Study cliquet options in a jump-diffusion model with Lévy processes.
problem Pricing cliquet options in a complex financial model with jumps.
method Developed semi-analytic expressions using Lévy process distribution and Fourier transform.
result Inferred semi-analytic expressions for cliquet option prices and derived Greeks.
We investigate the pricing of cliquet options in a geometric Meixner model. The considered option is of monthly sum cap style while the underlying stock price model is driven by a pure-jump Meixner--Lévy process yielding Meixner distributed log-returns. In this setting, we infer semi-analytic expressions for the clique…
Weighted Monte Carlo prices exotic options calibrating the probabilities of previously generated paths by a regular Monte Carlo to fit a set of option premiums. When only vanilla call and put options and forward prices are considered, the Martingale condition might not be preserved. This paper shows that this is indeed…
In the framework of Black-Scholes-Merton model of financial derivatives, a path integral approach to option pricing is presented. A general formula to price European path dependent options on multidimensional assets is obtained and implemented by means of various flexible and efficient algorithms. As an example, we det…
In this paper we present a new methodology for option pricing. The main idea consists to represent a generic probability distribution function (PDF) via a perturbative expansion around a given, simpler, PDF (typically a gaussian function) by matching moments of increasing order. Because, as shown in literature, the pri…
Second-order optimization speeds up deep hedging for complex options.
problem Hedging exotic options with market frictions in realistic markets.
method Second-order optimization scheme leveraging pathwise differentiability and Kronecker-factoring.
result Our method optimizes the policy in 1/4 the steps of standard optimization.
The model outperforms other models in option pricing, especially for short-term implied volatility.
problem Improper calibration and pricing of exotic options in financial models.
method Stochastic volatility model with double-exponential jumps, Fourier pricing techniques.
result The model outperforms other models in fitting the short-term implied volatility smile and pricing exotic options.
We extend the Bismut-Elworthy-Li formula to non-degenerate jump diffusions and "payoff" functions depending on the process at multiple future times. In the spirit of Fournie et al [13] and Davis and Johansson [9] this can improve Monte Carlo numerics for stochastic volatility models with jumps. To this end one needs so…
Novel pricing method for equity-indexed annuities under uncertain volatility and stochastic interest rate.
problem Pricing equity-indexed annuities with early surrender risk under uncertain market conditions.
method Advanced financial modeling techniques, including uncertain volatility framework and Hull-White model for interest rate dynamics. Numerical algorithm using tree-based framework with local volatility optimization.
result High effectiveness of the proposed numerical algorithm compared to machine learning-based methods.
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.
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.
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.
Paper proposes a Hellinger distance regularizer to disentangle options in reinforcement learning.
problem Temporal abstraction in reinforcement learning, specifically the mutual exclusivity of learned options.
method Introduces a Hellinger distance regularizer to disentangle options.
result Demonstrates the effectiveness of the Hellinger distance regularizer in disentangling options.
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.
Study optimizes reinforcement learning options under time constraints.
problem Learning useful options for diverse tasks with limited time.
method Directly searched for optimal option sets considering time budget.
result Discovered options outperform existing heuristics.
PODNet discovers plannable options from unstructured demonstrations.
problem Learning from unstructured, multi-objective demonstrations.
method Custom categorical variational autoencoder, recurrent option inference network, option-conditioned policy network, and option dynamics model.
result PODNet enables learning from demonstration for multiple tasks and planning.
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.
Derives pricing formulae for power binary and normal distribution standard options.
problem Developing pricing models for binary and standard options.
method Incorporates Buchen's formulae into power binary options and derives a formula for normal distribution standard options.
result Derives pricing formulae for power binary and normal distribution standard options.
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.
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.
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.
This work extends the options framework to learn at multiple temporal resolutions.
problem Autonomous creation of temporal abstractions from data in reinforcement learning.
method Developed a hierarchical option-critic architecture capable of learning at multiple temporal resolutions.
result Derived policy gradient theorems for a deep hierarchy of 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…
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…
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.
New algorithms improve learning of long-term actions in reinforcement learning.
problem Violation of parameter independence assumption in deep function approximation.
method Reconsidered option-critic and hierarchical option-critic training for deep settings.
result Significantly improved stability and faster convergence in Atari games.
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.
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.