{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,25]],"date-time":"2026-03-25T14:55:29Z","timestamp":1774450529082,"version":"3.50.1"},"reference-count":46,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2024,3,25]],"date-time":"2024-03-25T00:00:00Z","timestamp":1711324800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this paper, we explore a novel model for pricing Chinese convertible bonds that seamlessly integrates machine learning techniques with traditional models. The least squares Monte Carlo (LSM) method is effective in handling multiple state variables and complex path dependencies through simple regression analysis. In our approach, we incorporate machine learning techniques, specifically support vector regression (SVR) and random forest (RF). By employing Bayesian optimization to fine-tune the random forest, we achieve improved predictive performance. This integration is designed to enhance the precision and predictive capabilities of convertible bond pricing. Through the use of simulated data and real data from the Chinese convertible bond market, the results demonstrate the superiority of our proposed model over the classic LSM, confirming its effectiveness. The development of a pricing model incorporating machine learning techniques proves particularly effective in addressing the complex pricing system of Chinese convertible bonds. Our study contributes to the body of knowledge on convertible bond pricing and further deepens the application of machine learning in the field in an integrated and supportive manner.<\/jats:p>","DOI":"10.3390\/axioms13040218","type":"journal-article","created":{"date-parts":[[2024,3,25]],"date-time":"2024-03-25T12:32:36Z","timestamp":1711369956000},"page":"218","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Pricing Chinese Convertible Bonds with Learning-Based Monte Carlo Simulation Model"],"prefix":"10.3390","volume":"13","author":[{"given":"Jiangshan","family":"Zhu","sequence":"first","affiliation":[{"name":"Department of Financial and Actuarial Mathematics, School of Mathematics and Physics, Xi\u2019an Jiaotong-Liverpool University, Suzhou 215123, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3938-8108","authenticated-orcid":false,"given":"Conghua","family":"Wen","sequence":"additional","affiliation":[{"name":"Department of Financial and Actuarial Mathematics, School of Mathematics and Physics, Xi\u2019an Jiaotong-Liverpool University, Suzhou 215123, China"}]},{"given":"Rong","family":"Li","sequence":"additional","affiliation":[{"name":"Department of Financial and Actuarial Mathematics, School of Mathematics and Physics, Xi\u2019an Jiaotong-Liverpool University, Suzhou 215123, China"}]}],"member":"1968","published-online":{"date-parts":[[2024,3,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1093\/rfs\/14.1.113","article-title":"Valuing American options by simulation: A simple least-squares approach","volume":"14","author":"Longstaff","year":"2001","journal-title":"Rev. Financ. Stud."},{"key":"ref_2","first-page":"8610126","article-title":"Pricing Chinese Convertible Bonds with Default Intensity by Monte Carlo Method","volume":"2019","author":"Luo","year":"2019","journal-title":"Discret. Dyn. Nat. Soc."},{"key":"ref_3","first-page":"492134","article-title":"Pricing Chinese Convertible Bonds with Dynamic Credit Risk","volume":"2014","author":"Li","year":"2014","journal-title":"Discret. Dyn. Nat. Soc."},{"key":"ref_4","first-page":"301282","article-title":"Valuing Convertible Bonds Based on LSRQM Method","volume":"2014","author":"Liu","year":"2014","journal-title":"Discret. Dyn. Nat. Soc."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Nazemi, A., Rauch, J., and Fabozzi, F.J. (2022). Interpretable Machine Learning for Creditor Recovery Rates. SSRN Electron. J.","DOI":"10.2139\/ssrn.4190345"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"637","DOI":"10.1086\/260062","article-title":"The Pricing of Options and Corporate Liabilities","volume":"81","author":"Black","year":"1973","journal-title":"J. Political Econ."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"141","DOI":"10.2307\/3003143","article-title":"Theory of Rational Option Pricing","volume":"4","author":"Merton","year":"1973","journal-title":"Bell J. Econ. Manag. Sci."},{"key":"ref_8","first-page":"449","article-title":"On the pricing of corporate debt: The risk structure of interest rates","volume":"29","author":"Merton","year":"1974","journal-title":"J. Financ."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1016\/0304-405X(77)90004-6","article-title":"A contingent-claims valuation of convertible securities","volume":"4","author":"Ingersoll","year":"1977","journal-title":"J. Financ. Econ."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1699","DOI":"10.1111\/j.1540-6261.1977.tb03364.x","article-title":"Convertible bonds: Valuation and optimal strategies for call and conversion","volume":"32","author":"Brennan","year":"1977","journal-title":"J. Financ."