In this paper, we suggest a new model for establishing numerical study related to European options pricing problem where assets' prices can be described by stochastic equation with discontinuous sample path (Slow Growth Volatility Jump SGVJ model) which uses non-standard volatility. A special attention is given characteristics of the proposed represented its volatility defined parameters α and ...

Lookback options, in the terminology of finance, are a type of exotic option with path dependency whose the payoff depends on the optimal (maximum or minimum) underlying asset’s price occurring over the life of the option. In this paper, we exploit Mellin transform techniques to find a closed-form solution for European lookback options in BlackScholes model.

An alternative option pricing model is proposed, in which the asset prices follow the jump-diffusion and exhibits mean reversion. The stochastic volatility follows the jump-diffusion with mean reversion. We find a formulation for the European-style option in terms of characteristic functions.

In the context of a Black-Scholes economy and with a no-arbitrage argument, we derive arbitrarily accurate lower and upper bounds for the value of European options on a stock paying a discrete dividend. Setting the option price error below the smallest monetary unity, both bounds coincide, and we obtain the exact value of the option.

We consider a defaultable asset whose risk-neutral pricing dynamics are described by an exponential Lévy-type martingale subject to default. This class of models allows for local volatility, local default intensity and a locally dependent Lévy measure. Generalizing and extending the novel adjoint expansion technique of Pagliarani, Pascucci and Riga [SIAM J. Financial Math. 4 (2013) 265–296], we...