A Comparative Study of Pricing Option with Efficient Methods

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.

Numerical methods form an important part of options pricing and especially in cases where there is no closed form analytic formula. We discuss two of the primary numerical methods that are currently used by financial professionals for determining the price of an options namely Monte Carlo method and finite difference method. Then we compare the convergence of the two methods to the analytic Black-Scholes price of European option. Monte Carlo method is good for pricing exotic options while Crank Nicolson finite difference method is unconditionally stable, more accurate and converges faster than Monte Carlo method when pricing standard options.

Journal of the Korean Society for Industrial and Applied Mathematics, 2011

A new method for option pricing based on the trinomial tree method is introduced. The new method calculates the local average of option prices around a node at each time, instead of computing prices at each node of the trinomial tree. Local averaging has a smoothing effect to reduce oscillations of the tree method and to speed up the convergence. The option price and the hedging parameters are then obtained by the compact scheme and the Richardson extrapolation. Computational results for the valuation of European and American vanilla and barrier options show superiority of the proposed scheme to several existing tree methods.

This paper presents binomial model for pricing vanilla options. Binomial model can be used to accurately price American style options than the Black-Scholes model as it takes into consideration the possibilities of early exercise and other factors like dividends. The strength and weakness of this model were considered. This model is both computationally efficient and accurate but not adequate to deal with path dependent options.

Numerical methods form an important part of options pricing and especially in cases where there is no closed form analytic formula. We discuss two of the primary numerical methods that are currently used by financial professionals for determining the price of an options namely Monte Carlo method and finite difference method. Then we compare the convergence of the two methods to the analytic Black-Scholes price of European option. Monte Carlo method is good for pricing exotic options while Crank Nicolson finite difference method is unconditionally stable, more accurate and converges faster than Monte Carlo method when pricing standard options.

Winter Simulation Conference, 2000

Monte Carlo simulation is a popular method for pricing financial options and other derivative securities because of the availability of powerful workstations and recent advances in applying the tool. The existence of easy-to-use software makes simulation accessible to many users who would otherwise avoid programming the algorithms necessary to value derivative securities. This paper presents examples of option pricing and

Numerical methods form an important part of options pricing and especially in cases where there is no closed form analytic formula. We discuss two of the primary numerical methods that are currently used by financial professionals for determining the price of an options namely Monte Carlo method and finite difference method. Then we compare the convergence of the two methods to the analytic Black-Scholes price of European option. Monte Carlo method is good for pricing exotic options while Crank Nicolson finite difference method is unconditionally stable, more accurate and converges faster than Monte Carlo method when pricing standard options.

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.

International Journal of Scientific and Research Publications, 2023

In this paper we compare Weibull and Mixed-Lognormal-Weibull Option Pricing Models. The data for this study were obtained from Australian Clearing House of Australian Securities Exchange (ASX) which consists of 50 enlisted stocks in the clearing house as products of monthly market summary for long term options from 3rd January, 2017 to 31st December, 2019. The data were properly arranged according to 25, 27, 28, 29 and 30 maturity days. With the help R-package, we obtain the parameters of Weibull (WBS) and MLWBS and the goodness of fit test was conducted to find how best fit the two models are in Black-Scholes Option Pricing Model and the result revealed that under the null hypothesis of a good fit it is accepted (P>0.05) that WBS is a good fit in Black-Scholes option pricing model while MLWBS is a good fit only at the maturity days of 25 and 27 (shorter maturity days) Hence, we affirmed that WBS is a selective alternative option pricing model while MLWBS should only be applied when the expiration days of options are shorter.

— 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.