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We consider closed-form approximations for European put option prices within the Heston and GARCH diffusion stochastic volatility models with time-dependent parameters. Our methodology involves writing the put option price as an expectation…

The geometric L\'evy model (GLM) is a natural generalisation of the geometric Brownian motion model (GBM) used in the derivation of the Black-Scholes formula. The theory of such models simplifies considerably if one takes a pricing kernel…

This paper proposes an adaptive mechanism for price signal generation using a piecewise linear approximation of a flexibility function with unknown parameters. In this adaptive approach, the price signal is parameterized and the parameters…

In the option valuation literature, the shortcomings of one factor stochastic volatility models have traditionally been addressed by adding jumps to the stock price process. An alternate approach in the context of option pricing and…

Consider a discrete finite-dimensional, Markovian market model. In this setting, discretely sampled American options can be priced using the so-called ``non-recombining'' tree algorithm. By successively increasing the number of exercise…

Standard neural network architectures are non-linear only by virtue of a simple element-wise activation function, making them both brittle and excessively large. In this paper, we consider methods for making the feed-forward layer more…

In this paper, we introduce two novel methods to solve the American-style option pricing problem and its dual form at the same time using neural networks. Without applying nested Monte Carlo, the first method uses a series of neural…

The LIBOR market model is very popular for pricing interest rate derivatives, but is known to have several pitfalls. In addition, if the model is driven by a jump process, then the complexity of the drift term is growing exponentially fast…

This study investigates the application of machine learning algorithms, particularly in the context of pricing American options using Monte Carlo simulations. Traditional models, such as the Black-Scholes-Merton framework, often fail to…

This paper investigates how the compositional structure of neural networks shapes their optimization landscape and training dynamics. We analyze the gradient flow associated with overparameterized optimization problems, which can be…

The shortcomings of the popular Black-Scholes-Merton (BSM) model have led to models which could more accurately model the behavior of the underlying assets in energy markets, particularly in electricity and future oil prices. In this paper…

Multivariable parametric models are critical for designing, controlling, and optimizing the performance of engineered systems. The main aim of this paper is to develop a parametric identification strategy that delivers accurate and…

This paper presents a framework of imitating the principal investor's behavior for optimal pricing and hedging options. We construct a non-deterministic Markov decision process for modeling stock price change driven by the principal…

The aim of this paper is to present a simple stochastic model that accounts for the effects of a long-memory in volatility on option pricing. The starting point is the stochastic Black-Scholes equation involving volatility with long-range…

Nonparametric methods for the estimation of the Levy density of a Levy process are developed. Estimators that can be written in terms of the ``jumps'' of the process are introduced, and so are discrete-data based approximations. A model…

Signature methods have been widely and effectively used as a tool for feature extraction in statistical learning methods, notably in mathematical finance. They lack, however, interpretability: in the general case, it is unclear why…

Neural additive models (NAMs) enhance the transparency of deep neural networks by handling input features in separate additive sub-networks. However, they lack inherent mechanisms that provide calibrated uncertainties and enable selection…

We propose a new framework for modeling stochastic local volatility, with potential applications to modeling derivatives on interest rates, commodities, credit, equity, FX etc., as well as hybrid derivatives. Our model extends the…

Forecasting stock prices can be interpreted as a time series prediction problem, for which Long Short Term Memory (LSTM) neural networks are often used due to their architecture specifically built to solve such problems. In this paper, we…

Additive composition (Foltz et al, 1998; Landauer and Dumais, 1997; Mitchell and Lapata, 2010) is a widely used method for computing meanings of phrases, which takes the average of vector representations of the constituent words. In this…