Valuation of n-fold compound barrier options with stochastic interest rates

Liu, Yuhong; Jiang, I-Ming; Chen, Lichun

doi:10.1016/j.apmrv.2017.07.005

Cited by 5 publications

(3 citation statements)

References 26 publications

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“…However, some works contribute successfully to combine barrier options with the compound options logic that can model multistage projects (Bufalo et al 2022). For example, Liu et al (2018) proposed a valuation of n-fold compound barrier options in continuous time focusing on the down-and-out case that, generally, is also proposed to control the default risk. This work extends the real options literature in discrete time with the binomial model use.…”

Section: Introductionmentioning

confidence: 99%

A Compound Up-and-In Call like Option for Wind Projects Pricing

Bufalo

Bari

Villani

2023

Risks

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Wind energy projects represent, currently, a valid opportunity to support United Nations Sustainable Development Goal 7. However, these projects can appear financially unattractive considering the unfavorable meteorological conditions, uncertain electricity market price, uncertain market demand, unpredictable project performance, riskiness of investment stages, etc. This paper provides a real options pricing model applied for the evaluation of a wind farm project to include the uncertainty that can affect future performance. The methodology proposed uses a compound call option model with two barriers applied, respectively, to the twofold phase framework that would act as a sort of up-and-in barrier. The compound call option model allows us to valuate the managerial flexibility to proceed with the following investment stages depending on the success of the previous ones and, through the barriers, the methodology gives the investor the opportunity to consider some profitability thresholds below, past which the investment should be abandoned. We develop a discrete case methodology by using the binomial approach. A hypothetical case study is shown to implement the theoretical framework by using likely data.

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Section: Introductionmentioning

confidence: 99%

A Compound Up-and-In Call like Option for Wind Projects Pricing

Bufalo

Bari

Villani

2023

Risks

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“…Cheng et al (2011) used the binomial model approach, which was modified from sequential compound options, to analyze future GDP changes based on past historical data, their resulting impact on electricity demand, and their influences on the development path of clean energy investment strategies. Liu et al (2018) adopted the pricing of n-fold compound options with barriers. They developed a generalization of the compound barrier option with a stochastic interest rate to capture the interest rate risk.…”

Section: Introductionmentioning

confidence: 99%

Optimum Technology Product Life Cycle Technology Innovation Investment-Using Compound Binomial Options

Lin

Zeng

2018

Risks

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The study considers the product life cycle in the stages of technological innovation, and focuses on how to evaluate the optimal investment strategy and the project value. It applies different product stages (three stages including production innovation, manufacture innovation, and business innovation) factors to different risks to build a technology innovation strategy model. This study of option premiums aims for the best strategy timing for each innovation stage. It shows that the variation of business cycle will affect the purchasing power under the uncertainty of Gross Domestic Product (GDP). In application, the compound binomial options for the manufacture innovation will only be considered after the execution of the production innovation, whereas the operation innovation will only be considered after the execution of the manufacture innovation. Thus, this paper constructs the dynamic investment sequential decision model, assesses the feasibility of an investment strategy, and makes a decision on the appropriate project value and option premiums for each stage under the possible change of GDP. Numerically, the result shows the equity value of the investment is greater than 0. Therefore, this paper recommends the case firm to invest in its innovation project known as one-time passwords. Sensitivity analysis shows when the risk-adjusted discounted rate r increases, the risk of the investment market increases accordingly, hence the equity value must also be higher in order to attract the case firm’s investment interest. Also, the average GDP growth rate u sensitivity analysis results in different phenomena. The equity value gradually decreases when the average GDP growth rate rises. When the average GDP growth rate u rises to a certain extent, however, its equity value is gradually growing. The study investigates the product life cycle innovation investment topic by using the compound binomial options method and therefore provide a more flexible strategy decision compared with other trend forecast criteria.

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“…They analyzed the frequency of fires from a dynamic point of view, examined the fire damage data of an international city for ten years, and proposed the best time to purchase fire hazards or install fire safety systems. Liu et al (2017) adopted the pricing of n-fold compound options with barriers. They developed a generalization of the compound barrier option with a stochastic interest rate to capture the interest rate risk.…”

Section: Introductionmentioning

confidence: 99%

Optimum Technology Product Life Cycle Technology Innovation Investment—Using Compound Binomial Options

Ko¹,

Lin²,

Zeng³

2018

Preprint

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The purpose of this paper is to evaluate the timing of innovative investment in technology product life cycles using a compound binomial option with management flexibility. Considering the business cycles changes in the macroeconomic will affect consumer purchasing power. The focus is how to evaluate the optimal investment strategy and the project value. It was applied to different product stages (three stages including production innovation, manufacture innovation, and operation innovation) and factored to different risks to build a technology innovation strategy model. An aim of this study is the options premium of the best strategy timing for each innovation stage. Its application of the compound binomial options for the manufacture innovation will only be considered after the execution of the production innovation. The same condition is applied to the operation innovation, which will only be considered after the execution of the manufacture innovation. Then, this paper constructs the dynamic investment sequential decision model, assesses the feasibility of an investment strategy, and makes a decision on the appropriate project value and options premium for each stage under the possible change of Gross Domestic Product (GDP). This paper investigates the product life cycle innovation investment topic by using the compound binomial options method and will provide a more flexible strategy decision compared with other trend forecast criteria.

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Valuation of n-fold compound barrier options with stochastic interest rates

Cited by 5 publications

References 26 publications

A Compound Up-and-In Call like Option for Wind Projects Pricing

A Compound Up-and-In Call like Option for Wind Projects Pricing

Optimum Technology Product Life Cycle Technology Innovation Investment-Using Compound Binomial Options

Optimum Technology Product Life Cycle Technology Innovation Investment—Using Compound Binomial Options

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Valuation of n-fold compound barrier options with stochastic interest rates

Cited by 5 publications

References 26 publications

A Compound Up-and-In Call like Option for Wind Projects Pricing

A Compound Up-and-In Call like Option for Wind Projects Pricing

Optimum Technology Product Life Cycle Technology Innovation Investment-Using Compound Binomial Options

Optimum Technology Product Life Cycle Technology Innovation Investment&mdash;Using Compound Binomial Options

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Product

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Optimum Technology Product Life Cycle Technology Innovation Investment—Using Compound Binomial Options