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On short-time behavior of implied volatility in a market model with indexes 论指数市场模型中隐含波动率的短期行为
arXiv - QuantFin - Pricing of Securities Pub Date : 2024-02-26 DOI: arxiv-2402.16509
Huy N. Chau, Duy Nguyen, Thai Nguyen
{"title":"On short-time behavior of implied volatility in a market model with indexes","authors":"Huy N. Chau, Duy Nguyen, Thai Nguyen","doi":"arxiv-2402.16509","DOIUrl":"https://doi.org/arxiv-2402.16509","url":null,"abstract":"This paper investigates short-term behaviors of implied volatility of\u0000derivatives written on indexes in equity markets when the index processes are\u0000constructed by using a ranking procedure. Even in simple market settings where\u0000stock prices follow geometric Brownian motion dynamics, the ranking mechanism\u0000can produce the observed term structure of at-the-money (ATM) implied\u0000volatility skew for equity indexes. Our proposed models showcase the ability to\u0000reconcile two seemingly contradictory features found in empirical data from\u0000equity markets: the long memory of volatilities and the power law of ATM skews.\u0000Furthermore, the models allow for the capture of a novel phenomenon termed the\u0000quasi-blow-up phenomenon.","PeriodicalId":501355,"journal":{"name":"arXiv - QuantFin - Pricing of Securities","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139979642","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}
引用次数: 0
Alternative models for FX: pricing double barrier options in regime-switching Lévy models with memory 外汇的替代模型：在有记忆的制度转换莱维模型中为双障碍期权定价
arXiv - QuantFin - Pricing of Securities Pub Date : 2024-02-26 DOI: arxiv-2402.16724
Svetlana Boyarchenko, Sergei Levendorskiĭ
{"title":"Alternative models for FX: pricing double barrier options in regime-switching Lévy models with memory","authors":"Svetlana Boyarchenko, Sergei Levendorskiĭ","doi":"arxiv-2402.16724","DOIUrl":"https://doi.org/arxiv-2402.16724","url":null,"abstract":"This paper is a supplement to our recent paper ``Alternative models for FX,\u0000arbitrage opportunities and efficient pricing of double barrier options in\u0000L'evy models\". We introduce the class of regime-switching L'evy models with\u0000memory, which take into account the evolution of the stochastic parameters in\u0000the past. This generalization of the class of L'evy models modulated by Markov\u0000chains is similar in spirit to rough volatility models. It is flexible and\u0000suitable for application of the machine-learning tools. We formulate the\u0000modification of the numerical method in ``Alternative models for FX, arbitrage\u0000opportunities and efficient pricing of double barrier options in L'evy\u0000models\", which has the same number of the main time-consuming blocks as the\u0000method for Markovian regime-switching models.","PeriodicalId":501355,"journal":{"name":"arXiv - QuantFin - Pricing of Securities","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139979187","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}
引用次数: 0
Pricing of geometric Asian options in the Volterra-Heston model Volterra-Heston 模型中几何亚洲期权的定价
arXiv - QuantFin - Pricing of Securities Pub Date : 2024-02-24 DOI: arxiv-2402.15828
Florian Aichinger, Sascha Desmettre
{"title":"Pricing of geometric Asian options in the Volterra-Heston model","authors":"Florian Aichinger, Sascha Desmettre","doi":"arxiv-2402.15828","DOIUrl":"https://doi.org/arxiv-2402.15828","url":null,"abstract":"Geometric Asian options are a type of options where the payoff depends on the\u0000geometric mean of the underlying asset over a certain period of time. This\u0000paper is concerned with the pricing of such options for the class of\u0000Volterra-Heston models, covering the rough Heston model. We are able to derive\u0000semi-closed formulas for the prices of geometric Asian options with fixed and\u0000floating strikes for this class of stochastic volatility models. These formulas\u0000require the explicit calculation of the conditional joint Fourier transform of\u0000the logarithm of the stock price and the logarithm of the geometric mean of the\u0000stock price over time. Linking our problem to the theory of affine Volterra\u0000processes, we find a representation of this Fourier transform as a suitably\u0000constructed stochastic exponential, which depends on the solution of a\u0000Riccati-Volterra equation. Finally we provide a numerical study for our results\u0000in the rough Heston model.","PeriodicalId":501355,"journal":{"name":"arXiv - QuantFin - Pricing of Securities","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139978705","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}
