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.
Pricing of European basket call option with n-assets and a bond is discussed in this paper, where all prices of n-assets and the bond are driven by Exponential Ornstein-Uhlenbeck processes. The close-form of European basket option pricing formula is derived. Utilizing with 1-order differential approximate numerical sol…
New method for European option pricing faster and more robust.
problem Pricing European options efficiently and accurately.
method Fourier cosine series expansions for models with known characteristic functions.
result More robust and faster than the original COS method.
The study examines European option pricing using a generalized tempered stable distribution.
problem Investigating the pricing of European options under a generalized tempered stable distribution.
method Fitting the Generalized Tempered Stable (GTS) distribution to S\&P 500 Index returns, applying the Esscher transform, and using the Extended Black-Scholes and Generalized Black-Scholes formulas.
result The GTS distribution yields consistent European option prices for deep OTM and ITM options, but underprices near-the-money and in-the-money options compared to the Black-Scholes model.
This paper compares machine learning models for pricing European options.
problem Pricing European options using traditional methods like Black Scholes Model.
method Google AutoML Regressor, TensorFlow Neural Networks, and XGBoost Gradient Boosting Decision Trees.
result All models outperformed the Black Scholes Model in terms of mean absolute error.
Formula for European option pricing under jump diffusion model.
problem Option pricing under complex stochastic processes.
method Infinite series of Black-Scholes terms for Levy-driven processes.
result Series solution converges with a radius of convergence.
The paper calculates European option prices under a generalized skew normal distribution.
problem European option pricing under a generalized skew normal distribution.
method Proved existence of martingale measure, derived explicit option pricing formula, applied numerical methods.
result Explicit expressions for European option prices are derived.
Investigates how stochastic volatility models affect European option pricing under parameter uncertainty.
problem How do stochastic volatility models impact European option pricing when parameters are uncertain?
method Formalizes the problem as a control problem, uses dual representation with backward stochastic differential equations, and applies numerical solutions to market data.
result Conservative model-prices cover 98% of market-prices for European call options.
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.
A new method for pricing European options in changing market conditions.
problem Lack of closed-form solutions for pricing European options in regime-switching models.
method Physics-informed residual learning (PIRL) for efficient option pricing.
result PIRL eliminates the need for retraining and offers near-instantaneous pricing.
Our goal here is to discuss the pricing problem of European and American options in discrete time using elementary calculus so as to be an easy reference for first year undergraduate students. Using the binomial model we compute the fair price of European and American options. We explain the notion of Arbitrage and the…
The paper prices European options with transaction costs using a fractional Merton model.
problem Discrete-time option pricing with transaction costs.
method Mixed fractional Merton model with delta hedging.
result Formula for European call option pricing derived.
The paper presents a series representation for European option pricing driven by fractional diffusion.
problem Pricing European options under space-time fractional diffusion.
method Uses Mellin-Barnes representation and residue summation in the complex plane.
result Derives a rapidly convergent double-series formula for option pricing.
The paper connects semi-parametric estimates to European option pricing.
problem Estimating European option prices using semi-parametric methods.
method Connecting estimates by de la Peña, Ibragimov and Jordan, Scarf, and Lo.
result The estimates imply European option prices.
Develops European power option pricing under correlated interest rate and asset processes.
problem Pricing European power options under correlated interest rate and asset processes.
method Martingale method and Girsannov transform.
result Derives European power option pricing formulae under two market assumptions.
We offer new formulas for European option pricing under tempered stable processes.
problem Pricing European options under tempered stable processes.
method Series expansions for tempered stable densities and European option prices.
result Our formulas are hyperparameter-free and competitive with traditional methods.
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.
Study prices currency options using fractional delta hedging with transaction costs.
problem Pricing European currency options with transaction costs in fractional Black Scholes model.
method Applied delta hedging strategy to derive pricing formula and PDE.
result Fractional Black Scholes model with transaction costs is a satisfactory model.
