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.
This paper uses basket option formulas to price vanilla options with discrete dividends.
problem Pricing vanilla options on stocks with discrete cash dividends.
method Uses existing basket option formulas for European options on a single asset with cash dividends in the piecewise lognormal model.
result Explains the use of basket option formulas for a specific problem in the piecewise lognormal model.
Study delta-vega hedging for recalibrated options under model uncertainty.
problem Uncertainty in Black-Scholes model and recalibration to market prices.
method Dynamic recalibration of a Black-Scholes model to a liquid vanilla option, delta-vega hedging analysis.
result Delta-vega hedging is asymptotically optimal for small uncertainty aversion.
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.
Algorithm improves vanilla option pricing accuracy during and before COVID-19.
problem Improving vanilla option pricing accuracy during and before the pandemic.
method Combinational Mutation Strategy of Differential Evolution (CmDE) algorithm for bi-objective optimization.
result Algorithm approximates real market vanilla option prices more accurately than Black-Scholes.
The Bass model is calibrated to vanilla options using a fixed-point equation.
problem Calibration of the Bass local volatility model to vanilla options.
method Solving a fixed-point equation to achieve calibration.
result Existence and uniqueness of the solution to the fixed-point equation, and linear convergence of the fixed-point iteration scheme.
New method uses neural networks for better financial hedging.
problem Spanning multi-asset payoffs with vanilla options.
method One-hidden-layer feedforward neural networks for numerical solution.
result Better hedging results with neural networks compared to single-asset approaches.
Study optimizes option pricing with robust strategies, ensuring consistency with vanilla option prices.
problem Optimizing exotic option pricing with robust strategies.
method Introduces semistatic strategies and robust convex integral functionals on bounded continuous functions.
result Consistent indifference prices with observed vanilla option prices.
Deep neural networks speed up option pricing and calibration.
problem Efficiently pricing and calibrating options under various processes.
method Supervised deep neural networks (DNNs) with different architectures and loss functions.
result Deep neural networks significantly expedite option pricing and calibration.
Paper applies quantization to polynomial processes for option pricing.
problem Quantization for polynomial processes in finance.
method Two quantization procedures for stochastic volatility Jacobi process.
result Theoretical and practical tools for fast option pricing.
The paper redefines semi-static hedging as derivatives and calculates hedging errors.
problem The costs of maintaining hedging portfolios and the limitations of semi-static hedging.
method New integral representations, approximations, and efficient numerical methods for calculating Wiener-Hopf factors and Laplace-Fourier inversion.
result The hedging error of static hedging portfolios can be larger than variance-minimizing portfolios.
It is well known that any sufficiently regular one-dimensional payoff function has an explicit static hedge by bonds, forward contracts and lots of vanilla options. We show that the natural extension of the corresponding representation leads to a static hedge based on the same instruments along with traffic light optio…
Model-free approach to hedge path-dependent options using min-max optimization.
problem Hedging path-dependent options with maturity T using a static portfolio of vanilla options.
method Model-free approach based on primal-dual Martingale Optimal Transport (MOT) problem, solving a min-max optimization problem.
result Provides theoretical bounds on hedging error at maturity T.
This paper examines Bachelier implied volatility at extreme strikes.
problem Investigates appropriate implied volatility extrapolation at extreme strikes.
method Compares Bachelier and Black-Scholes models, focusing on normal distribution and vanilla options.
result Bachelier implied variance grows at most linearly in log-moneyness, similar to Black-Scholes.
The paper solves a stability issue in pricing derivatives using optimal Skorokhod embedding.
problem Optimizing the Skorokhod embedding problem for derivative pricing.
method Derives dualities and geometric characterizations, analyzes convergence rates.
result The optimization problem converges to an optimal Skorokhod embedding problem as more prices are given.
The paper finds optimal strategies for hedging in incomplete markets using derivatives.
problem Optimal static hedging in incomplete markets with two underlying assets and vanilla options.
method Formulated as a utility maximization problem, solved through variational methods and fixed point analysis.
result Semi-analytical solutions for exponential, power/logarithmic, and quadratic utilities, with convergence to a fixed point for exponential utility.