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"907","DOI":"10.2307\/2330567","article-title":"Analyzing convertible bonds","volume":"15","author":"Brennan","year":"1980","journal-title":"J. Financ. Quant. Anal."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"561","DOI":"10.1111\/j.1540-6261.1986.tb04516.x","article-title":"LYON taming","volume":"41","author":"McConnell","year":"1986","journal-title":"J. Financ."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"237","DOI":"10.2307\/2331065","article-title":"The Use of the Control Variate Technique in Option Pricing","volume":"23","author":"Hull","year":"1988","journal-title":"J. Financ. Quant. Anal."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"35","DOI":"10.2469\/faj.v49.n3.35","article-title":"A Model for Valuing Bonds and Embedded Options","volume":"49","author":"Kalotay","year":"1993","journal-title":"Financ. Anal. J."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1111\/j.1467-9965.1995.tb00099.x","article-title":"The GARCH Option Pricing Model","volume":"1","author":"Duan","year":"1995","journal-title":"Math. Financ."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1016\/0304-405X(79)90015-1","article-title":"Option pricing: A simplified approach","volume":"7","author":"Cox","year":"1979","journal-title":"J. Financ. Econ."},{"key":"ref_17","first-page":"75","article-title":"Pricing Convertible Bonds Subject to Default Risk","volume":"10","author":"Hung","year":"2002","journal-title":"Derivations"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1439","DOI":"10.1287\/mnsc.1070.0702","article-title":"An Integrated Model for Hybrid Securities","volume":"53","author":"Das","year":"2007","journal-title":"Manag. Sci."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"39","DOI":"10.21314\/JCF.2001.066","article-title":"Pricing American options: A comparison of Monte Carlo simulation approaches","volume":"4","author":"Fu","year":"2001","journal-title":"J. Comput. Financ."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1016\/j.cor.2006.02.016","article-title":"The valuation of multidimensional American real options using the LSM simulation method","volume":"35","author":"Cortazar","year":"2008","journal-title":"Comput. Oper. Res."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"196","DOI":"10.1016\/j.ejor.2016.06.020","article-title":"Comparison of least squares Monte Carlo methods with applications to energy real options","volume":"256","author":"Nadarajah","year":"2017","journal-title":"Eur. J. Oper. Res."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"104633","DOI":"10.1016\/j.jobe.2022.104633","article-title":"Data-driven decision support system for building stocks energy retrofit policy","volume":"54","author":"Cecconi","year":"2022","journal-title":"J. Build. Eng."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"216","DOI":"10.1016\/j.jbankfin.2018.05.006","article-title":"Pricing convertible bonds","volume":"92","author":"Batten","year":"2018","journal-title":"J. Bank. Financ."},{"key":"ref_24","first-page":"93","article-title":"Research on the Pricing of Convertible Bonds in China","volume":"162","author":"Zheng","year":"2004","journal-title":"J. Xiamen Univ. (Philos. Soc. Sci. Ed.)"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"924","DOI":"10.1016\/j.ejor.2009.02.012","article-title":"A note on \u201cMonte Carlo analysis of convertible bonds with reset clause\u201d","volume":"200","author":"Yang","year":"2010","journal-title":"Eur. J. Oper. Res."},{"key":"ref_26","first-page":"58","article-title":"Design and Impact Analysis of Convertible Bond Option Terms","volume":"30","author":"Feng","year":"2018","journal-title":"Manag. Rev."},{"key":"ref_27","first-page":"53","article-title":"Research on Pricing of Convertible Bonds Based on Black-Scholes Model\u2014Taking Oupai Convertible Bonds as an Example","volume":"11","author":"Xie","year":"2021","journal-title":"China Price"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1016\/j.matcom.2018.04.005","article-title":"Convertible bond pricing with partial integro-differential equation model","volume":"152","author":"Yang","year":"2018","journal-title":"Math. Comput. Simul."},{"key":"ref_29","first-page":"189","article-title":"Pricing of Convertible Bonds Based on Tsallis Entropy Distribution under Stochastic Interest Rate Model","volume":"29","author":"Chang","year":"2020","journal-title":"Oper. Res. Manag."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"121261","DOI":"10.1016\/j.physa.2019.121261","article-title":"Modeling financial time-series with generative adversarial networks","volume":"527","author":"Takahashi","year":"2019","journal-title":"Phys. A Stat. Mech. Appl."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Dogariu, M., \u015etefan, L.