{"title":"No-Arbitrage Valuation of Contingent Claims Depending on an Untradeable Asset","authors":"Erindi Allaj","doi":"10.1002/asmb.70007","DOIUrl":null,"url":null,"abstract":"<p>We consider an incomplete market situation with the presence of an untradeable asset and several tradeable assets. By an untradeable asset we mean an asset that cannot be traded on a public market. Typical examples of untradeable assets include real options and private credit/debt investments. We then exploit the relationship between the untradeable asset and tradeable assets to evaluate contingent claims depending on the untradeable asset. Under a multidimensional generalized Black–Scholes (GBS) framework, we study two different methods for pricing these kinds of contingent claims. The first is mean-variance hedging (MVH). The second is the method proposed in Jarrow (2023). We illustrate the two methods by applying them to two particular contingent claims: The option to defer and the spread option. No-arbitrage prices and admissible replicating trading strategies are derived. Lastly, we run simulations to test the performance of these replicating trading strategies.</p>","PeriodicalId":55495,"journal":{"name":"Applied Stochastic Models in Business and Industry","volume":"41 2","pages":""},"PeriodicalIF":1.3000,"publicationDate":"2025-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/asmb.70007","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Stochastic Models in Business and Industry","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/asmb.70007","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
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Abstract
We consider an incomplete market situation with the presence of an untradeable asset and several tradeable assets. By an untradeable asset we mean an asset that cannot be traded on a public market. Typical examples of untradeable assets include real options and private credit/debt investments. We then exploit the relationship between the untradeable asset and tradeable assets to evaluate contingent claims depending on the untradeable asset. Under a multidimensional generalized Black–Scholes (GBS) framework, we study two different methods for pricing these kinds of contingent claims. The first is mean-variance hedging (MVH). The second is the method proposed in Jarrow (2023). We illustrate the two methods by applying them to two particular contingent claims: The option to defer and the spread option. No-arbitrage prices and admissible replicating trading strategies are derived. Lastly, we run simulations to test the performance of these replicating trading strategies.
期刊介绍：
ASMBI - Applied Stochastic Models in Business and Industry (formerly Applied Stochastic Models and Data Analysis) was first published in 1985, publishing contributions in the interface between stochastic modelling, data analysis and their applications in business, finance, insurance, management and production. In 2007 ASMBI became the official journal of the International Society for Business and Industrial Statistics (www.isbis.org). The main objective is to publish papers, both technical and practical, presenting new results which solve real-life problems or have great potential in doing so. Mathematical rigour, innovative stochastic modelling and sound applications are the key ingredients of papers to be published, after a very selective review process.
The journal is very open to new ideas, like Data Science and Big Data stemming from problems in business and industry or uncertainty quantification in engineering, as well as more traditional ones, like reliability, quality control, design of experiments, managerial processes, supply chains and inventories, insurance, econometrics, financial modelling (provided the papers are related to real problems). The journal is interested also in papers addressing the effects of business and industrial decisions on the environment, healthcare, social life. State-of-the art computational methods are very welcome as well, when combined with sound applications and innovative models.
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