18 research outputs found

    Pricing European convertible bonds: geometric brownian motion vs. CGMY

    Get PDF
    Paper presented at Strathmore International Math Research Conference on July 23 - 27, 201

    Computational Methods for Game Options

    Get PDF
    Game options are American-type options with the additional property that the seller of the option has the right the cancel the option at any time prior to the buyer exercise or the expiration date of the option. The cancelation by the seller can be achieved through a payment of an additional penalty to the exercise payoff or using a payoff process greater than or equal to the exercise value. The main contribution of this thesis is a numerical framework for computing the value of such options with finite maturity time as well as in the perpetual setting. This framework employs the theory of weak solutions of parabolic and elliptic variational inequalities. These solutions will be computed using finite element methods. The computational advantage of this framework is that it allows the user to go from one type of process to another by changing the stiffness matrix in the algorithm. Several types of Levy processes will be used to show the functionality of this method. The processes considered are of pure diffusion type (Black-Scholes model), the CGMY process as a pure jump model and a combination of the two for the case of jump diffusion. Computational results of the option prices as well as exercise, hold and cancelation regions are shown together with numerical estimates of the error convergence rates with respect to the L2 norm and the energy norm

    Option Pricing Under the Variance Gamma Process

    Get PDF
    In this dissertation we price European and American vanilla and barrier options assuming that the underlying follows the variance gamma process. We solve numerically the problem implementing a finite difference algorithm and we present numerical experiments on the option pricing. This dissertation includes detailed algorithms as well as programming code in C++ to price European and American vanilla and barrier options under variance gamma.Variance Gamma Process; Option Pricing Under Variance Gamma; Numerical Solution of Option Prices Under Variance Gamma; Numerical Solution of Variance Gamma PIDE; Numerical Solutions of Variance Gamma Partial Differential Equation; Programming Code for Variance Gamma Option Pricing

    Stochastic time-changed Lévy processes with their implementation

    Get PDF
    Includes bibliographical references.We focus on the implementation details for Lévy processes and their extension to stochastic volatility models for pricing European vanilla options and exotic options. We calibrated five models to European options on the S&P500 and used the calibrated models to price a cliquet option using Monte Carlo simulation. We provide the algorithms required to value the options when using Lévy processes. We found that these models were able to closely reproduce the market option prices for many strikes and maturities. We also found that the models we studied produced different prices for the cliquet option even though all the models produced the same prices for vanilla options. This highlighted a feature of model uncertainty when valuing a cliquet option. Further research is required to develop tools to understand and manage this model uncertainty. We make a recommendation on how to proceed with this research by studying the cliquet option’s sensitivity to the model parameters

    Pricing Convertible Bonds with Credit Risk under Regime Switching and Numerical Solutions

    Get PDF
    This paper discusses the convertible bonds pricing problem with regime switching and credit risk in the convertible bond market. We derive a Black-Scholes-type partial differential equation of convertible bonds and propose a convertible bond pricing model with boundary conditions. We explore the impact of dilution effect and debt leverage on the value of the convertible bond and also give an adjustment method. Furthermore, we present two numerical solutions for the convertible bond pricing model and prove their consistency. Finally, the pricing results by comparing the finite difference method with the trinomial tree show that the strength of the effect of regime switching on the convertible bond depends on the generator matrix or the regime switching strength

    Option Pricing Under the Variance Gamma Process

    Get PDF
    In this dissertation we price European and American vanilla and barrier options assuming that the underlying follows the variance gamma process. We solve numerically the problem implementing a finite difference algorithm and we present numerical experiments on the option pricing. This dissertation includes detailed algorithms as well as programming code in C++ to price European and American vanilla and barrier options under variance gamma

    Option Pricing under the Variance Gamma Process

    Full text link

    Option Pricing Under the Variance Gamma Process

    Get PDF
    In this dissertation we price European and American vanilla and barrier options assuming that the underlying follows the variance gamma process. We solve numerically the problem implementing a finite difference algorithm and we present numerical experiments on the option pricing. This dissertation includes detailed algorithms as well as programming code in C++ to price European and American vanilla and barrier options under variance gamma
    corecore