Marcellino Gaudenzi

New insights on testing the efficiency of methods of pricing and hedging American options

Abstract With reference to the evaluation of the speed–precision efficiency of pricing and hedging of American Put options, we present and discuss numerical results obtained on the basis of four different large enough random samples according to the relevance of the American quality (relative importance of the early exercise opportunity) of the options. Here we provide a comparison of the best methods (lattice based numerical methods and an approximation of the American Premium analytical procedure) known in literature along with some key methodological remarks.

Pricing Ratchet Equity-Indexed Annuities with Early Surrender Risk in a CIR++ Model

In this article we propose a lattice algorithm for pricing simple Ratchet equity-indexed annuities (EIAs) with early surrender risk and global minimum contract value when the asset value depends on the CIR++ stochastic interest rates. In addition we present an asymptotic expansion technique that permits us to obtain a first-order approximation formula for the price of simple Ratchet EIAs without early surrender risk and without a global minimum contract value. Numerical comparisons show the reliability of the proposed methods.

Pricing And Hedging American Barrier Options By A Modified Binomial Method

The aim of this work is to present a modification of the standard binomial method which allows to price American barrier options improving the efficiency of the trinomial methods. Our approach is based on a suitable interpolation of binomial values and allows to price and hedge such options also in the critical case of near barriers. All the different types of single barrier options are considered, in the case of knock-in barriers a new implementation of the binomial method is provided.

Pricing cliquet options by tree methods

This paper focuses on the problem of pricing the cliquet options which provide a guaranteed minimum annual return. The tree method which we propose simplifies the standard binomial Cox–Ross–Rubinstein approach which, in this context, is problematic from a computational point of view. Our technique provides very efficient and reliable evaluations in a Black-Scholes framework with piecewise constant interest rates and volatilities.

Fast binomial procedures for pricing Parisian/ParAsian options

The discrete procedures for pricing Parisian/ParAsian options depend, in general, on three dimensions: time, space, time spent over the barrier. Here we present some combinatorial and lattice procedures which reduce the computational complexity to second order. In the European case the reduction was already given by Lyuu and Wu (Decisions Econ Finance 33(1):49–61, 2010) and Li and Zhao (J Deriv 16(4):72–81, 2009), in this paper we present a more efficient procedure in the Parisian case and a different approach (again of order 2) in the ParAsian case. In the American case we present new procedures which decrease the complexity of the pricing problem for the Parisian/ParAsian knock-in options. The reduction of complexity for Parisian/ParAsian knock-out options is still an open problem.