Hedging down-and-out puts (and up-and-out calls), where the maximum payoff is reached just before a barrier is hit that would render the claim worthless afterwards, is challenging. All hedging methods potentially lead to large errors when the underlying is already close to the barrier and the...

Hedging down-and-out puts (and up-and-out calls), where the maximum payoff is reached just before a barrier is hit that would render the claim worthless afterwards, is challenging. All hedging methods potentially lead to large errors when the underlying is already close to the barrier and the...

Sharp asymptotic lower bounds on the expected quadratic variation of the discretization error in stochastic integration are given when the integrator admits a predictable quadratic variation and the integrand is a continuous semimartingale with nondegenerate local martingale part. The theory...

The approach that allows find European option price on the assumption of hedging at discrete times is proposed. The routine allows find the option price not for lognormal distribution functions of underlying asset only but for other classes of distribution functions too. It is shown that there...

In the setting of the Black-Scholes option pricing market model, the seller of a European option must trade continuously in time. This is, of course, unrealistic from the practical viewpoint. He must then follow a discrete trading strategy. However, it does not seem natural to hedge at...