Mathematical Finance最新文献

{"title":"Do investors gain by selling the tails of return distributions?","authors":"Gurdip Bakshi,&nbsp;John Crosby,&nbsp;Xiaohui Gao","doi":"10.1111/mafi.12447","DOIUrl":"https://doi.org/10.1111/mafi.12447","url":null,"abstract":"<p>This paper examines whether investors gain by selling the tails of return distributions. To address this, we develop a way of ranking and scoring actively managed funds and investment strategies, which accounts for ambiguity aversion and risk aversion in decision-making. Using data relating to options on the S&amp;P 500 equity index and Treasury bond futures and to hedge funds, we provide evidence that suggests a negative answer to this question. We reinforce this evidence with data from options on the STOXX 50, FTSE, and Nikkei equity indices.</p>","PeriodicalId":49867,"journal":{"name":"Mathematical Finance","volume":"35 2","pages":"297-336"},"PeriodicalIF":1.6,"publicationDate":"2024-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143639056","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}

{"title":"Tackling nonlinear price impact with linear strategies","authors":"Xavier Brokmann,&nbsp;David Itkin,&nbsp;Johannes Muhle-Karbe,&nbsp;Peter Schmidt","doi":"10.1111/mafi.12449","DOIUrl":"https://doi.org/10.1111/mafi.12449","url":null,"abstract":"<p>Empirical studies in various contexts find that the price impact of large trades approximately follows a power law with exponent between 0.4 and 0.7. Yet, tractable formulas for the portfolios that trade off predictive trading signals, risk, and trading costs in an optimal manner are only available for quadratic costs corresponding to linear price impact. In this paper, we show that the resulting linear strategies allow to achieve virtually optimal performance also for realistic nonlinear price impact, <i>if</i> the “effective” quadratic cost parameter is chosen appropriately. To wit, for a wide range of risk levels, this leads to performance losses below 2% compared to a numerical algorithm proposed by Kolm and Ritter, run at very high accuracy. The effective quadratic cost depends on the portfolio risk and concavity of the impact function, but can be computed without any sophisticated numerics by simply maximizing an explicit scalar function.</p>","PeriodicalId":49867,"journal":{"name":"Mathematical Finance","volume":"35 2","pages":"422-440"},"PeriodicalIF":1.6,"publicationDate":"2024-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/mafi.12449","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143638748","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":"Designing stablecoins","authors":"Yizhou Cao,&nbsp;Min Dai,&nbsp;Steven Kou,&nbsp;Lewei Li,&nbsp;Chen Yang","doi":"10.1111/mafi.12445","DOIUrl":"10.1111/mafi.12445","url":null,"abstract":"<p>Existing cryptocurrencies are too volatile to be used as currencies for daily payments. Stablecoins, which are cryptocurrencies pegged to other stable financial assets such as the US dollar, are desirable for payments within blockchain networks, whereby being often called the “Holy Grail of cryptocurrency.” By using the option pricing theory and the Ethereum platform that allows running smart contracts, we design several dual-class structures that are written on the ETH cryptocurrency and offer a fixed-income crypto asset (Class A coin), a stablecoin (Class A′ coin) pegged to a traditional currency, and leveraged investment instruments (Class B and B′ coins). Our investigation of the values of stablecoins in the presence of jump risk and black swan-type events shows the robustness of the design. The design has been implemented on the Ethereum platform.</p>","PeriodicalId":49867,"journal":{"name":"Mathematical Finance","volume":"35 1","pages":"263-294"},"PeriodicalIF":1.6,"publicationDate":"2024-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142195735","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}

