{"title":"Dynamic equilibrium with insider information and general uninformed agent utility","authors":"Jerome Detemple, Scott Robertson","doi":"10.1111/mafi.12444","DOIUrl":"10.1111/mafi.12444","url":null,"abstract":"<p>We study a continuous time economy where agents have asymmetric information. The informed agent (“<span></span><math>\u0000 <semantics>\u0000 <mi>I</mi>\u0000 <annotation>$I$</annotation>\u0000 </semantics></math>”), at time zero, receives a private signal about the risky assets' terminal payoff <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Ψ</mi>\u0000 <mo>(</mo>\u0000 <msub>\u0000 <mi>X</mi>\u0000 <mi>T</mi>\u0000 </msub>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$Psi (X_T)$</annotation>\u0000 </semantics></math>, while the uninformed agent (“<span></span><math>\u0000 <semantics>\u0000 <mi>U</mi>\u0000 <annotation>$U$</annotation>\u0000 </semantics></math>”) has no private signal. <span></span><math>\u0000 <semantics>\u0000 <mi>Ψ</mi>\u0000 <annotation>$Psi$</annotation>\u0000 </semantics></math> is an arbitrary payoff function, and <span></span><math>\u0000 <semantics>\u0000 <mi>X</mi>\u0000 <annotation>$X$</annotation>\u0000 </semantics></math> follows a time-homogeneous diffusion. Crucially, we allow <span></span><math>\u0000 <semantics>\u0000 <mi>U</mi>\u0000 <annotation>$U$</annotation>\u0000 </semantics></math> to have von Neumann–Morgenstern preferences with a general utility function on <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mn>0</mn>\u0000 <mo>,</mo>\u0000 <mi>∞</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(0,infty)$</annotation>\u0000 </semantics></math> satisfying the standard conditions. This extends previous constructions of equilibria with asymmetric information used when all agents have exponential utilities and enables us to study the impact of <i>U</i>'s initial share endowment on equilibrium. To allow for <span></span><math>\u0000 <semantics>\u0000 <mi>U</mi>\u0000 <annotation>$U$</annotation>\u0000 </semantics></math> to have general preferences, we introduce a new method to prove existence of a partial communication equilibrium (PCE), where at time 0, <span></span><math>\u0000 <semantics>\u0000 <mi>U</mi>\u0000 <annotation>$U$</annotation>\u0000 </semantics></math> receives a less-informative signal than <span></span><math>\u0000 <semantics>\u0000 <mi>I</mi>\u0000 <annotation>$I$</annotation>\u0000 </semantics></math>. In the single asset case, this signal is recoverable by viewing the equilibrium price process over an arbitrarily short period of time, and hence the PCE is a dynamic noisy rational expectations equilibrium. Lastly, when <span></span><math>\u0000 <semantics>\u0000 <m","PeriodicalId":49867,"journal":{"name":"Mathematical Finance","volume":"35 1","pages":"111-160"},"PeriodicalIF":1.6,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141744388","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Francesca Biagini, Lukas Gonon, Andrea Mazzon, Thilo Meyer-Brandis
{"title":"Detecting asset price bubbles using deep learning","authors":"Francesca Biagini, Lukas Gonon, Andrea Mazzon, Thilo Meyer-Brandis","doi":"10.1111/mafi.12443","DOIUrl":"10.1111/mafi.12443","url":null,"abstract":"<p>In this paper, we employ deep learning techniques to detect financial asset bubbles by using observed call option prices. The proposed algorithm is widely applicable and model-independent. We test the accuracy of our methodology in numerical experiments within a wide range of models and apply it to market data of tech stocks in order to assess if asset price bubbles are present. Under a given condition on the pricing of call options under asset price bubbles, we are able to provide a theoretical foundation of our approach for positive and continuous stochastic asset price processes. When such a condition is not satisfied, we focus on local volatility models. To this purpose, we give a new necessary and sufficient condition for a process with time-dependent local volatility function to be a strict local martingale.</p>","PeriodicalId":49867,"journal":{"name":"Mathematical Finance","volume":"35 1","pages":"74-110"},"PeriodicalIF":1.6,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/mafi.12443","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141744389","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Corporate debt value under transition scenario uncertainty","authors":"Theo Le Guenedal, Peter Tankov","doi":"10.1111/mafi.12441","DOIUrl":"10.1111/mafi.12441","url":null,"abstract":"<p>We develop a structural model for pricing a defaultable bond issued by a company subject to climate transition risk. We assume that the magnitude of the transition risk impacts depends on a transition scenario, which is initially unknown but is progressively revealed through the observation of the carbon tax trajectory. The bond price, credit spread, and optimal default/restructuring thresholds are then expressed as function of the firm's revenue level and the carbon tax. Numerical implementation of the resulting formulas is discussed and illustrated using real data. Our results show that under transition scenario uncertainty, carbon tax adjustments are more likely to trigger a default than when the true scenario is known because after each adjustment, the more environmentally stringent scenario becomes more likely. We also find that faster discovery of scenario information leads to higher credit spreads since better information allows the shareholders to optimize the timing of default, increasing the value of default option and decreasing the bond price. As an extension, we consider the situation where the company may invest into abatement technology, increasing the value of both the share price and the bond price.</p>","PeriodicalId":49867,"journal":{"name":"Mathematical Finance","volume":"35 1","pages":"40-73"},"PeriodicalIF":1.6,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/mafi.12441","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141523259","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Long-term risk with stochastic interest rates","authors":"Federico Severino","doi":"10.1111/mafi.12440","DOIUrl":"https://doi.org/10.1111/mafi.12440","url":null,"abstract":"<p>In constant-rate markets, the average stochastic discount factor growth rate coincides with the instantaneous rate. When interest rates are stochastic, this average growth rate is given by the long-term yield of zero-coupon bonds, which cannot serve as instantaneous discount rate. We show how to reconcile the stochastic discount factor growth with the instantaneous relations between returns and rates in stochastic-rate markets. We factorize no-arbitrage prices and isolate a rate adjustment that captures the short-term variability of rates. The rate-adjusted stochastic discount factor features the same long-term growth as the stochastic discount factor in the market but has no transient component in its Hansen–Scheinkman decomposition, capturing the long-term interest rate risk. Moreover, we show how the rate adjustment can be used for managing the interest rate risk related to fixed-income derivatives and life insurances.