We derive a recursive formula for arithmetic Asian option prices with finite observation times in semimartingale models. The method is based on the relationship between the risk-neutral expectation of the quadratic variation of the return process and European option prices. The computation of arithmetic Asian option pr…
Compact method for option pricing under jump-diffusion models.
problem Pricing European and American options with jumps.
method Compact finite difference method using Crank-Nicolson Leap-Frog scheme.
result Fourth-order convergence rate achieved with smoothing operators.
We derive the implied volatility estimation formula in European power call options pricing, where the payoff functions are in the form of V=(STα−K)+ and V=(STα−Kα)+ (α>0)respectively. Using quadratic Taylor approximations, We develop the computing formula of implied volatility in European power call op…
Improved stable pricing for European options using Fourier-Cosine series.
problem Lack of robustness in the COS method for various cases.
method Stable pricing of call options based on Fourier cosine series expansion.
result Stability demonstrated through error analysis and numerical examples.
The paper shows that benchmark-neutral pricing minimizes option prices.
problem Pricing extreme-maturity European put options on diversified indices.
method Benchmark-neutral pricing applied to a drifted time-transformed squared Bessel process.
result Benchmark-neutral price is the minimal possible price, risk-neutral price is more expensive.
Quantum algorithm for pricing European call options.
problem Accurate valuation of financial derivatives, especially for complex models and options.
method Transforms classical FFT into quantum QFT for pricing European call options.
result Quantum algorithm outperforms classical Monte Carlo simulation in NISQ era.
Paper uses Gibbs sampler with jump diffusion for European option pricing.
problem Estimating market parameters for jump diffusion models in option pricing.
method Gibbs sampler applied to jump diffusion model for estimating drift, volatility, jump intensity, and occurrence.
result Demonstrates impact of jump effects on European call option and annuity pricing.
Signature payoffs price complex derivatives accurately.
problem Pricing complex derivatives like options.
method Signature of price path for continuous payoffs.
result Signature payoffs can price various derivatives accurately.
Study provides explicit pricing formula for options with volatility dependent on short rate.
problem Pricing European options with volatility dependent on short rate.
method Developed a class of models with explicit pricing formula using characteristic functions.
result Explicit pricing formula for European options is derived.
This paper deals with pricing of European and American options, when the underlying asset price follows Heston model, via the interior penalty discontinuous Galerkin finite element method (dGFEM). The advantages of dGFEM space discretization with Rannacher smoothing as time integrator with nonsmooth initial and boundar…
New model approximates slow volatility factor using parabolic arcs.
problem Modeling slow factor of volatility in stochastic volatility models.
method Perturbation technique to derive approximate European option prices.
result Simplified expression for European option prices around modified Black-Scholes price.
Choquet and minimax expectations are equivalent in European option pricing.
problem Pricing European options in incomplete markets.
method Comparing Choquet and minimax expectations in the context of European options.
result Choquet and minimax expectations are equal for European options.
We develop a trinomial tree model for pricing perpetual derivatives and European options.
problem Pricing perpetual derivatives and European options in a market with two risky assets and a perpetual derivative of one of them.
method We introduce a recombining trinomial tree model, consider a market with two risky assets and a perpetual derivative, and use a replicating portfolio to price options and generate relationships between risk-neutral and real-world parameters.
result We develop implied parameter surfaces for real-world parameters in the model using historical data.
The article provides representations of exchange option prices under SVJD dynamics.
problem Modeling and pricing exchange options under stochastic volatility and jumps.
method Develops representations for European and American exchange options using SVJD dynamics and equivalent martingale measures.
result Derives integro-partial differential equations and representations for exchange option prices.
Study of gamma-hedging using rough paths for European and exotic options.
problem Applying rough paths to gamma-hedging strategies for derivatives.
method Rough-path theory applied to discrete-time gamma-hedging strategy.
result Sure replication of European and exotic derivatives under regular pricing signals.
