Modern pricing models Essay Example | Topics and Well Written Essays - 500 words

Modern pricing models - Essay Example A geometric Brownian motion (GBM), or an exponential Brownian motion, refers to a stochastic process that runs continuously over time in which case the logarithm of the randomly varying quantity follows a Wiener process, or the Brownian motion with a drift. According to Vose (2008), the Brownian motion is a significant example of the stochastic processes that satisfy a stochastic differential equation (SDE). Most applications of Brownian motion incorporate, in particular, mathematical finance, especially in consideration of the model stock prices, such as is the case with Black-Scholes model. As such, the geometric Brownian motion is a core building block of modern finance. This is particularly in the case of the Black Scholes model whereby the underlying stock price is assumedly in line with the principles and expectations of the GBM dynamics (Vose 2008, p.37). When an investor wants to make an investment in the binary options, the most important element that he or she should account for is the fluctuation in the price that a particular commodity or good is likely to experience over a specific period of the trading process. As such, once an investor is able to track the volatility of the price changes with some degree of accuracy, they get to a better elevated position to determine the right the price of an option at the point when it expires, thereby increasing significantly his or her chances of being in the money at the right time. Therefore, such an investor will be in a better position to collect the highest level of return on his or her investment (Vose 2008, p.115). According to Benth (2004), it is quite fortunate that top economists conducted a great deal of research in the field of Wiener motion, such as Fischer Black and Myron Scholes who came up with the infamous Black-Scholes formula instrumental in predicting the market volatility of a stock. The geometric Brownian motion forms an important element of this formula, and