The Black Scholes Model

This paper examines the relationship between heat equation and the Black-Scholes model. It shows from both intuitive reasoning and mathematical proof, a derivation of the Black-Scholes model from the combustion equation. It further places the relationship of underlying assets as a two-part diffusion equation having a constant drift and a random shock part. Amount change in the price is equal to the certainty of movement of the price plus the uncertainty caused by the volatility. From here a simulation of a pension pricing from Monte Carlo method of forecasting asset prices was generated and further modelled to have Retirement Savings Account price as an underlying value to create an options product deemed suitable to resolve the need of including

The Black-Scholes equation was the mathematical justification for the trading that plunged the world's banks into catastrophe. It was the holy grail of investors. The Black-Scholes equation, brainchild of economists Fischer Black and Myron Scholes, provided a rational way to price a financial contract when it still had time to run. It was like buying or selling a bet on a horse, halfway through the race. It opened up a new world of ever more complex investments, blossoming into a gigantic global industry. But when the sub-prime mortgage market turned sour, the darling of the financial markets became the Black Hole equation, sucking money out of the universe in an unending

Position 3 guarantees temperature increase either way you move. Other positions may give higher or lower temperature depending on the direction of movement. We recall optimization local minimum and local maximum. In Egbe(2013) these are points on which define lowest points guaranteeing next upside and downside movements respectively. It follows that the number and arrow positions represent a kind of concavity of the temperature profile. Then we can say that, change in temperature is proportional to the concavity of temperature. The Black-Scholes equation was useful, it was precise, and its limitations were clearly stated. It provided an industry-standard method to assess the likely value of a financial derivative. So derivatives could be traded before they matured. The formula was fine if you used it sensibly and abandoned it when market conditions weren't appropriate. Black-Scholes underpinned massive economic growth. By 2007, the international financial system was trading derivatives valued at one quadrillion dollars per year. This is 10 times the total worth, adjusted for inflation, of all products made by the world's manufacturing industries over the last century. The downside was the invention of ever-more complex financial instruments whose value and risk were increasingly opaque. So companies hired mathematically talented analysts to develop similar formulas, telling