Brownian Motion It was the botanist Robert Brown\cite{Dmouji-2006} who first realized the Brownian Motion (also called Wiener process) when trying to describe the motion exhibited by particles immersed in a gas or liquid. The particles were essentially being bombarded by molecules present within the matter causing displacement or movement. Now as we look at the Brownian Motion from a financial perspective, in the modeling of financial market especially stock market, Brownian Motion plays an important role in building a statistical model. In order to understand this process and the role it plays in financial industry, we need to know that one of most important concepts in building financial models is to understand the Geometric Brownian Motion, …show more content…
The ideas of using a Brownian Motion process to explain the behavior of the risky asset prices were presented by Black-Scholes. Brownian Motion is usually used to model a stock price. However, Brownian Motion process has the independent increments property. This means that the present price must not affect the future price. In fact, the present stock price may influence the price at some time in the future. Hence, Brownian Motion process is not suitable to explain the stock price. Another process, a fractional Brownian Motion process, exhibits a long range dependent property. Therefore, a fractional Brownian Motion process can be used to describe the behavior of stock price instead of Brownian Motion process. The rate of return and volatility in general asset pricing model are usually the constant parameters\cite{HJX-2014}. Actually, the rate of return and volatility in the model are not constant at any time. These parameters are updated depending on time by using the new …show more content…
After evalutating both the Black-Scholes Model and the Brownian Motion, we have come to know that the Black-Scholes Model is quite predictive as it gets close to the observed price. We found that with the Brownian motion it may take on negative values which results certain modelling prices to be frowned upon , hence making Black-Scholes Model more realistic. As we ventured in this study, we found that there is still more research to be done since many of the modern option models stems from the Black-Scholes model. Thus making the modern option pricing models more
The Dow Theory was established from a series of Wall Street Journal editorials authored by Charles H. Dow from 1900 until the time of his death in 1902. Today, even after 110 years they remain the foundation of what we know today as technical analysis. Dow never published his complete theory, but several of his followers compiled his works and that has come to be known as "The Dow Theory”.
Equity markets have become much more volatile. The Chicago Board Options Exchange (CBOE) Volatility Index (VIX) is a “key measure of market expectations of near-term volatility conveyed by S&P 500 stock index option prices. Since its introduction in 1993, VIX has been considered by many to be the world's premier barometer of investor sentiment and market volatility.” When the last M&A Outlook was written, the VIX was at 11.57. At the start of November 2007, the VIX had increased to 23.21.
Our first customer is investor from China who invested large sum of money into KKB’s stocks. He decided to hedge his portfolio and contacted us. We offered him European put option on KKB’s stocks which matures in 9 months with the strike price of $13,1 per GDR. To estimate how much we are to charge for put option, we used data taken from the website of London Stock Exchange (www.londonstockexchange.com), as KKB’s GDR is quoted on this stock exchange. Latest price of the GDR is $16,29 (on 18 April,2008). To calculate volatility we used historical prices of the stock in the interval from 1 January until 18 April, and it is equal to 47,98%. Having all these figures we used Black-Scholes formula and found out the price of put option, which is $0,79. We also checked it on DerivaGem program.
Albert Einstein began to study the movement of particles, which led to “the hypothesis that matter is composed of atoms” (“Albert Einstein” 2). This made Einstein to begin to study the Brownian movement and explained that the reasoning to why “the motion of the pollen grains increased when the temperature increased but, decreased if larger particles were used” (“Albert Einstein.”2). His reasoning was explained “as be...
In 1905, Einstein’s Theory of Special Relativity was proposed. The reason that it is so "special" is because it was part of the more complex and extensive Theory of General Relativity, which was published in 1915. His theory reshaped the world of physics when it contradicted all previous laws of motion erected by Galileo and Newton. By mathematically manipulating these previous laws of motion, physicists in the nineteenth century were able to explain such phenomena as the flow of the ocean, the orbits of planets around the sun, the fall of rocks, and the random behavior of molecules in gases. At first, Einstein faced great opposition when he came up with his radical new theory because the previous laws of motion proposed by Galileo and expanded upon by Newton had remained valid for over two hundred years. However, it wouldn’t be long before the "cement" in the foundation of Newtonian and Galilean physics would begin to crumble.
...phases. Fabozzi and Francis (1977) conducted a study testing the differential effect of bull and bear market conditions for 700 individual securities listed on the NYSE. It was found that the estimated betas of most of the securities were stable in both market conditions. However, Ray (2010) conducted a similar study over a period of ten years using monthly returns of 30 stocks. The results obtained were both mixed and inconclusive. Bowie and Bradford (1997) found that the tests of beta stability are difficult to interpret on their own. Gombola and Kahl (1990) suggest that an OLS estimate of beta requires an estimation period during which the relationship between the market return and the stock return remain stable. However, without this stability, an alternative for forecasting a time-varying relationship such as the Bayesian adjustment process will be required.
