2025 RTP round - Advanced mathematical models and computational techniques for pricing real options in supply chains systems.

Status: Closed

Applications open: 1/07/2024
Applications close: 18/08/2024

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About this scholarship
Description/Applicant information

 

Project Overview

Supply chains are complex supply-demand systems used in any industries and government agencies. When a company enters into a supply-demand contract, it is exposed to risks from several major uncontrollable parameters such as fluctuations in commodity prices and change in market demands, economic conditions, interest rates and currency exchange rates. Some of these risk factors may jeopardise the survival or expansion of the company. (One example is the recent collapses of some Australian builders due to changes of economic environments and interest rates.) Therefore, it is desirable for a company to consider some measures to mitigate possible risks when signing a supply-demand contract. The best way to achieve this is to include some 'flexibilities' called real options in a contract. There are several typical types of real options such as option of contraction (decrease ordered amount), option of expansion (increase order amount) and option of  termination. Clearly, including an option of flexibility in a supply-chain contract  will incur a price adjustment  in the contract. For example, if a traveller buys air-tickets which allow the traveller to cancel his/hers travel prior to a given date before departure, the tickets should be more expansive than the ones without this option for the traveller, and the cost of this flexibility/option depends on the  agreed given date as well. This poses the question that how much more the traveller needs to pay for this flexibility.  
In general, the question is, if there is a real option imbedded in a supply-chain system, what is the fair value of the option. Therefore, how to accurately determine the fair value of an option in a supply-chain contract is crucial for all parties of the contract.  Despite the importance of real options in supply chain systems, there are very limited studies on pricing real options  in the open literature, letting alone practically important and computationally tractable mathematical models for pricing real options in supply-chains (see for example, [1,2,3,4]). 
References 
[1] Cucchiella  F, Gastaldi M. Risk management in supply chain: a real option approach. Journal of Manufacturing Technology Management, 17 (2006) 700-720. 
[2] Dizabadi AK, Arasteh A, Paydar MM. Real Options Based Analysis for Supply Chain Management. International Journal of Industrial Engineering & Production Research December 33 (2022) 1-26 
[3] He J , Alavifard F, Ivanov D , Jahani H. A real-option approach to mitigate disruption risk in the supply chain. Omega 88 (2019) 133–149. 
[4] Nembhard HB, Shi L, Aktan M. A real-options-based analysis for supply chain decisions. IIE Transactions, 37(10), 945–956.

 

Aims

As mentioned, it is known that flexibilities in the form of real options are crucial  for industries to mitigate risks in supply chain systems due to uncertainties in many economic and market parameters such as interest rates, commodity prices and demand volatility. However, unlike conventional options in financial markets, there are essentially no effective mathematical models and numerical tools for accurately pricing such a real option. This project aim at filling this gap by developing novel mathematical models for pricing options of demand decrease, demand increase and contract termination in supply chain systems under uncertainties of  the underlying asset price, interest rates and demand volatility, and advanced numerical methods for solving these models. More specifically, we will use stochastic differential equations and Ito's calculus to derive  partial differential equations and inequalities of Black-Scholes type for the respective options. Numerical methods based on optimisation techniques and differential equation discretisation schemes will be developed for solving the developed mathematical models. Computer codes in Python/Matlab/R implementing these models and numerical methods will be developed which can be used for solving real-world real option pricing problems in supply chain systems.

 

Objectives

Below is a list of objectives of this project 
1. Development of pricing models for three different types of real options of European style (options exercisable only on maturity) - option to decrease demand, option to increase demand and option to terminate in a supply-chain  contract. 
2. Extension of the models of options of European style mentioned above to those of options of American style (options exercisable anytime before or on maturity). 
3. Numerical algorithms for solving the option models developed in Items 1 and 2. 
4. Implementation and tests of the models and numerical methods using non-trivial pricing problems. 
5. At least 3 full research papers will be published in top quality international journals from this project.

 

Significance 

This project will result in novel mathematical models for pricing real options building in supply-chain contracts to help industries to mitigate risks from uncertainties in commodity prices, interest rates, etc. The developed mathematical and computational models will provide efficient tools for Australian industries and government agencies to optimise their supply chain systems and minimise arbitrage,  and thus to increase their productivities. The outcomes of this project will also help Curtin University to enhance its international reputation in the relevant fields, particularly computational mathematics, operations research and financial engineering.

 

Prof. Wang and A/Prof. Zhou have complementary expertise which is ideal for and can insure the success of this project. This project is in the combined area of computational mathematics and operations research which are priority research areas of Maths & Stats Discipline within SEECMS. In particularly, Curtin's computational mathematics was ranked 5 in the latest ERA ranking exercise. Thus, this project will help the School to further enhance its international reputation in these areas. It will also help the School to maintain the top ranking on its computational mathematics  discipline in future ERA exercises.

 

Student type

• Future Students

Faculties and centres

• Faculty of Science & Engineering
  • Science courses
  • Engineering courses

Course type

• Higher Degree by Research

Citizenship

• Australian Citizen
• Australian Permanent Resident
• New Zealand Citizen
• Permanent Humanitarian Visa
• International Student

Scholarship base

• Merit Based

Value

The annual scholarship package, covering both stipend and tuition fees, amounts to approximately $70,000 per year.

In 2024, the RTP stipend scholarship offers $35,000 per annum for a duration of up to three years. Exceptional progress and adherence to timelines may qualify students for a six-month completion scholarship.

Selection for these scholarships involves a competitive process, with shortlisted applicants notified of outcomes by November 2024.

Scholarship Details
Maximum number awarded

1

Eligible courses

All applicable HDR courses.

Eligibility criteria

The candidate needs to have a degree in applied or financial mathematics, or actuarial science. The candidate should be familiar with differential equations, computational mathematics and optimisation techniques. He/She should also have experience in a programming language or is willing to be a quick learner of a programming language.
 

Application process

Please send your CV, academic transcripts and brief rationale why you want to join this research project via the HDR Expression of Interest form to the project lead researcher, listed below. 

Enrolment Requirements

You must be enrolled in a Higher Degree by Research Course at Curtin University by March 2025.

Enquiries

Project Lead: Professor Song Wang

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