引用次数: 0
Short-maturity asymptotics for option prices with interest rates effects 具有利率效应的期权价格的短期到期渐近线
arXiv - QuantFin - Pricing of Securities Pub Date : 2024-02-21 DOI: arxiv-2402.14161
Dan Pirjol, Lingjiong Zhu
{"title":"Short-maturity asymptotics for option prices with interest rates effects","authors":"Dan Pirjol, Lingjiong Zhu","doi":"arxiv-2402.14161","DOIUrl":"https://doi.org/arxiv-2402.14161","url":null,"abstract":"We derive the short-maturity asymptotics for option prices in the local\u0000volatility model in a new short-maturity limit $Tto 0$ at fixed $rho = (r-q)\u0000T$, where $r$ is the interest rate and $q$ is the dividend yield. In cases of\u0000practical relevance $rho$ is small, however our result holds for any fixed\u0000$rho$. The result is a generalization of the Berestycki-Busca-Florent formula\u0000for the short-maturity asymptotics of the implied volatility which includes\u0000interest rates and dividend yield effects of $O(((r-q) T)^n)$ to all orders in\u0000$n$. We obtain analytical results for the ATM volatility and skew in this\u0000asymptotic limit. Explicit results are derived for the CEV model. The\u0000asymptotic result is tested numerically against exact evaluation in the\u0000square-root model model $sigma(S)=sigma/sqrt{S}$, which demonstrates that\u0000the new asymptotic result is in very good agreement with exact evaluation in a\u0000wide range of model parameters relevant for practical applications.","PeriodicalId":501355,"journal":{"name":"arXiv - QuantFin - Pricing of Securities","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139953613","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}
引用次数: 0
Denoised Monte Carlo for option pricing and Greeks estimation 用于期权定价和希腊字母估算的去噪蒙特卡洛算法
arXiv - QuantFin - Pricing of Securities Pub Date : 2024-02-19 DOI: arxiv-2402.12528
Andrzej Daniluk, Evgeny Lakshtanov, Rafal Muchorski
{"title":"Denoised Monte Carlo for option pricing and Greeks estimation","authors":"Andrzej Daniluk, Evgeny Lakshtanov, Rafal Muchorski","doi":"arxiv-2402.12528","DOIUrl":"https://doi.org/arxiv-2402.12528","url":null,"abstract":"We present a novel technique of Monte Carlo error reduction that finds direct\u0000application in option pricing and Greeks estimation. The method is applicable\u0000to any LSV modelling framework and concerns a broad class of payoffs, including\u0000path-dependent and multi-asset cases. Most importantly, it allows to reduce the\u0000Monte Carlo error even by an order of magnitude, which is shown in several\u0000numerical examples.","PeriodicalId":501355,"journal":{"name":"arXiv - QuantFin - Pricing of Securities","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139922011","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}
引用次数: 0
Exact simulation scheme for the Ornstein-Uhlenbeck driven stochastic volatility model with the Karhunen-Loève expansions 采用卡胡宁-洛埃夫扩展的奥恩斯坦-乌伦贝克驱动随机波动模型的精确模拟方案
arXiv - QuantFin - Pricing of Securities Pub Date : 2024-02-14 DOI: arxiv-2402.09243
Jaehyuk Choi
