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t is difficult to compute the volatility of real R&D options. Due to the fact that even commodities like oil, silver and gold are traded on exchange, it is easier to calculate their value volatility or in other words volatility of their return by means of their stock prices. However with respect to my research, the traditional approach of computing volatility by means of historic stock prices was not possible and therefore an alternative method is used. In order to compute value volatility or in other words the revenue volatility without availability of stock prices, I have used the ARPU figures for cellular industry of Pakistan during the period of 2004-2009 which are demonstrated in figure 5.12 shown below.

 

Furthermore I have computed the Natural log of ARPU which was necessary step in order to calculate the variance and standard deviation of ARPU. Due to the fact that volatility is one of the most critical variables in real options, therefore standard deviation of ARPU which seems to be a realistic representation is considered as value volatility for the 3G market. Based on my analysis, the annualized standard deviation of ARPU turns out to be approximately 0.223 or 22.3% whereas the annualized variance turns out to be approximately 0.050 or 5%.

 

QUANTITY VOLATILITY:

 

The analysis of my first pre-emption model “RIVALRY UNDER PRICE AND QUANTITY UNCERTAINITY” required a measure of quantity volatility. In order to calculate the quantity volatility or in other words the volatility of subscribers with respect to my research, the first step was acquiring the net addition in cellular subscribers of Pakistan annually during the period of 2006 and 2010. The following data was obtained from various PTA annual reports and it is demonstrated below in figure 5.13.

 

It can be grasped from the figure above that I have also computed the average of additional cellular subscriber that joined 2G market during 2006-2010. Furthermore the next step towards the calculation of quantity volatility required the computation of Natural Log of average number of subscribers in order to obtain precise annualized volatility which has been illustrated in figure 5.14 shown below.

 

Finally by means of using Natural Log of subscriber, I managed to compute the annualized standard deviation of subscribers which turned out to be approximately 0.693 or 69.3%, where as the annualized variance of subscribers (quantity) was estimated to be approximately 0.481 or 48.1%.

 

INVESTMENT COST VOLATILITY:

 

Investment cost volatility is an essential variable for the analysis of my second pre-emption model “RIVALRY UNDER NET REVENUE & INVESTMENT COST UNCERTAINTY”. In Paxson and Pinto (2004) “THIRD GENERATION MOBILE GAMES - An application of real competition games”, th本论文由英语论文网提供整理，提供论文代写，英语论文代写，代写论文，代写英语论文，代写留学生论文，代写英文论文，留学生论文代写相关核心关键词搜索。