The Management of Financial Assets - Essay Example

RESEARCH PROPOSAL NO ARBITRAGE VALUATION OF ASIAN OPTIONS The management of financial assets is a tricky affair especially in the case ofa market that has a certain degree of friction attached to it. There is a certain degree of uncertainty as well as a certain amount of risk involved in the modeling of financial markets. Therefore, any modeling of financial assets is directed towards the reduction of the uncertainties & risks involved with the value of an asset or the pricing agreements that govern the variation of the determinants of financial assets' evaluation. Therefore, any such evaluation is performed so s to strike a perfect balance between the non-risky assets and the non-risky assets. Under financial discussions & research, options fall under a particular style or family. Theoretically speaking, the style or the family of options refers to a class that signifies the category into which that particular option comes under. The options are generally verified & studied by analyzing the dates on which these options may be exercised. Such options come under the purview of the European & American Styles. There are many more types of options available. The similarity between all of them is that they come under the 'Vanilla Options' wherein, the options are evaluated on the basis of the payoff. There are also numerous Non-Vanilla options such as the Russian & the Asian options. The proposed research is aimed at studying the various arbitrage options that fall under the Asian option. Under the proposed research, there are a number of issues that are planned to be studied. The first & the foremost would be to perform an analysis & assessment of the various techniques that have been devised for assessing the Asian option. The study of these techniques is very important in order to assess each one for its effectiveness & compare & contrast between all of them for their numerous features & capabilities. In general, it's a well known fact that the values of an Asian option is obtained by evaluating a Partial Differential Equation (PDE). In fact, this aspect is central to all the techniques that are proposed to be studied. As is common with other options, the analysis of an Asian option is made by calculating the payoff that is usually given by the average price of the stock (asset) over a certain period of time. The reason why this topic is being studied is that though there are numerous techniques available for determining the payback, none of them is able to provide a clear-cut & a fully observable solution. This is because the evaluation of the Partial Differential Equations (PDE) involves a certain degree of adjustments in terms of the areas being evaluated under the integrals that varies with each technique. Nevertheless, numerous options have been devised that tend to improve the degree of efficiency and accuracy with which these options can be worked out. Some of the techniques that are proposed to be covered under the proposed research are discussed below: Roger & Shi's one-dimensional Model: This model is suitable for both fixed & floating Asian options. This method uses the Strike & the average value of a stock over a time period for the evaluation of the PDE. But there are certain problems with this technique that need to be investigated. Jan vecer technique: this method falls under the traded account option wherein the gains & losses from trading are evaluated using a special Partial Differential Equation. The PDE for this model takes into account the rate of reinvestment as well as the trading strategy with the intent of maximizing the price of agreement. Under the Asian option, the payoff is calculated as a function of the stock & the strike value. Monte-Carlo Approach: this approach is adopted when the dimensional space is larger than usual wherein the share of price is evaluated by the Black & Scholes model while the price of an asset has been given Lapeyre & Temam. This model utilized the standard Brownian motion & additionally considers the risk. In addition to evaluation of the price & the value of an asset, the research will also focus on simulating the average value of the stock over a time period. The Monte Carlo method is also characterized by a set of error namely the Monte Carlo error & the time set error. In order to reduce these errors, a Taylor expansion is used. Therefore, all these techniques need to be mathematically derived & evaluated. The technique of variance reduction is also used for improving the efficiency of the Monte Carlo method. Finally, iterative evaluation of the price for longer periods of time under the numerical approach provides a convergent technique which scaled down the errors to a final constant value due to the increased iterations. Finally, it is also important to identify the symmetries in the pricing strategies. This essentially comprises the exponential levy model. It has been established through prior research that this technique leads to an enhanced efficiency & a price evaluation with optimum accuracy. Financial experts are of the opinion that the assumptions that have been made for the Black-Scholes model for the stock price have not been able to provide optimum efficiency when applied under practical situations. On similar lines, the other techniques that have been mentioned above & others tat are proposed to assessed as part of the proposed research are known to be characterized with specific advantages & deficiencies in comparison to other models. All such parameters are represented by the brownian motion, the risk factor etc. these parameters in addition to the strike & the price are the standard parameters for the evaluation of the payoff that is the standard for the evaluation under the Asian option. The above-mentioned models are just a subset of the various theories & techniques that are proposed to be taken up under the project. In addition to evaluating every model for their efficiencies & the standard error & deviations produced by them, the research will also focus on the effective simulation of the various models proposed under the study. The research will mainly concentrate on using academic literature in the form of books & journals for the purpose of citing the various evaluations pertaining to the various models & techniques that have been performed by noted experts & academicians in the past. REFERENCE Investor Dictionary (2006), Definition of Option Style. Found at: http://www.investordictionary.com/definition/option+style.aspx Read More