No-Arbitrage Valuation of Contingent Claims Depending on an Untradeable Asset

IF 1.3 4区数学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Applied Stochastic Models in Business and Industry Pub Date : 2025-03-23 DOI:10.1002/asmb.70007

Erindi Allaj

引用次数: 0

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.

Abstract Image

查看原文本刊更多论文

基于不可交易资产的或有债权的无套利估值

我们考虑存在一项不可交易资产和若干项可交易资产的不完全市场情况。不可交易资产是指不能在公开市场上交易的资产。不可交易资产的典型例子包括实物期权和私人信贷/债务投资。然后，我们利用不可交易资产和可交易资产之间的关系来评估依赖于不可交易资产的或有债权。在多维广义Black-Scholes （GBS）框架下，研究了这类或有债权的两种不同定价方法。第一种是均值方差套期保值（MVH）。第二种是Jarrow（2023）提出的方法。我们通过将这两种方法应用于两个特定的或有债权来说明这两种方法：延期期权和价差期权。推导出无套利价格和允许复制交易策略。最后，我们运行模拟来测试这些复制交易策略的性能。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Applied Stochastic Models in Business and Industry 数学-数学跨学科应用

CiteScore

2.70

自引率

0.00%

发文量

审稿时长

>12 weeks

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.