-D., Boteanu, B.A., Lamba, C., and Ionescu, B. (2021, January 23\u201327). Towards Realistic Financial Time Series Generation via Generative Adversarial Learning. Proceedings of the 29th European Signal Processing Conference (EUSIPCO), Dublin, Ireland.","DOI":"10.23919\/EUSIPCO54536.2021.9616176"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Zhou, W., Yang, M., and Han, L. (August, January 30). A Nonparametric Approach to Pricing Convertible Bond via Neural Network. Proceedings of the Eighth ACIS International Conference on Software Engineering, Artificial Intelligence, Networking, and Parallel\/Distributed Computing (SNPD 2007), Qingdao, China.","DOI":"10.1109\/SNPD.2007.399"},{"key":"ref_33","first-page":"58","article-title":"Pricing and Empirical Analysis of Convertible Bonds Based on Machine Learning","volume":"5","author":"Niu","year":"2021","journal-title":"J. Party Sch. Guizhou Prov."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Ren, G., and Meng, T. (2024). Research on Pricing Methods of Convertible Bonds Based on Deep Learning GAN Models. Int. J. Financ. Stud., 11.","DOI":"10.3390\/ijfs11040145"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"698","DOI":"10.1016\/j.ejor.2017.05.048","article-title":"An improved least squares Monte Carlo valuation method based on heteroscedasticity","volume":"263","author":"Fabozzi","year":"2017","journal-title":"Eur. J. Oper. Res."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"865","DOI":"10.1007\/s10614-019-09947-2","article-title":"Fast Monte Carlo Simulation for Pricing Equity-Linked Securities","volume":"56","author":"Jang","year":"2019","journal-title":"Comput. Econ."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Andreasson, J., and Shevchenko, P.V. (2021). A bias-corrected Least-Squares Monte Carlo for solving multi-period utility models. Soc. Sci. Res. Netw.","DOI":"10.1007\/s13385-021-00288-9"},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Boire, F.M., Reesor, R.M., and Stentoft, L. (2022). Bias Correction in the Least-Squares Monte Carlo Algorithm. SSRN Electron. J.","DOI":"10.2139\/ssrn.4221111"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"85","DOI":"10.12660\/rbfin.v19n3.2021.83815","article-title":"American option pricing with machine learning: An extension of the Longstaff-Schwartz method","volume":"19","author":"Lin","year":"2021","journal-title":"Braz. Rev. Financ."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"121","DOI":"10.21314\/JCF.2014.279","article-title":"Pricing American-style options by Monte Carlo simulation: Alternatives to ordinary least squares","volume":"18","author":"Tompaidis","year":"2014","journal-title":"J. Comput. Financ."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1515\/fcds-2018-0011","article-title":"Supervised machine learning with control variates for American option pricing","volume":"43","author":"Mu","year":"2018","journal-title":"Found. Comput. Decis. Sci."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"573","DOI":"10.1080\/14697688.2019.1701698","article-title":"Machine learning for pricing American options in high-dimensional Markovian and non-Markovian models","volume":"20","author":"Molent","year":"2020","journal-title":"Quant. Financ."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1023\/A:1010933404324","article-title":"Random Forests","volume":"45","author":"Breiman","year":"2001","journal-title":"Mach. Learn."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"1113","DOI":"10.1137\/21M1460648","article-title":"Pricing Bermudan Options Using Regression Trees\/Random Forests","volume":"14","author":"Lelong","year":"2023","journal-title":"SIAM J. Financ. Math."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"107201","DOI":"10.1016\/j.geomorph.2020.107201","article-title":"A random forest model of landslide susceptibility mapping based on hyperparameter optimization using Bayes algorithm","volume":"362","author":"Sun","year":"2020","journal-title":"Geomorphology"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"109714","DOI":"10.1016\/j.engfracmech.2023.109714","article-title":"A random forest regression with Bayesian optimization-based method for fatigue strength prediction of ferrous alloys","volume":"293","author":"Guo","year":"2023","journal-title":"Eng. Fract. Mech."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/13\/4\/218\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T14:18:29Z","timestamp":1760105909000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/13\/4\/218"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,3,25]]},"references-count":46,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2024,4]]}},"alternative-id":["axioms13040218"],"URL":"https:\/\/doi.org\/10.3390\/axioms13040218","relation":{},"ISSN":["2075-1680"],"issn-type":[{"value":"2075-1680","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,3,25]]}}}