</p>","PeriodicalId":49867,"journal":{"name":"Mathematical Finance","volume":"35 1","pages":"3-39"},"PeriodicalIF":1.6,"publicationDate":"2024-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/mafi.12440","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143110961","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Distortion risk measures: Prudence, coherence, and the expected shortfall","authors":"Massimiliano Amarante, Felix-Benedikt Liebrich","doi":"10.1111/mafi.12435","DOIUrl":"10.1111/mafi.12435","url":null,"abstract":"<p>Distortion risk measures (DRM) are risk measures that are law invariant and comonotonic additive. The present paper is an extensive inquiry into this class of risk measures in light of new ideas such as qualitative robustness, prudence and no reward for concentration, and tail relevance. Results include several characterizations of prudent DRMs, a novel representation of coherent DRMs as well as an axiomatization of the Expected Shortfall alternative to the one recently provided by Wang and Zitikis. By linking the two axiomatizations, the paper provides a new perspective on the idea of no reward for concentration. The paper also contains results of independent interest such as the lower semicontinuity with respect to convergence in distribution of the Haezendonck–Goovaerts risk measures, the extension of non-necessarily convex risk measures as well as the structure of the core of a general submodular distortion.</p>","PeriodicalId":49867,"journal":{"name":"Mathematical Finance","volume":"34 4","pages":"1291-1327"},"PeriodicalIF":1.6,"publicationDate":"2024-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/mafi.12435","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141191393","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Stability of the Epstein–Zin problem","authors":"Michael Monoyios, Oleksii Mostovyi","doi":"10.1111/mafi.12434","DOIUrl":"10.1111/mafi.12434","url":null,"abstract":"<p>We investigate the stability of the Epstein–Zin problem with respect to small distortions in the dynamics of the traded securities. We work in incomplete market model settings, where our parametrization of perturbations allows for joint distortions in returns and volatility of the risky assets and the interest rate. Considering empirically the most relevant specifications of risk aversion and elasticity of intertemporal substitution, we provide a condition that guarantees the convexity of the domain of the underlying problem and results in the existence and uniqueness of a solution to it. Then, we prove the convergence of the optimal consumption streams, the associated wealth processes, the indirect utility processes, and the value functions in the limit when the model perturbations vanish.</p>","PeriodicalId":49867,"journal":{"name":"Mathematical Finance","volume":"34 4","pages":"1263-1290"},"PeriodicalIF":1.6,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141146340","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Lorenzo Bastianello, Alain Chateauneuf, Bernard Cornet
{"title":"Put–Call Parities, absence of arbitrage opportunities, and nonlinear pricing rules","authors":"Lorenzo Bastianello, Alain Chateauneuf, Bernard Cornet","doi":"10.1111/mafi.12433","DOIUrl":"10.1111/mafi.12433","url":null,"abstract":"<p>When prices of assets traded in a financial market are determined by nonlinear pricing rules, different parities between call and put options have been considered. We show that, under monotonicity, parities between call and put options and discount certificates characterize ambiguity-sensitive (Choquet and/or Šipoš) pricing rules, that is, pricing rules that can be represented via discounted expectations with respect to non-additive probability measures. We analyze how nonadditivity relates to arbitrage opportunities and we give necessary and sufficient conditions for Choquet and Šipoš pricing rules to be arbitrage free. Finally, we identify violations of the Call-Put Parity with the presence of bid–ask spreads.</p>","PeriodicalId":49867,"journal":{"name":"Mathematical Finance","volume":"34 4","pages":"1242-1262"},"PeriodicalIF":1.6,"publicationDate":"2024-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/mafi.12433","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140301553","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The rough Hawkes Heston stochastic volatility model","authors":"Alessandro Bondi, Sergio Pulido, Simone Scotti","doi":"10.1111/mafi.12432","DOIUrl":"10.1111/mafi.12432","url":null,"abstract":"<p>We study an extension of the Heston stochastic volatility model that incorporates rough volatility and jump clustering phenomena. In our model, named the rough Hawkes Heston stochastic volatility model, the spot variance is a rough Hawkes-type process proportional to the intensity process of the jump component appearing in the dynamics of the spot variance itself and the log returns. The model belongs to the class of affine Volterra models. In particular, the Fourier-Laplace transform of the log returns and the square of the volatility index can be computed explicitly in terms of solutions of deterministic Riccati-Volterra equations, which can be efficiently approximated using a multi-factor approximation technique. We calibrate a parsimonious specification of our model characterized by a power kernel and an exponential law for the jumps. We show that our parsimonious setup is able to simultaneously capture, with a high precision, the behavior of the implied volatility smile for both S&P 500 and VIX options. In particular, we observe that in our setting the usual shift in the implied volatility of VIX options is explained by a very low value of the power in the kernel. Our findings demonstrate the relevance, under an affine framework, of rough volatility and self-exciting jumps in order to capture the joint evolution of the S&P 500 and VIX.</p>","PeriodicalId":49867,"journal":{"name":"Mathematical Finance","volume":"34 4","pages":"1197-1241"},"PeriodicalIF":1.6,"publicationDate":"2024-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140037372","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