{"title":"Exact simulation scheme for the Ornstein-Uhlenbeck driven stochastic volatility model with the Karhunen-Loève expansions","authors":"Jaehyuk Choi","doi":"arxiv-2402.09243","DOIUrl":"https://doi.org/arxiv-2402.09243","url":null,"abstract":"This study proposes a new exact simulation scheme of the Ornstein-Uhlenbeck\u0000driven stochastic volatility model. With the Karhunen-Lo`eve expansions, the\u0000stochastic volatility path following the Ornstein-Uhlenbeck process is\u0000expressed as a sine series, and the time integrals of volatility and variance\u0000are analytically derived as the sums of independent normal random variates. The\u0000new method is several hundred times faster than Li and Wu [Eur. J. Oper. Res.,\u00002019, 275(2), 768-779] that relies on computationally expensive numerical\u0000transform inversion. The simulation algorithm is further improved with the\u0000conditional Monte-Carlo method and the martingale-preserving control variate on\u0000the spot price.","PeriodicalId":501355,"journal":{"name":"arXiv - QuantFin - Pricing of Securities","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139772641","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}
引用次数: 0
Quantum Amplitude Loading for Rainbow Options Pricing 彩虹期权定价的量子振幅加载
arXiv - QuantFin - Pricing of Securities Pub Date : 2024-02-08 DOI: arxiv-2402.05574
Francesca Cibrario, Or Samimi, Giacomo Ranieri, Emanuele Dri, Mattia Ippoliti, Ron Cohen, Christian Mattia, Bartolomeo Montrucchio, Amir Naveh, Davide Corbelletto
{"title":"Quantum Amplitude Loading for Rainbow Options Pricing","authors":"Francesca Cibrario, Or Samimi, Giacomo Ranieri, Emanuele Dri, Mattia Ippoliti, Ron Cohen, Christian Mattia, Bartolomeo Montrucchio, Amir Naveh, Davide Corbelletto","doi":"arxiv-2402.05574","DOIUrl":"https://doi.org/arxiv-2402.05574","url":null,"abstract":"This work introduces a novel approach to price rainbow options, a type of\u0000path-independent multi-asset derivatives, with quantum computers. Leveraging\u0000the Iterative Quantum Amplitude Estimation method, we present an end-to-end\u0000quantum circuit implementation, emphasizing efficiency by delaying the\u0000transition to price space. Moreover, we analyze two different amplitude loading\u0000techniques for handling exponential functions. Experiments on the IBM QASM\u0000simulator validate our quantum pricing model, contributing to the evolving\u0000field of quantum finance.","PeriodicalId":501355,"journal":{"name":"arXiv - QuantFin - Pricing of Securities","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139760302","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}
引用次数: 0
Measuring the performance of investments in information security startups: An empirical analysis by cybersecurity sectors using Crunchbase data 衡量信息安全初创企业的投资绩效：利用 Crunchbase 数据按网络安全行业进行实证分析
arXiv - QuantFin - Pricing of Securities Pub Date : 2024-02-07 DOI: arxiv-2402.04765
Loïc Maréchal, Alain Mermoud, Dimitri Percia David, Mathias Humbert
{"title":"Measuring the performance of investments in information security startups: An empirical analysis by cybersecurity sectors using Crunchbase data","authors":"Loïc Maréchal, Alain Mermoud, Dimitri Percia David, Mathias Humbert","doi":"arxiv-2402.04765","DOIUrl":"https://doi.org/arxiv-2402.04765","url":null,"abstract":"Early-stage firms play a significant role in driving innovation and creating\u0000new products and services, especially for cybersecurity. Therefore, evaluating\u0000their performance is crucial for investors and policymakers. This work presents\u0000a financial evaluation of early-stage firms' performance in 19 cybersecurity\u0000sectors using a private-equity dataset from 2010 to 2022 retrieved from\u0000Crunchbase. We observe firms, their primary and secondary activities, funding\u0000rounds, and pre and post-money valuations. We compare cybersecurity sectors\u0000regarding the amount raised over funding rounds and post-money valuations while\u0000inferring missing observations. We observe significant investor interest\u0000variations across categories, periods, and locations. In particular, we find\u0000the average capital raised (valuations) to range from USD 7.24 mln (USD 32.39\u0000mln) for spam filtering to USD 45.46 mln (USD 447.22 mln) for the private cloud\u0000sector. Next, we assume a log process for returns computed from post-money\u0000valuations and estimate the expected returns, systematic and specific risks,\u0000and risk-adjusted returns of investments in early-stage firms belonging to\u0000cybersecurity sectors. Again, we observe substantial performance variations\u0000with annualized expected returns ranging from 9.72% for privacy to 177.27%\u0000for the blockchain sector. Finally, we show that overall, the cybersecurity\u0000industry performance is on par with previous results found in private equity.\u0000Our results shed light on the performance of cybersecurity investments and,\u0000thus, on investors' expectations about cybersecurity.","PeriodicalId":501355,"journal":{"name":"arXiv - QuantFin - Pricing of Securities","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139760292","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}
