This paper presents a method to determine the price of a cliquet option, as well as its sensitivity to changes in the market, the Greeks, for deterministic (also incorporating skews) and stochastic (Hestonian) volatility and, lognormal and jump-diffusion asset price - processes, with almost...

The paper introduces a method which reduces the computation of the Greeks back to a similar problem as of computing the price of the derivative in question; that is, if there is an efficient algorithm pricing the derivative then in order to compute the Greeks we will use the same efficient...

We demonstrate a fast and numerically stable pricing algorithm that can determine the price of a guaranteed rate product, as well as its sensitivity to changes in the market (the Greeks) both for lognormal and jump-diffusion asset price processes, with almost machine precision in a fraction of a...

Multi-dimensional transformation algorithms can be an excellent tool for solving multi-variate stochastic models, such as a financial model with features including underlying modeled by a stochastic process, stochastic volatility, stochastic interest rates. Our algorithm builds on the recently...

In this paper, we use the key concept of arbitrage free valuation to close the gap between option pricing and ALM. We derive a continuous-time equivalent of the discrete ALM model and show how, e.g., equity options and swaptions ought to be valued. We demonstrate that normally distributed equity...

The use of Panjer's algorithm has meanwhile become a widespread standard technique for actuaries (Kuon et al., 1955). Panjer's recursion formula is used for the evaluation of compound distributions and can be applied to life and general insurance problems. The discrete version of Panjer's...

Numerical inversion of Laplace transforms is a powerful tool in computational probability. It greatly enhances the applicability of stochastic models in many fields. The present paper introduces a numerical inversion method which employs a Gaussian quadrature rule in order to perform a numerical...

The most recent optimization algorithm for (s, S) order policies with continuous demand was developed byFedergruen and Zipkin (1985). This was also the first efficient algorithm, which uses policy iteration instead ofdiscretization. Zheng and Federgruen (1991) developed an even more efficient...

This paper extends a fundamental result about single-item inventory systems. This approach allows more general performance measures, demand processes and order policies, and leads to easier analysis and implementation, than prior research. We obtain closed form expressions for the Laplace...