The paper develops Hawkes-based models for LOB and applies them to European, spread, and basket option pricing.
problem Developing accurate models for pricing options in the context of limit order books (LOB).
method Introduces multivariate Hawkes processes and their limit theorems, applies to European, spread, and basket options.
result Hawkes-based models provide more market forecast information than classical models.
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.
This paper examines the value of a cancellable European option in a finite time horizon setting. The specifications of this generalized European option allow the seller to cancel the option at any point in time for a fixed penalty paid directly to the holder. Here, we provide an explicit valuation formula for the Europ…
The paper presents an approximate formula for European mortgage options pricing.
problem Pricing European mortgage options with accuracy and efficiency.
method Approximation of the underlying price distribution using lognormal distributions and matching moments.
result The proposed formula provides a good approximation with high accuracy compared to Monte Carlo simulations.
A statistical decision problem is hidden in the core of option pricing. A simple form for the price C of a European call option is obtained via the minimum Bayes risk, R_B, of a 2-parameter estimation problem, thus justifying calling C Bayes (B-)price. The result provides new insight in option pricing, among others obt…
The paper analyzes a five-parameter Variance-Gamma model for European option pricing.
problem Developing a stochastic volatility model for accurate European option pricing.
method Introduced a five-parameter Variance-Gamma model and applied it to empirical data.
result The five-parameter VG model produces underpriced OTM and overpriced ITM options compared to the Black-Scholes model.
The CONLeg method prices and hedges various option types using Legendre series.
problem Pricing and hedging European-type, early-exercise, and discrete-monitored barrier options.
method Algorithm for the convolution of Legendre series (CONLeg method) applied to Levy process.
result High accuracy in pricing and hedging, especially for deep out-of-the-money and long/mature options.
We consider the pricing of American put options in a model-independent setting: that is, we do not assume that asset prices behave according to a given model, but aim to draw conclusions that hold in any model. We incorporate market information by supposing that the prices of European options are known. In this setting…
In this article, we consider the small-time asymptotics of options on a \emph{Leveraged Exchange-Traded Fund} (LETF) when the underlying Exchange Traded Fund (ETF) exhibits both local volatility and jumps of either finite or infinite activity. Our main results are closed-form expressions for the leading order terms of …
This paper develops a European option pricing formula for fractional market models. Although there exist option pricing results for a fractional Black-Scholes model, they are established without accounting for stochastic volatility. In this paper, a fractional version of the Constant Elasticity of Variance (CEV) model …
Improved option pricing for assets with jumps and spikes.
problem Inaccurate pricing of European and American options using lognormal diffusion.
method Developed a jump-diffusion model and reduced complexity of pricing algorithms.
result Reduced complexity of European option pricing from O(n^3) to O(n ln n).
Develops a new framework for currency option pricing with transaction costs.
problem Pricing currency options under transaction costs and fractional Brownian motion.
method Analytic formula derived using mean self-financing delta-hedging in a discrete time setting.
result Minimal price formula for currency options under transaction costs.
The paper models financial asset prices with jumps and evaluates European option prices using numerical methods.
problem Modeling and pricing European options with jumps in delayed stochastic systems.
method Existence, uniqueness, and positivity of solutions to delayed stochastic differential equations with jumps. Application of Fourier transformation for analytical pricing and Monte-Carlo simulation with a logarithmic Euler-Maruyama scheme for numerical approximation.
result The logarithmic Euler-Maruyama scheme provides a positive and convergent method for approximating the solution to the delayed stochastic differential equations with jumps.
Combines option pricing and portfolio theory for optimal hedging.
problem Optimal hedging of European options in various price dynamics.
method Derives optimal holdings and unhedged risk for different price dynamics.
result Derives solutions for various price dynamics including binomial, diffusion, volatility, volatility-of-volatility, and jump diffusion.
The study uses Fisher information to estimate volatility uncertainty in Heston model.
problem Estimating volatility uncertainty in financial models like Heston.
method Fit likelihood function on VIX options, compute Fisher information matrices from Heston model Greeks.
result Option prices can reliably estimate volatility when it's large, but become unreliable below a critical value.