Black Scholes Case Study

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This chapter will mainly discuss about Black Scholes model, which is applied in this research. The history of Black Scholes will be introduced followed by Geometric Brownian motion equation history. Besides these two, we will also explain briefly about financial application of gold share price.

2.2 Gold Share Price

Shahriar Shafiee (2010) is concerned about global gold market and gold price forecasting. He stated that in practice, the price and production behavior of gold differs from most other mineral commodities. In the 2008 financial crisis, the gold price increased by 6% while many key mineral prices fell and other equities dropped by around 40%. The unique and diverse of gold demand and supply do not correlate highly with changes in other financial assets. He had concluded that the gold supply showed that around 160,000 tons of gold has been mined in history up to the end of 2008. Gold demand by jewelry, industrial and central bank reserves equate to approximately 100,000, 30,000 and 30,000 tons, respectively. A significant proportion of the demand side of gold is attributed to jewelry, which can in turn be injected into the supply side.

There are a number of different price modeling methods that have been discussed in financial literature. The geometric Brownian motion and mean reversion are two classical approaches which form the basis for some newer methods, such as stochastic price forecasting and mean reverting jump diffusion models. These models focus on historical price movements and a random term to estimate future prices. They do not consider price jumps or dips in the models (Shahriar Shafiee, 2010).

2.3 Black Scholes Option Pricing Model

In the research made by Arend (2008) on the emergence Blac...

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We have devoted our study to apply statistical methods to stochastic differential equations, initially to estimate by the historical method, which uses the property of independence and normality of the outputs. The Black-Scholes model and its alternatives are largely used by the professionals. For that, the estimate of its parameters deserves that we interested in other techniques more adapted: discrete method. The discrete method makes it possible to estimate the parameters of Black-Scholes model in the case of the discrete paths. In this method, it is necessary to observe the process during a certain interval of time i.e. to use all the observations of the paths. The discrete method being based on the criterion which minimizes the variances of the estimators and the small errors with the true values of the share price of gold(Khaldi Khaled, 2010).

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