{"title":"Systemic risk in markets with multiple central counterparties","authors":"Luitgard Anna Maria Veraart,&nbsp;Iñaki Aldasoro","doi":"10.1111/mafi.12446","DOIUrl":"10.1111/mafi.12446","url":null,"abstract":"<p>We provide a framework for modeling risk and quantifying payment shortfalls in cleared markets with multiple central counterparties (CCPs). Building on the stylized fact that clearing membership is shared among CCPs, we develop a modeling framework that captures the interconnectedness of CCPs and clearing members. We illustrate stress transmission mechanisms using simple examples as well as empirical evidence based on calibrated data. Furthermore, we show how stress mitigation tools such as variation margin gains haircutting by one CCP can have spillover effects on other CCPs. The framework can be used to enhance CCP stress-testing, which currently relies on the “Cover 2” standard requiring CCPs to be able to withstand the default of their two largest clearing members. We show that who these two clearing members are can be significantly affected if one considers higher-order effects arising from interconnectedness through shared clearing membership. Looking at the full network of CCPs and shared clearing members is, therefore, important from a financial stability perspective.</p>","PeriodicalId":49867,"journal":{"name":"Mathematical Finance","volume":"35 1","pages":"214-262"},"PeriodicalIF":1.6,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/mafi.12446","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142195718","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":"Joint calibration to SPX and VIX options with signature-based models","authors":"Christa Cuchiero,&nbsp;Guido Gazzani,&nbsp;Janka Möller,&nbsp;Sara Svaluto-Ferro","doi":"10.1111/mafi.12442","DOIUrl":"10.1111/mafi.12442","url":null,"abstract":"<p>We consider a stochastic volatility model where the dynamics of the volatility are described by a linear function of the (time extended) signature of a primary process which is supposed to be a polynomial diffusion. We obtain closed form expressions for the VIX squared, exploiting the fact that the truncated signature of a polynomial diffusion is again a polynomial diffusion. Adding to such a primary process the Brownian motion driving the stock price, allows then to express both the log-price and the VIX squared as linear functions of the signature of the corresponding augmented process. This feature can then be efficiently used for pricing and calibration purposes. Indeed, as the signature samples can be easily precomputed, the calibration task can be split into an offline sampling and a standard optimization. We also propose a Fourier pricing approach for both VIX and SPX options exploiting that the signature of the augmented primary process is an infinite dimensional affine process. For both the SPX and VIX options we obtain highly accurate calibration results, showing that this model class allows to solve the joint calibration problem without adding jumps or rough volatility.</p>","PeriodicalId":49867,"journal":{"name":"Mathematical Finance","volume":"35 1","pages":"161-213"},"PeriodicalIF":1.6,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141866751","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}

{"title":"Dynamic equilibrium with insider information and general uninformed agent utility","authors":"Jerome Detemple,&nbsp;Scott Robertson","doi":"10.1111/mafi.12444","DOIUrl":"10.1111/mafi.12444","url":null,"abstract":"&lt;p&gt;We study a continuous time economy where agents have asymmetric information. The informed agent (“&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;I&lt;/mi&gt;\u0000 &lt;annotation&gt;$I$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;”), at time zero, receives a private signal about the risky assets' terminal payoff &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;Ψ&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;mi&gt;T&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$Psi (X_T)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, while the uninformed agent (“&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;U&lt;/mi&gt;\u0000 &lt;annotation&gt;$U$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;”) has no private signal. &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;Ψ&lt;/mi&gt;\u0000 &lt;annotation&gt;$Psi$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is an arbitrary payoff function, and &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;annotation&gt;$X$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; follows a time-homogeneous diffusion. Crucially, we allow &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;U&lt;/mi&gt;\u0000 &lt;annotation&gt;$U$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; to have von Neumann–Morgenstern preferences with a general utility function on &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;∞&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$(0,infty)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; 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 &lt;i&gt;U&lt;/i&gt;'s initial share endowment on equilibrium. To allow for &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;U&lt;/mi&gt;\u0000 &lt;annotation&gt;$U$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; to have general preferences, we introduce a new method to prove existence of a partial communication equilibrium (PCE), where at time 0, &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;U&lt;/mi&gt;\u0000 &lt;annotation&gt;$U$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; receives a less-informative signal than &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;I&lt;/mi&gt;\u0000 &lt;annotation&gt;$I$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. 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 &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;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}

{"title":"Detecting asset price bubbles using deep learning","authors":"Francesca Biagini,&nbsp;Lukas Gonon,&nbsp;Andrea Mazzon,&nbsp;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,&nbsp;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,&nbsp;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}