# Essays on Risk Neutral Methods and Black-Scholes Formula Coursework

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The paper "Risk Neutral Methods and Black-Scholes Formula" is an outstanding example of management coursework. The investors usually intend to make a high profit when they invest in a particular venture. This influences the prices of goods and services in the market due to the need for profitability. Risks and uncertainties are however common in any market despite their quest for profitability by the investors. The investors usually carry out market research in order to determine the probable market risks (Bolton, et al, 43). The market risk data is usually used for the purposes of making decisions with regards to the prices in the market.

Various methods are usually used for the purposes of estimating the risk probabilities. Mathematical calculations are usually involved during the process. Three common methods are usually used to calculate market risk probabilities and they include Black-Scholes formula, binomial approximation and risk-neutral methods. The paper thus discusses the use of the three methods in calculating the market risk probabilities. Discussion Risk neutral methods This method involves adjusting the future outcomes with the risks for the purposes of computing the asset values.

When using this method, the real-world probabilities are usually different from the theoretical risk-neutral probabilities. The method usually assumes that the arbitrage is absent during the computation process. An arbitrage is provided positive profits with positive probability and it also has a zero probability of loss. The method is commonly used for the purposes of pricing derivatives. In terms of pricing, the price of one security is usually calculated in relation to the price of other securities. It is also important to note that no-arbitrage condition is the fundamental pricing in terms of finance.

Through these assumptions, it is possible to obtain the multi-factor models of the cost of capital and option pricing (Lai, 12). Complete markets concepts are usually used during the calculation of the risks. The expected cash flows are usually applied during the calculations. A replication and option pricing is usually used during the computational process as it simplifies the process. The use of A-D prices is also important in terms of ensuring that the risks are calculated based on the prices. However, during the process of calculating the risks, multiple mathematical tables and formulas are usually used.

This method has its pros as well as cons. The main benefit of this method is that once the risk-neutral benefit has been computed, it can be used for the purposes of pricing every asset depending on its expected payoff. On the other hand, the computational process is simple due to the formulas that have been put in place. It is also important to note that the concepts of A-D securities may be complicated in some of the markets and hence offering a disadvantage in terms of using the method.

The assumptions that are made may also impact negatively on the actual probable risk in the market. Black-Scholes formula The Black-Scholes formula is useful in terms of determining the theoretical estimates of prices and risks in the European market. The formula is derived from the Black-Scholes equation that is also useful in calculating the prices (Davis, 13). Various assumptions are usually made during the process of using the formula to calculate the risks. The formula usually assumes that no dividends are paid and the markets are efficient.

On the other hand, the formula also makes assumptions that the risk-free rates are constant while the volatility of the underlying is known and they are also constant. Factors such as the current underlying prices are also considered during the calculation when using the formula. Other factors that are considered in the formula during the calculation using the formula includes options strike price and implied volatility. The expected benefits of the purchasing price can also be found through the use of the formula and hence determining the probability of the risk.

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