Related papers: Approximate option pricing formula for Barndorff-N…
We develop a theory for option pricing with perfect hedging in an inefficient market model where the underlying price variations are autocorrelated over a time tau. This is accomplished by assuming that the underlying noise in the system is…
We investigate the pricing of financial options under the 2-hypergeometric stochastic volatility model. This is an analytically tractable model that reproduces the volatility smile and skew effects observed in empirical market data. Using a…
We develop a general method for derivative pricing. This approach has its roots in Shannon's Information Theory. The notion of $\lambda$-analyticity of L\'{e}vy models is introduced on the basis of which new representations of the pricing…
The aim of this study is to devise numerical methods for dealing with very high-dimensional Bermudan-style derivatives. For such problems, we quickly see that we can at best hope for price bounds, and we can only use a simulation approach.…
Options on baskets (linear combinations) of assets are notoriously challenging to price using even the simplest log-normal continuous-time stochastic models for the individual assets. The paper [5] gives a closed form approximation formula…
We present an approach for pricing European call options in presence of proportional transaction costs, when the stock price follows a general exponential L\'{e}vy process. The model is a generalization of the celebrated work of Davis,…
Assuming that price of the underlying stock is moving in range bound, the Black-Scholes formula for options pricing supports a separation of variables. The resulting time-independent equation is solved employing different behavior of the…
This note revisits the SWIFT method based on Shannon wavelets to price European options under models with a known characteristic function in 2023. In particular, it discusses some possible improvements and exposes some concrete drawbacks of…
We explore the performance of various artificial neural network architectures, including a multilayer perceptron (MLP), Kolmogorov-Arnold network (KAN), LSTM-GRU hybrid recursive neural network (RNN) models, and a time-delay neural network…
We propose a quasi maximum likelihood estimation method for Bergomi-type stochastic volatility models with parametrized kernels, focusing on the estimation of the kernel parameters from high-frequency time-series observations of option…
A master equation approach to the numerical solution of option pricing models is developed. The basic idea of the approach is to consider the Black--Scholes equation as the macroscopic equation of an underlying mesoscopic stochastic option…
The main purpose of this article is to give a general overview and understanding of the first widely used option-pricing model, the Black-Scholes model. The history and context are presented, with the usefulness and implications in the…
We derive a forward equation for arbitrage-free barrier option prices, in terms of Markovian projections of the stochastic volatility process, in continuous semi-martingale models. This provides a Dupire-type formula for the coefficient…
Recent progress in the development of efficient computational algorithms to price financial derivatives is summarized. A first algorithm is based on a path integral approach to option pricing, while a second algorithm makes use of a neural…
We derive analytic formulae which link $\alpha$, $\nu$ and $\rho$ parameters in Andreasen-Huge style SABR model to the ATM price and option prices at four strikes close to ATM. Based on these formulae we give a characterisation for the SABR…
In Neri and Schneider (2012) we presented a method to recover the Maximum Entropy Density (MED) inferred from prices of call and digital options on a set of n strikes. To find the MED we need to numerically invert a one-dimensional function…
We consider high-dimensional asset price models that are reduced in their dimension in order to reduce the complexity of the problem or the effect of the curse of dimensionality in the context of option pricing. We apply model order…
We show how the prices of options can be determined with the help of double-fractional differential equation in such a way that their inclusion in a portfolio of stocks provides a more reliable hedge against dramatic price drops that the…
This paper explores the use of the multinode Shepard method for the numerical solution of the two-dimensional Black-Scholes equation. The proposed approach integrates a spatial approximation via the multinode Shepard operator with a…
We determine an explicit formula for the Laplace transform of the price of an option on a maximal interest rate when the instantaneous rate satisfies Cox-Ingersoll-Ross's model. This generalizes considerably one result of Leblanc-Scaillet.