This work explores a finite liquidity model to price spread options and assess the liquidity impact. We employ Kirk approximation for computing the spread option price and its delta. The latter is needed since the liquidity impact is caused by the delta hedging of a large investor. Our main...

In this short paper, we study the asymptotics for the price of call options for very large strikes and put options for very small strikes. The stock price is assumed to follow the Black-Scholes models. We analyze European, Asian, American, Parisian and perpetual options and conclude that the...

This paper proposes a data-driven approach, by means of an Artificial Neural Network (ANN), to value financial options and to calculate implied volatilities with the aim of accelerating the corresponding numerical methods. With ANNs being universal function approximators, this method trains an...

In this paper, we consider non-linear transformations of classical telegraph process. The main results consist of deriving a general partial differential Equation (PDE) for the probability density (pdf) of the transformed telegraph process, and then presenting the limiting PDE under Kac's...

In a thorough study of binomial trees, Joshi introduced the split tree as a two-phase binomial tree designed to minimize oscillations, and demonstrated empirically its outstanding performance when applied to pricing American put options. Here we introduce a "flexible" version of Joshi's tree,...

In this work, we adapt a Monte Carlo algorithm introduced by Broadie and Glasserman in 1997 to price a π-option. This method is based on the simulated price tree that comes from discretization and replication of possible trajectories of the underlying asset's price. As a result, this algorithm...