Capital Asset Pricing Model (CAPM) is an ex ante concept, which is built on the portfolio theory established by Markowitz (Bhatnagar and Ramlogan 2012). It enhances the understanding of elements of asset prices, specifically the linear relationship between risk and expected return (Perold 2004). The direct correlation between risk and return is well defined by the security market line (SML), where market risk of an asset is associated with the return and risk of the market along with the risk free rate to estimate expected return on an asset (Watson and Head 1998 cited in Laubscher 2002).
The option pricing models is somewhat of a gamble to some investors and a to others a pattern-based method of investing. According to Hoadley Trading & Investment tools (2011), Black-Scholes model is used most commonly to determine the fair market value of the option in play. This model uses five key determinants of an option’s price such as price, strike price, volatility, time to expiration and short term interest rate. This model will let you calculate the option prices quickly but unfortunately it is not too accurate. This limitation is due to it inability to analyze a continuous flow of possibilities, instead the model can only calculate the option price at one point in time.
Recently a new trend has taken up Wall Street. Savvy broker firms have realized that the market is probably controlled by some rules, and those rules have to be found to make more money with the least risk. They hired many mathematicians to look for any formulas that would seem to express the market. Those analyzed previous market trends and used laws of statistics to try to predict the “future” of the market. The funny thing is that at times this approach actually worked. It yielded a slightly more than fifty percent accuracy, and that was enough. (When dealing with tremendous amounts, even a small percentage is not meager.)
The strength of the Big Bang theory lies in the evidence for it, not the mechanism used to explain it. Actually, the theory has been revised a great deal since its first proposition and is probably not exactly as you think it is. I'll explain it in the order of historical development. My apologies if this is a bit technical - don't worry if you don't understand it all.
Good examples of stochastic process among many are exchange rate and stock market fluctuations, blood pressure, temperature, Brownian motion, random walk.
Chapter 11 closes our discussion with several insights into the efficient market theory. There have been many attempts to discredit the random walk theory, but none of the theories hold against empirical evidence. Any pattern that is noticed by investors will disappear as investors try to exploit it and the valuation methods of growth rate are far too difficult to predict. As we said before the random walk concludes that no patterns exist in the market, pricing is accurate and all information available is already incorporated into the stock price. Therefore the market is efficient. Even if errors do occur in short-run pricing, they will correct themselves in the long run. The random walk suggest that short-term prices cannot be predicted and to buy stocks for the long run. Malkiel concludes the best way to consistently be profitable is to buy and hold a broad based market index fund. As the market rises so will the investors returns since historically the market continues to rise as a whole.
Among all the programs available, I firmly believe that the Master in Finance program at Princeton University will be the ideal preparation for my career because of its strong emphasis on quantitative techniques with practical business problem solving. The core courses offered by the program will help me build concrete foundation in financial theories and computational methods; the elective courses, such as Forecasting and Time Series Analysis, will further enhance my modeling techniques for financial forecasting in a broader application. Besides excellent teaching fellows at Princeton University, the close personal attention from academic and career advisors will be invaluable to my professional growth. Furthermore, the small cla...
Physics began when man first started to study his surroundings. Early applications of physics include the invention of the wheel and of primitive weapons. The people who built Stone Henge had knowledge of physical mechanics in order to move the rocks and place them on top of each other. It was not until during the period of Greek culture that the first systematic treatment of physics started with the use of mechanics. Thales is often said to have been the first scientist, and the first Greek philosopher. He was an astronomer, merchant and mathematician, and after visiting Egypt he is said to have originated the science of deductive geometry. He also discovered theorems of elementary geometry and is said to have correctly predicted an eclipse of the sun. Many of his studies were in astronomy but he also observed static electricity. Phythogoras was a Greek philosopher. He discovered simple numerical ratios relating the musical tones of major consonances, to the length of the strings used in sounding them. The Pythagorean theorem was named after him, although this fundamental statements of deductive geometry was most likely first an idea from Egyptian methods of measurements. With the help of his followers he discovered that the earth was a sphere, but he did not believe it revolved around the sun.
In the modern world, financial markets play a significant role, with huge volumes of everyday dealings. They form part of contemporary economic lifestyle and determine the level of success of many people. Humans have always been uncertain of what the future holds and thus, tried to forecast it. The forecast of course cannot omit the likelihood of “easy money” by forecasting the prices of equity markets in the future.