A Stochastic Process to Model the Fluctuations of Asphalt Cement Price

Transportation agencies and highway contractors are facing great challenges of variations in construction costs for transportation projects. Significant volatility in costs of construction materials, such as asphalt cement, is one of the most important drivers of uncertainty about transportation project costs. This type of uncertainty leads to serious difficulties for contractors in estimating project costs accurately. However, there is little knowledge about how asphalt cement price fluctuates over time. This gap in knowledge makes it difficult for contractors and transportation agencies to estimate project costs accurately. The research objective of this paper was to model fluctuations of asphalt cement price by using an appropriate stochastic process. It is concluded that the geometric brownian motion (GBM) is a good stochastic process to model random variations of asphalt cement price over time. A probabilistic approach based on the Monte Carlo simulation is applied on the GBM model to simulate future random paths for asphalt cement price index. It is expected that this work helps contractors and transportation agencies systematically analyze variations in the price of asphalt cement and develop more accurate estimations for their transportation projects.

[1]  D. J. Finney.  The Advanced Theory of Statistics. By Maurice G. Kendall , 1943 .

[2]  Sarah M. Ryan,et al.  Capacity Expansion for Random Exponential Demand Growth with Lead Times , 2004, Manag. Sci..

[3]  Chester G. Wilmot,et al.  Estimating future highway construction costs , 2003 .

[4]  Viswanathan Arunachalam,et al.  Introduction to Mathematical Finance , 2012 .

[5]  Morris Myers Blair.  Elementary statistics with general applications , 1944 .

[6]  Min Liu,et al.  Prices of Highway Resurfacing Projects in Economic Downturn: Lessons Learned and Strategies Forward , 2012 .

[7]  Jian Lu,et al.  Time Series Analysis of ENR Construction Cost Index , 2010 .

[8]  Richard A. Davis,et al.  Introduction to time series and forecasting , 1998 .

[9]  Sarah M. Ryan,et al.  On The Validity of The Geometric Brownian Motion Assumption , 2005 .

[10]  H. M. Taylor,et al.  An introduction to stochastic modeling , 1985 .

[11]  I. Damnjanovic,et al.  Optimal Hedging of Commodity Price Risks in Highway Contracts , 2011 .

[12]  Kenneth Dixon,et al.  Introduction to Stochastic Modeling , 2011 .

[13]  Steven C. Wheelwright,et al.  Forecasting: Methods and Applications, 3rd Ed , 1997 .

[14]  Leyuan Shi,et al.  A real options design for quality control charts , 2000, 2000 Winter Simulation Conference Proceedings (Cat. No.00CH37165).

[15]  Bo Jellesmark Thorsen,et al.  Afforestation as a Real Option: Some Policy Implications , 1999, Forest Science.

[16]  A. Whitehead.  An Introduction to Mathematics , 1949, Nature.

[17]  Steven C. Wheelwright,et al.  Forecasting methods and applications. , 1979 .

[18]  S. Shapiro,et al.  An analysis of variance test for normality ( complete samp 1 es ) t , 2007 .

[19]  I. Damnjanovic,et al.  Impact of crude oil market behaviour on unit bid prices: the evidence from the highway construction sector , 2009 .

[20]  S. Shapiro,et al.  An Analysis of Variance Test for Normality (Complete Samples) , 1965 .

[21]  J. Cockcroft.  Investment in Science , 1962, Nature.