturity, linking it to Fukasawa's invertible map.
result The short-dated implied volatility approaches the arithmetic mean of the local volatility in a new coordinate system.
Pricing Bermudan swaptions with few exercise dates using analytic methods.
problem Pricing Bermudan swaptions with few exercise dates
method Analytic decomposition and backward induction under rolling forward measures
result Pricing formulas with decomposition and boundary linearity
We develop an optimal currency hedging strategy for fund managers who own foreign assets to choose the hedge tenors that maximize their FX carry returns within a liquidity risk constraint. The strategy assumes that the offshore assets are fully hedged with FX forwards. The chosen liquidity risk metric is Cash Flow at R…
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.
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.
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…
Learning from demonstration has been widely studied in machine learning but becomes challenging when the demonstrated trajectories are unstructured and follow different objectives. This short-paper proposes PODNet, Plannable Option Discovery Network, addressing how to segment an unstructured set of demonstrated traject…
The options framework is a popular approach for building temporally extended actions in reinforcement learning. In particular, the option-critic architecture provides general purpose policy gradient theorems for learning actions from scratch that are extended in time. However, past work makes the key assumption that ea…
Reinforcement learning can greatly benefit from the use of options as a way of encoding recurring behaviours and to foster exploration. An important open problem is how can an agent autonomously learn useful options when solving particular distributions of related tasks. We investigate some of the conditions that influ…
Study proves duality in exotic option pricing under uncertain model and delayed information.
problem Pricing and hedging of multi-action exotic options under nondominated model uncertainty and delayed information.
method Reformulated superhedging problem as a European option problem, proving duality results.
result Superhedging price equals model-based price with future look-up power.
Study evaluates cryptocurrency option pricing models, finds Kou and Bates models perform best.
problem High volatility and low liquidity in cryptocurrency futures contracts make traditional option pricing models unreliable.
method Calibrated and evaluated the performance of six option pricing models (Black-Scholes, Merton Jump Diffusion, Variance Gamma, Kou, Heston, and Bates) on BTC and ETH futures options.
result Kou and Bates models achieve the lowest pricing errors, with Kou outperforming Bates for BTC and ETH options respectively.
The study finds flaws in methods used to estimate foreign exchange option prices.
problem Flaws in estimating foreign exchange option prices.
method Provided counterexamples of popular FX option interpolation methods.
result Popular FX option interpolation methods fail in certain scenarios.
We price and hedge American options robustly in continuous time.
problem Pricing and hedging American options in continuous time with model uncertainty.
method Assumes continuous semimartingale asset prices and closed convex constraints on volatility. Proves robust pricing-hedging duality and identifies American options as European options on an enlarged space.
result We prove robust pricing-hedging duality and show it holds against richer models with dynamic trading of European options.