The paper introduces a measure to assess the relative value of a delta-Symmetric Strangle under the Black-Scholes model.
problem Measuring the relative value of a delta-Symmetric Strangle under the Black-Scholes model.
method Developed a new measure of relative value in terms of delta and volatility, bounded by a simple function of delta.
result The relative value of a delta-Symmetric Strangle is bounded by a simple function of delta and is independent of other factors.
The paper optimizes financial derivatives for market completion in SV models.
problem Optimizing financial derivatives for market completion in stochastic volatility models.
method Simulation-based method to approximate optimal portfolio strategy, using double optimization approach (utility maximization and risk exposure minimization).
result Strangle options are the best choices for market completion in equity options.
This work analyzes impermanent loss in decentralized markets and provides a hedging strategy.
problem Impermanent loss in automated market makers (AMMs).
method Analytical derivation of a static replication formula using European options, and numerical example with real data.
result Guaranteed hedging coverage for all final prices within a predefined interval.
The performance of trend following strategies can be ascribed to the difference between long-term and short-term realized variance. We revisit this general result and show that it holds for various definitions of trend strategies. This explains the positive convexity of the aggregate performance of Commodity Trading Ad…
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.
Paper compares neural networks and time-series models for weather derivative pricing.
problem Pricing accuracy and regime adaptation for temperature and precipitation weather derivatives.
method Benchmarked harmonic-regression/ARMA vs. feed-forward neural network for temperature. Used CNN for precipitation, adapting to seasonal heterogeneity.
result CNN yields more accurate pricing, especially for regime-adapted seasonal data.
Families of explicit solutions are found to a nonlinear Black-Scholes equation which incorporates the feedback-effect of a large trader in case of market illiquidity. The typical solution of these families will have a payoff which approximates a strangle. These solutions were used to test numerical schemes for solving …
This paper provides fast estimates for complex option types.
problem Estimating prices for constrained multiple exercise American options.
method Lookahead search for lower estimates and nearest-neighbor martingale for upper estimates.
result Probabilistic convergence guarantees for the algorithms.
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.
American options can be equivalent to European options under certain conditions.
problem Determining when American options can be simplified to European options.
method Using methods from Jourdain and Martini, Chrsitensen, and convex duality.
result A first step towards verifying representability of American options.
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.
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.
This paper surveys options pricing under arithmetic Brownian motion and derives formulas for various types of options.
problem The use of arithmetic Brownian motion in finance is not widely adopted.
method Risk-neutral valuation and derivation of formulas for European options under three types of underlying assets.
result Derivation of formulas for European options and partial differential equations for American options.
We explore inverse and quanto inverse crypto options, their pricing, and applications.
problem Market incompleteness in crypto options trading.
method Comparison of direct and inverse options, and introduction of currency-protected 'quanto' options.
result Pricing and hedging characteristics of inverse and quanto inverse options in a Black-Scholes framework.
It is well known that options can make planning more efficient, among their many benefits. Thus far, algorithms for autonomously discovering a set of useful options were heuristic. Naturally, a principled way of finding a set of useful options may be more promising and insightful. In this paper we suggest a mathematica…
The option is a financial derivative, which is regularly employed in reducing the risk of its underlying securities. However, investing in option is still risky. Such risk becomes much severer for speculators who utilize option as a means of leverage to increase their potential returns. In order to mitigate risk on the…