The Classical and Stochastic Approach to Option Pricing

Black-Scholes model (BS) and lattices are well-known methodologies applied to option pricing, with their own specific features and properties. Briefly, lattices are discrete in the inner computing process and stochastically based, while BS is represented by a continuous functional form without single steps, but deterministic only. The strong assumption of constant volatility and the inability of application in valuing "American" options represent major disadvantages of the BS model. Its main advantage is its simplicity and ease of application. The use of Monte Carlo simulations constitutes an alternative to this model. Its main advantages include a relatively easy procedure of calculation and efficiency. Problems can arise when applied to the "American" option. Likewise, this method does not belong among highly sophisticated ones due to the requirements of prerequisites. If we were to consider a model that can work with the "American" option, i.e. an option that may be exercised at any time before maturity, then calculation using the lattice approach is conceivable. In contrast, the disadvantage of this method lies in the lack of ability to apply continuous consistency with price development history as well as inability to work with a model that would require more underlying assets. Finally, the two approaches, Black-Scholes model and the lattice approach, considered for pricing options, derived their value from IBM stocks as an underlying asset. On individual valuations, accuracy of these valuation models will be observed in accordance with the real option price.