The simulation of the Libor Market Model (LMM) is extensively studied in the framework of quantum finance. The imperfectly correlated Libor rates are simulated based on a Gaussian quantum field and a recursion equation of nontrivial stochastic drift. The Libor options are studied using both the...

In this paper we are interested in Monte Carlo pricing of American options via the Longstaff–Schwartz algorithm. In particular, we show that it is possible to obtain a variance reduction technique based on importance sampling by means of Girsanov theorem. The almost sure convergence of the...

In this paper we propose a model of electricity market based on the forward rate dynamics described by a diffusion with jumps as a generalization of the classical diffusion approach. We consider jump components resulting from a coupled continuous-time random walk (CTRW) with jump lengths...

Neural network algorithms are applied to the problem of option pricing and adopted to simulate the nonlinear behavior of such financial derivatives. Two different kinds of neural networks, i.e. multi-layer perceptrons and radial basis functions, are used and their performances compared in...

High-frequency returns of the DAX German blue chip stock index are used to test geometric Brownian motion, the standard model for financial time series. Even on a 15-s time scale, the linear correlations of DAX returns have a zero-time delta function which carries 90% of the weight, while the...

We show that our earlier generalization of the Black–Scholes partial differential equation (pde) for variable diffusion coefficients is equivalent to a Martingale in the risk neutral discounted stock price. Previously, the equivalence of Black–Scholes to a Martingale was proven for the case...

In this paper, we extend a delayed geometric Brownian model by adding a stochastic volatility term, which is driven by a hidden process of fast mean reverting diffusion, to the delayed model. Combining a martingale approach and an asymptotic method, we develop a theory for option pricing under...

The industry standard Black–Scholes option pricing formula is based on the current value of the underlying security and other fixed parameters of the model. The Black–Scholes formula, with a fixed volatility, cannot match the market’s option price; instead, it has come to be used as a...

Continuous-time random walks are a well suited tool for the description of market behaviour at the smallest scale: the tick-to-tick evolution. We will apply this kind of market model to the valuation of perpetual American options: derivatives with no maturity that can be exercised at any time....

This paper deals with the problem of discrete time option pricing by a mixed Brownian-fractional subdiffusive Black–Scholes model. Under the assumption that the price of the underlying stock follows a time-changed mixed Brownian-fractional Brownian motion, we derive a pricing formula for the...