引用次数: 0
Signature volatility models: pricing and hedging with Fourier 特征波动模型：用傅立叶定价和对冲
arXiv - QuantFin - Pricing of Securities Pub Date : 2024-02-02 DOI: arxiv-2402.01820
Eduardo Abi Jaber, Louis-Amand Gérard
{"title":"Signature volatility models: pricing and hedging with Fourier","authors":"Eduardo Abi Jaber, Louis-Amand Gérard","doi":"arxiv-2402.01820","DOIUrl":"https://doi.org/arxiv-2402.01820","url":null,"abstract":"We consider a stochastic volatility model where the dynamics of the\u0000volatility are given by a possibly infinite linear combination of the elements\u0000of the time extended signature of a Brownian motion. First, we show that the\u0000model is remarkably universal, as it includes, but is not limited to, the\u0000celebrated Stein-Stein, Bergomi, and Heston models, together with some\u0000path-dependent variants. Second, we derive the joint characteristic functional\u0000of the log-price and integrated variance provided that some infinite\u0000dimensional extended tensor algebra valued Riccati equation admits a solution.\u0000This allows us to price and (quadratically) hedge certain European and\u0000path-dependent options using Fourier inversion techniques. We highlight the\u0000efficiency and accuracy of these Fourier techniques in a comprehensive\u0000numerical study.","PeriodicalId":501355,"journal":{"name":"arXiv - QuantFin - Pricing of Securities","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139760370","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}
引用次数: 0
The Carbon Premium: Correlation or Causation? Evidence from S&P 500 Companies 碳溢价：相关性还是因果关系？来自标准普尔 500 指数公司的证据
arXiv - QuantFin - Pricing of Securities Pub Date : 2024-01-29 DOI: arxiv-2401.16455
Namasi G. Sankar, Suryadeepto Nag, Siddhartha P. Chakrabarty, Sankarshan Basu
{"title":"The Carbon Premium: Correlation or Causation? Evidence from S&P 500 Companies","authors":"Namasi G. Sankar, Suryadeepto Nag, Siddhartha P. Chakrabarty, Sankarshan Basu","doi":"arxiv-2401.16455","DOIUrl":"https://doi.org/arxiv-2401.16455","url":null,"abstract":"In the context of whether investors are aware of carbon-related risks, it is\u0000often hypothesized that there may be a carbon premium in the value of stocks of\u0000firms, conferring an abnormal excess value to firms' shares as a form of\u0000compensation to investors for their transition risk exposure through the\u0000ownership of carbon instensive stocks. However, there is little consensus in\u0000the literature regarding the existence of such a premium. Moreover few studies\u0000have examined whether the correlation that is often observed is actually\u0000causal. The pertinent question is whether more polluting firms give higher\u0000returns or do firms with high returns have less incentive to decarbonize? In\u0000this study, we investigate whether firms' emissions is causally linked to the\u0000presence of a carbon premium in a panel of 141 firms listed in the S&P500\u0000index using fixed-effects analysis, with propensity score weighting to control\u0000for selection bias in which firms increase their emissions. We find that there\u0000is a statistically significant positive carbon premium associated with Scope 1\u0000emissions, while there is no significant premium associated with Scope 2\u0000emissions, implying that risks associated with direct emissions by the firm are\u0000priced, while bought emissions are not.","PeriodicalId":501355,"journal":{"name":"arXiv - QuantFin - Pricing of Securities","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139646209","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}
引用次数: 0
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