Application of Monte Carlo Simulation in the Assessment of European Call Options (original) (raw)
Related papers
OPTIONS: A MONTE CARLO APPROACH
This paper develops a Monte Carlo simulation method for solving option valuation problems. The method simulates the process generating the returns on the underlying asset and invokes the risk neutrality assumption to derive the value of the option. Techniques for improving the efficiency of the method are introduced. Some numerical examples are given to illustrate the procedure and additional applications are suggested.
The Art of Modeling Financial Options: Monte Carlo Simulation
Modeling is important because scientists investigate the world around us by building models that simulate real-world problems. Modeling is neither science nor mathematics; it is the craft that builds bridges between the two. Progress in modeling dynamics has always been closely associated with advances in computing. Monte Carlo simulation/modeling or probability simulation is a technique frequently used in the financial markets to understand complex financial instruments. It is used to scrutinise the impact of risk and uncertainty in financial and other forecasting models. It is very useful when complex financial instruments need to be priced. Exotic options are listed on the JSE on its Can-Do platform. Most listed exotic options are marked-to-model and the JSE needs accurate values at the end of every day. Monte Carlo methods in a local volatility framework are implemented. This paper discusses how Monte Carlo (MC) simulation is implemented when exotic options like Barriers are valued. We further summarise the historical development in modern computing and the development of the Monte Carlo 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.
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.
Options pricing: using simulation for option pricing
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
Option Pricing And Monte Carlo Simulations
Journal of Business & Economics Research (JBER), 2011
The advantage of Monte Carlo simulations is attributed to the flexibility of their implementation. In spite of their prevalence in finance, we address their efficiency and accuracy in option pricing from the perspective of variance reduction and price convergence. We demonstrate that increasing the number of paths in simulations will increase computational efficiency. Moreover, using a t-test, we examine the significance of price convergence, measured as the difference between sample means of option prices. Overall, our illustrative results show that the Monte Carlo simulation prices are not statistically different from the Black-Scholes type closed-form solution prices.
The Comparative Study of Finite Difference Method and Monte Carlo Method for Pricing European Option
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.
Remarks on Monte Carlo Method in Simulating Financial Problems
Mathematical Theory and Modeling, 2012
In this paper, an exposition is made on the use of Monto Carlo method in simulation of financial problems. Some selected problems in financial economics such as pricing of plain vanilla options driven by continuous and jump stochastic processes are simulated and results obtained.
Monte Carlo simulation in the case of a single risk factor and evaluation of a European option
2014
This article presents the Monte Carlo method in the context of stochastic simulation models. It is used to calculate a numerical value using random processes. Indeed, it is to isolate a number of variables and their effect a probability distribution. Our research aims to make practical use of the main operative techniques[1] of Monte Carlo simulation applied to finance. In this article, we describe how to develop Monte Carlo simulations in the presence of a single risk factor Y.
Monte Carlo Methods in Finance
In this thesis, Monte Carlo methods are elaborated in terms of the notion of the performance of games of chance and observing their out- comes based on sampling random numbers and calculating the volume of possible outcomes. The basic tool of generating random numbers is the Monte Carlo simulation. The variance reduction techniques and their applications to pricing options are also being reviewed for their crucial role in ensuring the reduction of the error occurrence in variance. More- over, the use of deterministic low-discrepancy sequences, also known as quasi-Monte Carlo methods for the valuation of complex derivative se- curities are being described. Monte Carlo simulation is a widely used tool in finance for computing the prices of options as well as their price sensitivities, which are known as Greeks. Furthermore, background about stochastic differential equations (SDEs) is introduced and defined in terms of stochastic calculus.