This paper discusses the pitfalls in the pricing of barrier options using approximations of the underlying continuous processes via discrete lattice models. These problems are studied first in a Black-Scholes model. Improvements result from a trinomial model and a further modified model where...

In this paper we study Binomial Models with random time steps. We explain, how calculating values for European and American Call and Put options is straightforward for the Random-Time Binomial Model. We present the conditions to ensure weak-convergence to the Black-Scholes setup and convergence...

At first time in the 124 years old history of the International Statistical Institute (ISI) a session was hold in southern of the Sahara region in Africa, from 16 to 22 August in Durban/South Africa. Hence Denise Lievesley, first female president of ISI said in the Opening Ceremony: „I hope...

The problem of term structure of interest rates modelling is considered in a continuous-time framework. The emphasis is on the bond prices, forward bond prices or LIBOR rates, rather than on the instantaneous rates as in the traditional models. Forward and spot probability measures are...

The forward measure in the discrete time Ho/Lee model is derived and passages to the continuous time limit are carried out under this measure. In particular the continuous time valuation formula for call options on zero coupon bonds is obtained as a limit of its discrete time equivalent as well...

Based on multiparameter subadditive ergodic theorems of Akcoglu and Krengel (1981) and Schürger (1988) we derive an almost sure limit theorem for families of random matrices with a multiparameter which satisfy a supermultiplicativity condition. This gives a multiparameter analogue of results of...

In this paper we present a new approach to incorporate default dependency in intensity-based default risk models. The model uses an arbitrary default dependency structure which is specified by the Copula of the times of default, this is combined with individual intensity-based models for the...

In this paper a new credit risk model for credit derivatives is presented. The model is based upon the ‘Libor market’ modelling framework for default-free interest rates. We model effective default-free forward rates and effective forward credit spreads as lognormal diffusion processes, and...