Essays about: "Black-Scholes PDE"

Showing result 1 - 5 of 7 essays containing the words Black-Scholes PDE.

  1. 1. Pricing American and European options under the binomial tree model and its Black-Scholes limit model

    University essay from Linnéuniversitetet/Institutionen för matematik (MA)

    Author : Yuankai Yang; [2017]
    Keywords : European option; American option; Binomial tree model; Black-Scholes PDE; Black-Scholes option pricing formula;

    Abstract : We consider the N step binomial tree model of stocks. Call options and put options of European and American type are computed explicitly. With appropriate scaling in time and jumps,  convergence of the stock prices and the option prices are obtained as N-> infinite. READ MORE

  3. 2. Convertible Bonds: a Qualitative and Numerical Analysis

    University essay from KTH/Matematik (Inst.)

    Author : Bianca Dufour Partanen; Emelie Järnberg; [2014]
    Keywords : ;

    Abstract : A convertible bond is a nancial instrument which has both an equity part and a xed-income part. The pricing of nancial securities has for quite obvious reasons become extensively studied in the past decades. In this paper we study the Black-Scholes model, based on the equity value, where the equity is modelled by geometric brownian motion. READ MORE

  4. 3. Inverse Parameter Estimation using Hamilton-Jacobi Equations

    University essay from KTH/Numerisk analys, NA

    Author : Mikael Helin; [2013]
    Keywords : Hamilton-Jacobi equation. Optimal control. Euler method.; Hamilton-Jacobi ekvationer. Optimal styrning. Eulers stegmetoder;

    Abstract : Inthis degree project, a solution on a coarse grid is recovered by fitting apartial differential equation to a few known data points. The PDE to consideris the heat equation and the Dupire’s equation with their synthetic data,including synthetic data from the Black-Scholes formula. READ MORE

  5. 4. Pricing a Multi-Asset American Option in a Parallel Environment by a Finite Element Method Approach

    University essay from Matematiska institutionen

    Author : Deniz Kaya; [2011]
    Keywords : multi-asset American options; Parallel Computing; Finite Element Method-of-lines; Projected Successive Over Relaxation for American option pricing;

    Abstract : There is the need for applying numerical methods to problems that cannot be solved analytically and as the spatial dimension of the problem is increased the need for computational recourses increase exponentially, a phenomenon known as the “curse of dimensionality”. In the Black-Scholes-Merton framework the American option pricing problem has no closed form solution and a numerical procedure has to be employed for solving a PDE. READ MORE

  6. 5. Meshfree methods in option pricing

    University essay from Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE); Tillämpad matematik och fysik (MPE-lab)

    Author : Anna Belova; Tamara Shmidt; [2011]
    Keywords : Financial Mathematics; option pricing; RBF; PDE; meshfree methods;

    Abstract : A meshfree approximation scheme based on the radial basis function methods is presented for the numerical solution of the options pricing model. This thesis deals with the valuation of the European, Barrier, Asian, American options of a single asset and American options of multi assets. The option prices are modeled by the Black-Scholes equation. READ MORE