Quasi Pricing of European Options

Pricing European Options without Probability∗

It is well known that in the case where the stock price St is governed by the equation dSt/St = μdt + σdWt, any European option satisfying weak regularity conditions has a fair price (the Black—Scholes formula and its generalizations). We consider the case where no probabilistic assumptions are made about St; instead, we assume that the derivative security D which pays a dividend of (dSt/St) (t...

European Options Pricing Using Monte Carlo Simulation

European options can be priced using the analytical solution of the Black-Scholes-Merton differential equation with the appropriate boundary conditions. A different approach and the one commonly used in situations where no analytical solution is available is the Monte Carlo Simulation. We present the results of Monte Carlo simulations for pricing European options and we compare with the analyti...

Pricing European Options in Realistic Markets

We investigate the relation between the fair price for European-style vanilla options and the probability of short-term returns on the underlying asset in the absence of transaction costs. If the asset’s future price has finite expectation, the option’s fair value satisfies a parabolic partial differential equation of the Black-Scholes type in the absence of arbitrage opportunities. However, th...

A Parallel Quasi-Monte Carlo Approach to Pricing American Options

A Quasi-radial Basis Functions Method for American Options Pricing