This paper suggests a simple method based on a Chebyshev approximation at Chebyshev nodes to approximate partial differential equations. It consists in determining the value function by using a set of nodes and basis functions. We provide two examples: pricing a European option and determining...

This paper introduces a new computational tool for the analysis of the risks embedded in a set of prices of European-style options. The software enables the estimation of the risk-neutral density (RND) from the observed option prices by means of orthogonal polynomial expansions. Orthogonal...

This paper studies the superhedging prices and the associated superhedging strategies for European and American options in a non-linear incomplete market with default. We present the seller's and the buyer's point of view. The underlying market model consists of a risk-free asset and a risky...

We consider the problem of maximizing the worst-case return of a portfolio when the manager can invest in stocks as well as European options on those stocks, and the stock returns are modeled using an uncertainty set approach. Specifically, the manager knows a range forecast for each factor...

The paper analyses the impact of illiquidity of a stock paying no dividends on the pricing of European options written on that stock. In particular, it is shown how illiquidity generates price bounds on an option on this stock, even in the absence of other imperfections, such as transaction...

We introduce a method for the approximation of a lognormal stock price process by a Cox, Ross and Rubinstein (CRR) type of binomial scheme, which allows to reach arbitrary speed of convergence of order O(n^{-(N/2)}), for any integer N>0.

We study the value of European security derivatives in the Black-Scholes model when the underlying asset ξ is approximated by random walks ξ⁽ⁿ⁾. We obtain an explicit error formula, up to a term of order O(n^{-(3/2)}), which is valid for general approximating schemes and general payoff...

<Para ID="Par1">We consider the valuation of options with stressed-beta in a reduced form model. Under this two-state beta model, we provide the analytic pricing formulae for the European options and American options as the integral forms. Specifically, we provide the integral representation of the early...</para>

This paper presents a European option pricing model by applying the Model-Order-Reduction (MOR) method. A European option pricing theorem based on Black–Scholes' equation is implemented by the Finite-Difference Method (FDM). However, the numerical models generated by the FDM could be...