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 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…
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.
In this paper we introduce an additive two-factor model for electricity futures prices based on Normal Inverse Gaussian Lévy processes, that fulfills a no-overlapping-arbitrage (NOA) condition. We compute European option prices by Fourier transform methods, introduce a specific calibration procedure that takes into acc…
This paper presents hedging strategies for European and exotic options in a Levy market. By applying Taylor's Theorem, dynamic hedging portfolios are con- structed under different market assumptions, such as the existence of power jump assets or moment swaps. In the case of European options or baskets of European optio…
The paper solves European option pricing under Heston model using artificial boundary method.
problem Valuation of European call options under Heston stochastic volatility model.
method Asymptotic solution in powers of volatility, artificial boundary method for truncated domain, artificial boundary conditions.
result Artificial boundary conditions improve accuracy and outperform Heston's original boundary conditions.
Closed-form pricing method for multi-asset options.
problem Pricing multi-asset contingent claims in an incomplete market.
method Proving extremal martingale measures and constructing algorithms for bounds and hedging.
result Closed-form formulas for no-arbitrage price intervals and hedging strategies.
We propose a general framework for the simultaneous modeling of equity, government bonds, corporate bonds and derivatives. Uncertainty is generated by a general affine Markov process. The setting allows for stochastic volatility, jumps, the possibility of default and correlation between different assets. We show how to…
We consider a financial market with liquidity cost as in Çetin, Jarrow and Protter [2004], where the supply function Sε(s,ν) depends on a parameter ε≥0 with S0(s,ν)=s corresponding to the perfect liquid situation. Using the PDE characterization of Çetin, Soner and Touzi [2010] of the super-hedging cost of a…
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.
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…
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.
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.
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…
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…
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.
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.
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 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.
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.
This paper extends static hedging for European options over multiple maturities.
problem Hedging European options over multiple time periods.
method Developed a spanning relation for multiple shorter-term options using a Markovian framework.
result Demonstrated a practical implementation using Gaussian Quadrature for finite sets of shorter-term options.
New method uses tensor networks to price multi-asset options efficiently.
problem Pricing multi-asset options via classical full-grid solvers is computationally infeasible due to the curse of dimensionality.
method Quantized tensor trains (QTT) transform the d-asset Black-Scholes PDE into a tractable high-dimensional problem.
result Full-grid prices and Greeks for correlated basket and max-min options in three to five dimensions can be computed with high accuracy.
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.
Study calculates liquidity costs for delta hedging of European options.
problem Determining expected liquidity costs in delta hedging.
method Derives an integration formula for liquidity costs, including option prices and delta process.
result Expected liquidity costs can be calculated faster than Monte Carlo simulations.
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 short-maturity VIX and European option prices with jumps.
problem Analyzing VIX and European options with jumps in short-maturity models.
method Local-stochastic volatility models with compound Poisson jumps, leading-order asymptotics in closed-form.
result Closed-form solutions for VIX and European option prices in short-maturity models.
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.
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.
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.
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.
We develop series expansions in powers of q−1 and q−1/2 of solutions of the equation ψ(z)=q, where ψ(z) is the Laplace exponent of a hyperexponential Lévy process. As a direct consequence we derive analytic expressions for the prices of European call and put options and their Greeks (Theta, Delta, and G…
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.
The paper solves a financial mathematics problem using polytopes and probability measures.
problem Maximizing the expectation of functions on probability measures.
method Identifying specific functions and using polytopes to find optimal probability measures.
result The supervertex and subvertex of polytopes maximize or minimize the expected value of certain functions.
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.
Using Maple, we compute some analytical solutions of a modified Black-Scholes equation, recently proposed, in the case of the European put option. We show that the modified Black-Scholes equation with the European put option is exactly solvable in terms of associated Laguerre polynomials. We make some numerical experim…
In the context of stochastic volatility models, we study representation formulas in terms of expectations for the power series' coefficients associated to the call price-function. As in a recent paper by Antonelli and Scarlatti the expansion is done w.r.t. the correlation between the noises driving the underlying asset…
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…
In the context of a Black-Scholes economy and with a no-arbitrage argument, we derive arbitrarily accurate lower and upper bounds for the value of European options on a stock paying a discrete dividend. Setting the option price error below the smallest monetary unity, both bounds coincide, and we obtain the exact value…
Under a generalized skew normal distribution we consider the problem of European option pricing. Existence of the martingale measure is proved. An explicit expression for a given European option price is presented in terms of the cumulative distribution function of the univariate skew normal and the bivariate standard …
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…
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 …
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.
The paper analyzes implied volatility for European and Asian options under stochastic volatility Bachelier model.
problem Analyzing implied volatility for European and Asian options under stochastic volatility.
method Using Malliavin calculus and anticipating Ito's formula, the paper computes and finds asymptotic formulas for implied volatility and skew.
result The paper provides a short maturity asymptotic formula for the skew of implied volatility that depends on the roughness of the volatility model.
In this article, a compact finite difference method is proposed for pricing European and American options under jump-diffusion models. Partial integro-differential equation and linear complementary problem governing European and American options respectively are discretized using Crank-Nicolson Leap-Frog scheme. In pro…
Introduces a new Lévy process for modeling illiquid markets.
problem Modeling dynamic of assets in illiquid markets.
method Introduces Variance Gamma++ process, a new Lévy process, and provides efficient path simulation algorithms.
result Efficient pricing formula and parameter estimation for European options.
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.
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.
Derives short-term option pricing asymptotics in local-stochastic volatility models.
problem Short-term option pricing in local-stochastic volatility models.
method Large deviations theory and variational methods.
result Explicit series expansions for implied volatility and asymptotic results for European and VIX options.