We propose a new algorithm for computing the Greeks in jump-diffusion settings using binomial trees. We further demonstrate that the Greeks for European options converge to the Malliavin Greeks in the continuous time model. Our proposed algorithm is efficient, because the price and the Greeks...

This paper proposes a new efficient algorithm for the computation of Greeks for options using the binomial tree. We also show that Greeks for European options introduced in this article are asymptotically equivalent to the discrete version of Malliavin Greeks. This fact enables us to show that...

In the last decade, many kinds of exotic options have been traded and introduced in the financial market. This paper describes a new kind of exotic option, lookback options with knock-out boundaries. These options are knock-out options whose pay-offs depend on the extrema of a given securities...

The pricing problems of credit derivatives have received much attention in the last decade. An important unresolved problem, however, is the pricing of credit derivatives under the general environment in which the interest rate process and the hazard rate process are stochastic. This article...

The pricing problem of options with an early exercise feature, such as American options, is one of the important topics in mathematical finance. The pricing formulas for American options, however, have not been found in general and the numerical methods are required to derive the price of these...