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This paper enhances option pricing accuracy by incorporating financial expertise into a neural network (NN) design and optimizing data sample quality through cleaning and synthesis. Instead of directly estimating option values (OVs) with NNs, we leverage ...

The knock-out options are considered as path-dependent barrier options that only expire worthless once the value of the underlying asset reaches a specific threshold. The uncertain differential equations are typically used to describe stock fluctuations ...

This paper proposes an option pricing model with an interval-valued fuzzy interest rate, volatility, and stock price. The interval-valued fuzzy pattern of the Black-Scholes option formula is also investigated. With the presented option pricing model, the ...

We investigate a new method in learning to fix the existence of an unsuitable subfunction of a general system. We assume this subfunction is dependent on the system input variables. In this process, we put a learner instead of the unsuitable ...

Optimal stopping is the problem of deciding when to stop a stochastic system to obtain the greatest reward, arising in numerous application areas such as finance, healthcare, and marketing. State-of-the-art methods for high-dimensional optimal stopping ...

In this paper, we study the option pricing problems for rough volatility models. As the framework is non-Markovian, the value function for a European option is not deterministic; rather, it is random and satisfies a backward stochastic partial ...

In this paper we provide a general mathematical framework for distributional transforms, which allows for many examples that are used extensively in the literature of finance, economics, and optimization. We put a special focus on the class of probability ...

Using a new specification of multifactor volatility, we estimate the hidden risk factors spanning S&P 500 index (SPX) implied volatility surfaces and the risk premia of volatility-sensitive payoffs. SPX implied volatility surfaces are well-explained by ...

We propose a hybrid quantum-classical algorithm, which originated from quantum chemistry, to price European and Asian options in the Black--Scholes model. Our approach is based on the equivalence between the pricing PDE and the Schrödinger equation in ...

We explore the abilities of two machine learning approaches for no-arbitrage interpolation of European vanilla option prices, which jointly yield the corresponding local volatility surface: a finite dimensional Gaussian process (GP) regression approach under ...

We introduce a new Brownian path generation method using a second degree polynomial chaos expansion, and use a conjugate gradient algorithm to find the orthogonal transformation that minimizes the mean truncation dimension of this polynomial. We combine ...

We prove the existence and uniqueness of the viscosity solution of an integro-differential equation (IDE) arising in the pricing of American-style multi-asset options in a multivariate Ornstein--Uhlenbeck-type stochastic volatility model. The main ...

The impact of operational risk on the option pricing through the extension of Mitra's model with Merton's jump diffusion model is assessed. A partial integral differential equation (PIDE) is derived and the impact of parameters of Merton's model on ...

We develop a mixed least squares Monte Carlo--partial differential equation (LSMC-PDE) method for pricing Bermudan style options on assets under stochastic volatility. The algorithm is formulated for an arbitrary number of assets and volatility processes, ...

This paper documents the fact that in options markets, the (percentage) implied volatility bid-ask spread increases at an increasing rate as the option’s maturity date approaches. To explain this stylized fact, this paper provides a market microstructure ...

We present a novel method for deriving tight Monte Carlo confidence intervals for solutions of stochastic dynamic programming equations. Taking some approximate solution to the equation as an input, we construct pathwise recursions with a known bias. ...

In this paper, we study the error of a second order finite difference scheme for the one-dimensional convection-diffusion equation. We consider nonsmooth initial conditions commonly encountered in financial pricing applications. For these initial conditions, ...

In this paper, we study a partial differential equation (PDE) framework for option pricing where the underlying factors exhibit stochastic correlation, with an emphasis on computation. We derive a multidimensional time-dependent PDE for the corresponding ...

Under a mild condition on the branching mechanism, we provide an eigenvalue expansion for the pricing semigroup in a one-dimensional positive affine term structure model. This representation, which is based on results from Ogura [Publ. Res. Inst. Math. ...

The computation of the matrix exponential is a ubiquitous operation in numerical mathematics, and for a general, unstructured $n\times n$ matrix it can be computed in $\mathcal{O}(n^3)$ operations. An interesting problem arises if the input matrix is a ...