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Int. J. Financial Stud. 2015, 3(2), 136-150; doi:10.3390/ijfs3020136

Convergence Studies on Monte Carlo Methods for Pricing Mortgage-Backed Securities

1
Department of Mathematics, North Carolina State University, Raleigh, NC 27695-8205, USA
2
Department of Mathematics, University of Houston-Clear Lake, 2700 Bay Area Blvd., Houston, TX 77058, USA
3
ZM Financial Systems, 5915 Farrington Road, Unit 201, Chapel Hill, NC 27517, USA
*
Author to whom correspondence should be addressed.
Academic Editor: Nicholas Apergis
Received: 16 February 2015 / Revised: 22 April 2015 / Accepted: 24 April 2015 / Published: 5 May 2015
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Abstract

Monte Carlo methods are widely-used simulation tools for market practitioners from trading to risk management. When pricing complex instruments, like mortgage-backed securities (MBS), strong path-dependency and high dimensionality make the Monte Carlo method the most suitable, if not the only, numerical method. In practice, while simulation processes in option-adjusted valuation can be relatively easy to implement, it is a well-known challenge that the convergence and the desired accuracy can only be achieved at the cost of lengthy computational times. In this paper, we study the convergence of Monte Carlo methods in calculating the option-adjusted spread (OAS), effective duration (DUR) and effective convexity (CNVX) of MBS instruments. We further define two new concepts, absolute convergence and relative convergence, and show that while the convergence of OAS requires thousands of simulation paths (absolute convergence), only hundreds of paths may be needed to obtain the desired accuracy for effective duration and effective convexity (relative convergence). These results suggest that practitioners can reduce the computational time substantially without sacrificing simulation accuracy. View Full-Text
Keywords: Monte Carlo method; mortgage-backed securities (MBS); coefficient ofvariation (CV); absolute convergence; relative convergence; option-adjusted spread (OAS);effective duration (DUR); effective convexity (CNVX); Greeks Monte Carlo method; mortgage-backed securities (MBS); coefficient ofvariation (CV); absolute convergence; relative convergence; option-adjusted spread (OAS);effective duration (DUR); effective convexity (CNVX); Greeks
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Pang, T.; Yang, Y.; Zhao, D. Convergence Studies on Monte Carlo Methods for Pricing Mortgage-Backed Securities. Int. J. Financial Stud. 2015, 3, 136-150.

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