We present a fully non-parametric method for extracting risk neutral densities (RNDs) from observed option prices. The aim is to obtain a continuous, smooth, monotonic, and convex pricing function that is twice differentiable. Thus, irregularities such as negative probabilities that afflict many...

This paper deals with the problem of discrete time option pricing using the multifractional Black–Scholes model with transaction costs. Using a mean self-financing delta hedging argument in a discrete time setting, a European call option pricing formula is obtained. The minimal price of an...

We use supersymmetry to find the isospectral partners of Black–Scholes Hamiltonian without a potential and with a double knock out barrier potential. The pricing kernels for these Hamiltonians have also been obtained.

It is shown that the arbitrage free portfolio paradigm being applied to a portfolio with an arbitrary number of shares N allows for the extended solution in which the option price F depends on N. However the resulting stock hedging expense Q=MF (where M is the number of options in the portfolio)...

There is a well-developed framework, the Black–Scholes theory, for the pricing of contracts based on the future prices of certain assets, called options. This theory assumes that the probability distribution of the returns of the underlying asset is a Gaussian distribution. However, it is...

Extending previous work on non-equilibrium option pricing theory (Eur. Phys. J. 14 (2000) 383–394), a mean field approach is developed to understand the curvature of (implied by Black–Scholes (BS)) volatility surfaces (curves) as a function of moneyness (strike price divided by price). The...

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 network parameterization of option prices. The accuracy...

We propose a new ‘hedged’ Monte-Carlo (HMC) method to price financial derivatives, which allows to determine simultaneously the optimal hedge. The inclusion of the optimal hedging strategy allows one to reduce the financial risk associated with option trading, and for the very same reason...

This paper presents a model for option pricing in markets that experience financial crashes. The stochastic differential equation (SDE) of stock price dynamics is coupled to a post-crash market index. The resultant SDE is shown to have stock price and time dependent volatility. The partial...

This paper deals with the problem of pricing European currency options in the mixed fractional Brownian environment. Both the pricing formula and the mixed fractional partial differential equation for European call currency options are obtained. Some Greeks and the estimator of volatility are...