Using Computer Algebra Packages to Complement the Spreadsheet Construction of Binomial Option Trees: The Example of Mathcad (original) (raw)

The Binomial and Black-Scholes Option Pricing Models: A Pedagogical Review with Vba Implementation

— In this paper, a pedagogical review of two option pricing models is presented; specifically, the Binomial and the Black-Scholes pricing models. Theoretically these models converge for a very large number of exercise periods within a single option contract by virtue of the central limit theorem being based on the random walk and the Brownian motion processes respectively. This relationship is graphically illustrated by the use of an MS VBA implementation of the models.

The CRR Binomial Option Pricing Model An analysis of Accuracy, Convergence and Stability Using Python

In finance, the binomial options pricing model provides a generalizable numerical method for the valuation of options. Essentially, the model uses a "discrete-time" (lattice based) model of the varying price over time of the underlying financial instrument, addressing cases where the closed-form Black-Scholes formula is wanting. The binomial model was first proposed by William Sharpe in the 1978 and was formalized by Cox, Ross and Rubinstein (CR) in 1979 and by Rendleman and Bartter in that same year. This paper will calculate the value of the range of options under the CRR model using Python. It will then investigate the pricing accuracy and convergence of the algorithm. We will then investigate other methods to increase the efficiency, convergence, and stability of the method.

Option pricing: A simplified approach

Journal of Financial Economics, 1979

This paper presents a simple discrete-time model for valuing options. The fundamental economic principles of option pricing by arbitrage methods are particularly clear in this setting. Its development requires only elementary mathematics, yet it contains as a special limiting case the celebrated Black-Scholes model, which has previously been derived only by much more difficult methods. The basic model readily lends itself to generalization in many ways. Moreover, by its very construction, it gives rise to a simple and efficient numerical procedure for valuing options for which premature exercise may be optimal.

A Numerical Investigation in Option Valuation

In modern finance, derivatives like options are actively traded on many exchanges throughout the world. Since pricing option is a challenging task, it attracts the attention of many researchers nowadays. In many cases calculation of large number of prices is required in short time, so fast and accurate calculation of option price is crucial. This paper introduces some fundamental concepts on underlying option valuation theory including implementation of computational tools. To do this, numerical methods such as Binomial Trees, Monte Carlo Simulation are discussed. Both these numerical techniques are used to price the most desirable European options. Hence the results are compared with the standard Black-Scholes-Merton Model with the help of a computer algebra system MATLAB.