A new method combines MLMC and particle filters for more efficient option pricing.
problem Efficiently pricing options with reduced computational effort.
method Multilevel Particle Filter (MLPF) combining MLMC and particle filters.
result MLPF demonstrates computational savings over Particle Filter (PF) for option pricing.
We show that the frequent claim that the implied tree prices exotic options consistently with the market is untrue if the local volatilities are subject to change and the market is arbitrage-free. In the process, we analyse -- in the most general context -- the impact of stochastic variables on the P&L of a hedged port…
A new method solves SABR and Heston equations for option pricing.
problem Solving SABR and Heston equations for option pricing.
method Semi-analytical method based on path integrals, integrating analytically one set and numerically the other using Monte-Carlo.
result Compact expressions for correlated stochastic variables, efficient for Vanilla and Asian options.
Study utility indifference pricing in a Bachelier model with small linear price impact.
problem Utility indifference pricing in a model with linear price impact.
method Analyzes the Bachelier model with exponential utility indifference prices for vanilla European options.
result Computes the scaling limit of utility indifference prices for a vanishing price impact inversely proportional to risk aversion.
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.
Scaling limits for super-replication costs in models with transient price impact.
problem Analyzing the cost of options in models with transient price impact.
method Proving a scaling limit theorem using a Cox--Ross--Rubinstein binomial model.
result The scaling limit coincides with PDE methods for purely temporary price impact models, expanding to path-dependent options.
Mathematical models for financial asset prices which include, for example, stochastic volatility or jumps are incomplete in that derivative securities are generally not replicable by trading in the underlying. In earlier work (2004) the first author provided a geometric condition under which trading in the underlying a…
Develops a deep learning method for enforcing no-arbitrage in local volatility surfaces.
problem No-arbitrage conditions not enforced in deep learning approaches for local volatility.
method Jointly interpolates European vanilla option prices, enforcing no-arbitrage through modified loss functions or network architectures.
result Demonstrates the effectiveness of enforcing no-arbitrage in local volatility surfaces using deep learning.
Develops a nonparametric model for arbitrage-free pricing of illiquid derivatives.
problem Modeling joint dynamics of liquid vanilla options for arbitrage-free pricing of illiquid derivatives.
method Derives a state space for prices respecting underlying financial constraints using neural networks and imposes constraints to preserve no-arbitrage conditions.
result Neural SDE models are guaranteed to satisfy a set of linear inequalities and validated with numerical experiments.
Analyzes pricing formulas for barrier options with discrete dividends.
problem Complexity introduced by discrete dividends in pricing formulas.
method Compares Buryak and Guo's analytic approach for European options with Dai and Chiu's barrier option formulas.
result Analytic approach effective for European puts and calls, but performance varies for barrier options.
A hybrid framework prices options using neural networks and VAE latent space.
problem Lack of explicit asset dynamics information in compressed volatility surfaces.
method Combining Weighted Monte Carlo with neural networks trained on VAE latent space.
result Effective pricing of vanilla and exotic options on idealized vol surface.
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.
Analytical model prices options with moving barriers under non-Gaussian distributions.
problem Pricing options with moving barriers under non-Gaussian distributions.
method Path-integral formalism adapted from galaxy formation models, incorporating higher-order cumulants.
result Analytical pricing model for vanilla and barrier options without volatility smile.
Fourier methods fail to accurately approximate option Greeks in realistic market conditions.
problem Failure of Fourier pricing techniques to approximate Greeks in realistic market parameters.
method Used Fourier techniques like Carr-Madan formula, COS method, and Lewis formula to approximate Greeks, which failed in some market conditions.
result Empirically showed that Fourier methods completely fail to approximate Greeks in realistic market environments.
