{"title":"A LÉVY-DRIVEN ORNSTEIN–UHLENBECK PROCESS FOR THE VALUATION OF CREDIT INDEX SWAPTIONS","authors":"YOSHIHIRO SHIRAI","doi":"10.1142/s021902492350022x","DOIUrl":"https://doi.org/10.1142/s021902492350022x","url":null,"abstract":"<p>A Lévy-driven Ornstein–Uhlenbeck process is proposed to model the evolution of the risk-free rate and default intensities for the purpose of evaluating option contracts on a credit index. Time evolution in credit markets is assumed to follow a gamma process in order to reflect the different speed at which credit products are exchanged with respect to securities, such as Treasuries, deemed risk-free. Formulas for the characteristic function, zero coupon bonds, moments of the process and its stationary distribution are derived. Numerical experiments showing convergence of standard numerical methods for the valuation PIDE to analytical and Monte Carlo solutions are shown. Calibration to market prices of options on a credit index is performed, and model- and market-implied summary statistics for the underlying credit spreads are estimated and compared.</p>","PeriodicalId":47022,"journal":{"name":"International Journal of Theoretical and Applied Finance","volume":"17 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140201781","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Systemic Perspective of Term Risk in Bank Funding Markets","authors":"Andrea Macrina, Obeid Mahomed","doi":"10.1142/s0219024924500018","DOIUrl":"https://doi.org/10.1142/s0219024924500018","url":null,"abstract":"","PeriodicalId":47022,"journal":{"name":"International Journal of Theoretical and Applied Finance","volume":"91 7","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139450370","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"PORTFOLIO CHOICE WITH TIME HORIZON RISK","authors":"ALEXIS DIRER","doi":"10.1142/s0219024923500267","DOIUrl":"https://doi.org/10.1142/s0219024923500267","url":null,"abstract":"<p>I study the allocation problem of investors who hold their portfolio until reaching a target wealth. The strategy suppresses final wealth uncertainty but creates a time horizon risk. I begin with a classical mean variance model transposed in the duration domain, then study a dynamic portfolio choice problem with Generalized Expected Discounted Utility preferences. Using long-term US return data, I show in the mean variance model that a large amount of time horizon risk can be diversified away by investing a significant share of equities. In the dynamic model, more impatient investors are also more averse to timing risk and invest less in equities. The optimal equity share is downward trending as accumulated wealth approaches its target.</p>","PeriodicalId":47022,"journal":{"name":"International Journal of Theoretical and Applied Finance","volume":"30 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140197807","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
ENRICO DALL’ACQUA, RICCARDO LONGONI, ANDREA PALLAVICINI
{"title":"ROUGH-HESTON LOCAL-VOLATILITY MODEL","authors":"ENRICO DALL’ACQUA, RICCARDO LONGONI, ANDREA PALLAVICINI","doi":"10.1142/s0219024923500218","DOIUrl":"https://doi.org/10.1142/s0219024923500218","url":null,"abstract":"<p>In industrial applications it is quite common to use stochastic-volatility models driven by semi-martingale Markov volatility processes. However, in order to fit exactly market volatilities, these models are usually extended by adding a local-volatility term. Here, we consider the case of singular Volterra processes, and we extend them by adding a local-volatility term to their Markov lift by preserving the stylized results implied by these models on plain-vanilla options. In particular, we focus on the rough-Heston model, and we analyze the small-time asymptotics of its implied local-volatility function in order to provide a proper extrapolation scheme to be used in calibration.</p>","PeriodicalId":47022,"journal":{"name":"International Journal of Theoretical and Applied Finance","volume":"25 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140197809","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Short-Maturity Asymptotics for Option Prices with Interest Rates Effects","authors":"D. Pirjol, Lingjiong Zhu","doi":"10.1142/s0219024923500231","DOIUrl":"https://doi.org/10.1142/s0219024923500231","url":null,"abstract":"","PeriodicalId":47022,"journal":{"name":"International Journal of Theoretical and Applied Finance","volume":"919 ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139204411","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Polynomial Utility","authors":"A. S. Lollike, Mogens Steffensen","doi":"10.1142/s0219024923500243","DOIUrl":"https://doi.org/10.1142/s0219024923500243","url":null,"abstract":"","PeriodicalId":47022,"journal":{"name":"International Journal of Theoretical and Applied Finance","volume":"47 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139201830","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Marcello Basili, Alain Chateauneuf, Giuliano Antonio Curatola, G. Scianna
{"title":"A Representation of Keynes's long-term expectation in financial markets","authors":"Marcello Basili, Alain Chateauneuf, Giuliano Antonio Curatola, G. Scianna","doi":"10.1142/s0219024923500255","DOIUrl":"https://doi.org/10.1142/s0219024923500255","url":null,"abstract":"","PeriodicalId":47022,"journal":{"name":"International Journal of Theoretical and Applied Finance","volume":"664 ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139203171","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"PDEs for reflected BSDENMs applied to American options","authors":"Mohamed El Jamali, Hatim Tayeq","doi":"10.1142/s0219024923300019","DOIUrl":"https://doi.org/10.1142/s0219024923300019","url":null,"abstract":"","PeriodicalId":47022,"journal":{"name":"International Journal of Theoretical and Applied Finance","volume":" 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135191731","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Withdrawal Success Estimation","authors":"Hayden Brown","doi":"10.1142/s0219024923500140","DOIUrl":"https://doi.org/10.1142/s0219024923500140","url":null,"abstract":"Given an asset having a geometric Lévy alpha-stable wealth process, a log-Lévy alpha-stable lower bound is constructed for the terminal wealth of a regular investing schedule. Using a transformation, the lower bound is applied to a schedule of withdrawals occurring after an initial investment. As a result, an upper bound is described on the probability to complete a given schedule of withdrawals. For withdrawals of a constant amount at equidistant times, necessary conditions are given on the initial investment and parameters of the wealth process such that [Formula: see text] withdrawals can be made with 95% confidence. When withdrawing from an annually rebalanced portfolio maintaining 100[Formula: see text]% in the S&P Composite Index and 100([Formula: see text])% in inflation protected bonds, the initial investment must be at least [Formula: see text] times the amount of each withdrawal for [Formula: see text] and [Formula: see text].","PeriodicalId":47022,"journal":{"name":"International Journal of Theoretical and Applied Finance","volume":"6 5","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135011740","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Pricing American option using a modified fractional Black-Scholes Model under multi-state regime switching","authors":"M. Yousuf, A. Q. M. Khaliq","doi":"10.1142/s021902492350019x","DOIUrl":"https://doi.org/10.1142/s021902492350019x","url":null,"abstract":"","PeriodicalId":47022,"journal":{"name":"International Journal of Theoretical and Applied Finance","volume":"77 8","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135221277","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}