Macquarie University
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Advanced Monte Carlo methods for pricing Bermudan options and their applications in real options analysis

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posted on 2022-03-28, 02:25 authored by Jie Zhu
Pricing options with early exercise features is a challenging problem in mathematical finance. There is no general closed-form solutions available. We have implemented three established Monte Carlo methods in R for pricing Bermudan options: the random tree method, the stochastic mesh method and the least-squares Monte Carlo method (LSMC). We have also adopted the expectation-maximization (EM) control algorithm recently pro- posed in the literature and adapted this method for pricing Bermudan options. The numerical analyses find LSMC has the best performance; and have been extended to the improvements on LSMC via considering regression schemes such as piecewise linear regression and smoothing splines, random number generating process using low-discrepancy sequences and the usage of European options as control variates. The algorithm has also been applied to study a standard real option problem, the option to delay an investment project. The implemented algorithm is a powerful tool to solve many important application problems of decision under uncertainty in realistic settings that can be considered in further research.


Table of Contents

1. Introduction -- 2. Monte Carlo methods for options pricing -- 3. Pricing Bermuda options -- 4. Simiulations results and algorithm improvement -- 5. LSMC for real options analysis -- 6. Conclusions and directions of future research.


Theoretical thesis. Bibliography: pages 95-101

Awarding Institution

Macquarie University

Degree Type

Thesis MRes


MRes, Macquarie University, Faculty of Business and Economics, Department of Applied Finance and Actuarial Studies

Department, Centre or School

Department of Applied Finance and Actuarial Studies

Year of Award


Principal Supervisor

Pavel Shevchenko

Additional Supervisor 1

Ken Siu


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