CDS options allow investors to express a view on spread volatility and obtain a wider range of payoffs than are possible with vanilla CDS. We give a detailed exposition of different types of single-name CDS option, including options with upfront protection payment, recovery options and recovery swaps, and also presents…
Study optimal liquidation under high risk aversion and small price impact.
problem Optimal liquidation of options under high risk aversion and linear price impact.
method Analyzes Bachelier model with linear price impact, computes utility indifference prices, and finds asymptotically optimal portfolios.
result Establishes a scaling limit for vanishing price impact and computes corresponding utility indifference prices.
In this paper, we give a numerical method for pricing long maturity, path dependent options by using the Markov property for each underlying asset. This enables us to approximate a path dependent option by using some kinds of plain vanillas. We give some examples whose underlying assets behave as some popular Levy proc…
Finite element method for SABR model pricing under various interest rates.
problem Pricing vanilla and barrier options under the SABR stochastic volatility model.
method Finite element discretization of non-symmetric Dirichlet forms for degenerate parabolic equations.
result Well-posedness of the variational formulation and error analysis for finite element discretization.
Method interpolates option prices and volatilities without arbitrage.
problem Interpolating option prices and volatilities without arbitrage.
method Sparse modeling approach based on integral equations and SVD.
result Flexible and efficient framework for arbitrage-free interpolation.
A new method for pricing American options using exercise rate optimization.
problem Pricing American options efficiently and accurately.
method Monte Carlo simulation and optimization of exercise rates.
result The method provides the correct option price and is efficient for various models.
Novel method recovers market regime changes from option prices.
problem Recovering market regime changes from option prices.
method Assumed Markov regime switching, computed implied volatility, validated recovery of regime changes.
result Implied volatility time series can recover market regime changes.
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…
Paper presents new expansions for option pricing with cash dividends.
problem No exact formula for European options with cash dividends.
method Uses Etore and Gobet's technique for piecewise lognormal process with jumps.
result Provides more robust first, second, and third-order expansions.
We present a path integral method to derive closed-form solutions for option prices in a stochastic volatility model. The method is explained in detail for the pricing of a plain vanilla option. The flexibility of our approach is demonstrated by extending the realm of closed-form option price formulas to the case where…
Perpetual American options are financial instruments that can be readily exercised and do not mature. In this paper we study in detail the problem of pricing this kind of derivatives, for the most popular flavour, within a framework in which some of the properties |volatility and dividend policy| of the underlying stoc…
In this article, we consider European options of type h(XT1,XT2,…,XTn) depending on several underlying assets. We study how such options can be valued in terms of simple vanilla options in non-specified market models. We consider different approaches related to static hedging and derive several pricing f…
New formulas for barrier options in stochastic volatility models with nonzero correlation.
problem Calculating barrier options prices in models with nonzero correlation.
method Derivation of two novel closed-form formulas: Hull and White type and Alòs-like decomposition.
result Closed-form formulas for barrier options in stochastic volatility models with nonzero correlation.
It turns out that in the bivariate Black-Scholes economy Margrabe type options exhibit symmetry properties leading to semi-static hedges of rather general barrier options. Some of the results are extended to variants obtained by means of Brownian subordination. In order to increase the liquidity of the hedging instrume…
We characterize the set of market models when there are a finite number of traded Vanilla and Barrier options with maturity T written on the asset S. From a probabilistic perspective, our result describes the set of joint distributions for (ST,supu≤TSu) when a finite number of marginal law constraint…
The paper models asset prices with random volatility to match option prices.
problem Matching asset price dynamics with observed option prices.
method Uses a mixture of diffusion processes with random volatility.
result Derives explicit pricing formulas for derivatives.
The vast majority of works on option pricing operate on the assumption of risk neutral valuation, and consequently focus on the expected value of option returns, and do not consider risk parameters, such as variance. We show that it is possible to give explicit formulae for the variance of European option returns (vani…
LOV model calibrates European and American options with path-dependent volatility.
problem Calibrating European and American options with path-dependent volatility.
method Designing a local volatility model that incorporates path-dependent shocks through an occupation sensitivity function.
result LOV model successfully calibrates options chains with automatic European vanilla option calibration and path-dependent flexibility.