In a thorough study of binomial trees, Joshi introduced the split tree as a two-phase binomial tree designed to minimize oscillations, and demonstrated empirically its outstanding performance when applied to pricing American put options. Here we introduce a "flexible" version of Joshi's tree,...

I document a sizeable bias that might arise when valuing out of the money American options via the Least Square Method proposed by Longstaff and Schwartz (2001). The key point of this algorithm is the regression-based estimate of the continuation value of an American option. If this regression...

In this short paper, we study the asymptotics for the price of call options for very large strikes and put options for very small strikes. The stock price is assumed to follow the Black-Scholes models. We analyze European, Asian, American, Parisian and perpetual options and conclude that the...

We provide ready-to-use formulas for European options prices, risk sensitivities, and P&L calculations under Lévy-stable models with maximal negative asymmetry. Particular cases, efficiency testing, and some qualitative features of the model are also discussed.

We present a method for the arbitrage-free interpolation of plain-vanilla option prices and implied volatilities, which is based on a system of integral equations that relates terminal density and option prices. Using a discretization of the terminal density, we write these integral equations as...

The replicating portfolio approach is a well-established approach carried out by many life insurance companies within their Solvency II framework for the computation of risk capital. In this note, we elaborate on one specific formulation of a replicating portfolio problem. In contrast to the two...

In this paper, we consider a two-dimensional risk process in which the companies split each claim and premium in a fixed proportion. It serves as a classical framework of a quota-share reinsurance contract for a given business line. Such a contract reduces the insurer's exposure to the...

This paper presents a comprehensive extension of pricing two-dimensional derivatives depending on two barrier constraints. We assume randomness on the covariance matrix as a way of generalizing. We analyse common barrier derivatives, enabling us to study parameter uncertainty and the risk...

Binomial trees are very popular in both theory and applications of option pricing. As they often suffer from an irregular convergence behavior, improving this is an important task. We build upon a new version of the Edgeworth expansion for lattice models to construct new and quickly converging...