Risk Neutral Methods and Black-Scholes Formula - Coursework Example

Risk probabilities Name Date Course Introduction 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 a 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 provides 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 the no arbitrage condition is the fundamental pricing in terms of the 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 cashflows 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. This method has its pros and cons during the process of calculating the risk probability. The main benefit of the method is that it is easy to use when it has been well understood. It is also useful when making approximations with regards to the prices and hence making it useful in determining the probability of the risk. The method is also robust and can be adjusted for the purposes of dealing with its own failures. However, it also has some disadvantages due to its mathematical nature. The formula could scare most people who are not good in mathematical concepts. It also underestimates some of the extreme move and hence impacting negatively on the tail risks. A lot of assumptions are also made when using the formula and hence impacting negatively on the accuracy when it comes to risks. The results also differ from the real world results due to the assumptions and hence impacting negatively on its levels of accuracy. Binomial approximation The binomial expression method is usually used in the calculation of prices and also the probability of the risks. This is usually achieved through the use of varying process over time with regards to the financial instrument. The use of binomial lattice is usually used during the process of making the approximations. The determination of the prices is useful in terms of calculating the risks. This is because the prices are usually determined based on the possible risks. A tree is usually generated and it is used for the purposes of making the calculations. It is however important to note that various assumptions are usually made during the process for the purposes of obtaining values. Mathematical formulas are however applied during the calculations for the purposes of obtaining different values that are required to come up with the probabilities. The risk probability is then applied in the valuation process and hence obtaining the prices. The use of this method is common in the American and European market (Grasselli, 744). Just like the other methods, it has its own pros and cons. However when compared to Black-Scholes formula, it is more accurate. This method is also easy to use during the calculations as computer spreadsheets can be used for the purposes of carrying out the calculations. The method is also based on underlying instruments as opposed to the single points and hence increasing on its levels of efficiency during the process. The disadvantage of this method is that it is computationally slower as it takes a lot of time during the calculations. It also had complicated features which makes it difficult to use. Depending on the nature of the market, it may also have a high number of steps and hence increasing its level of complexity. It is also important to note the method is susceptible to the sampling errors due to the use of discrete time units. The use of this method also requires an expertise as any error may be carried forward and hence producing wrong results with regards to the risks. UAE vs. International levels Market risks are also common in various sectors of the United Arab Emirates market. The calculation for the risk probabilities are usually carried out using different methods including the 5Csprobability methods. The use of risk neutral methods, Black-Scholes formula and binomial approximations are not common in the UAE market. This is because the market condition in the UAE makes it difficult to make some of the assumptions and approximations and hence limiting its use. On the other hand, it is also important to note that the three methods also require some expertise which is not readily available in the UAE market. Simple methods of approximations and use of simple parameters are usually employed in the UAE market during the process of risk approximation (Giannopoulos, 106). The use of simple methods has been successful considering that the level of risks cannot be compared with the European and American markets which have higher risks. The levels of accuracies with regards to the use of the methods are however low. The risk probability methods that are used in the United Arab Emirates however meet the international standards as most of the factors are usually considered during the process. Improvements are however required for the purposes of ensuring that the methods are more accurate and effective. Trends and future perspectives The three methods of approximating the market probability are increasingly becoming popular among most of the investors. This is because the investors are always keen on understanding the risks in the market and their probability before making decisions. However, the technological concepts are being embraced when using the method for the purposes of increasing on its levels of accuracies. Software are also being developed for the purposes of simplifying the calculations. In future the methods are set to be used widely but with the aid of computer software. Conclusion and recommendations In conclusion, it is evident that the three methods of approximating the market risk have their own pros and cons. However, a lot of approximations and assumptions are made when using the methods to come up with the probabilities. It is evident that these methods are common in the European and American markets as opposed to the UAE market where simple methods are used. It is recommended that technological concepts should be encouraged when using the methods as the trends indicates more are embracing technology. Works Cited Bolton, Patrick, et al. "Market timing, investment, and risk management." Journal of Financial Economics 109.1 (2013): 40-62. Lai, Wan-Ni. "Comparison of methods to estimate option implied risk-neutral densities." Quantitative Finance ahead-of-print (2011): 1-17. Davis, Mark HA. "Black–Scholes Formula." Encyclopedia of Quantitative Finance (2010). Grasselli, M. R. "Getting Real with Real Options: A Utility–Based Approach for Finite–Time Investment in Incomplete Markets." Journal of Business Finance & Accounting 38.5‐6 (2011): 740-764. Giannopoulos, Kostas, et al. "A Market Risk Model for Asymmetric Distributed Series of Return." APPLIED FINANCE (2012): 106. Read More