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Realized Volatility Analysis in A Spin Model of Financial Markets 金融市场自旋模型中的已实现波动率分析
arXiv: Computational Finance Pub Date : 2015-11-29 DOI: 10.7566/JPSCP.1.019007
T. Takaishi
{"title":"Realized Volatility Analysis in A Spin Model of Financial Markets","authors":"T. Takaishi","doi":"10.7566/JPSCP.1.019007","DOIUrl":"https://doi.org/10.7566/JPSCP.1.019007","url":null,"abstract":"We calculate the realized volatility in the spin model of financial markets and examine the returns standardized by the realized volatility. We find that moments of the standardized returns agree with the theoretical values of standard normal variables. This is the first evidence that the return dynamics of the spin financial market is consistent with the view of the mixture-of-distribution hypothesis that also holds in the real financial markets.","PeriodicalId":197400,"journal":{"name":"arXiv: Computational Finance","volume":"50 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127378933","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: 3
Explicit solution to dynamic portfolio choice problem: The continuous-time detour 动态投资组合选择问题的显式解:连续时间迂回
arXiv: Computational Finance Pub Date : 2015-04-13 DOI: 10.13140/2.1.4715.3449
Franccois Legendre, D. Togola
{"title":"Explicit solution to dynamic portfolio choice problem: The continuous-time detour","authors":"Franccois Legendre, D. Togola","doi":"10.13140/2.1.4715.3449","DOIUrl":"https://doi.org/10.13140/2.1.4715.3449","url":null,"abstract":"This paper solves the dynamic portfolio choice problem. Using an explicit solution with a power utility, we construct a bridge between a continuous and discrete VAR model to assess portfolio sensitivities. We find, from a well analyzed example that the optimal allocation to stocks is particularly sensitive to Sharpe ratio. Our quantitative analysis highlights that this sensitivity increases when the risk aversion decreases and/or when the time horizon increases. This finding explains the low accuracy of discrete numerical methods especially along the tails of the unconditional distribution of the state variable.","PeriodicalId":197400,"journal":{"name":"arXiv: Computational Finance","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123572524","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
Monte Carlo Calculation of Exposure Profiles and Greeks for Bermudan and Barrier Options under the Heston Hull-White Model 在赫斯顿赫尔-怀特模型下百慕大和障碍期权的敞口剖面和希腊的蒙特卡罗计算
arXiv: Computational Finance Pub Date : 2014-12-01 DOI: 10.2139/ssrn.2494233
Qian Feng, C. Oosterlee
{"title":"Monte Carlo Calculation of Exposure Profiles and Greeks for Bermudan and Barrier Options under the Heston Hull-White Model","authors":"Qian Feng, C. Oosterlee","doi":"10.2139/ssrn.2494233","DOIUrl":"https://doi.org/10.2139/ssrn.2494233","url":null,"abstract":"Valuation of Credit Valuation Adjustment (CVA) has become an important field as its calculation is required in Basel III, issued in 2010, in the wake of the credit crisis. Exposure, which is defined as the potential future loss of a default event without any recovery, is one of the key elementsfor pricing CVA. This paper provides a backward dynamics framework for assessing exposure profiles of European, Bermudan and barrier options under the Heston and Heston Hull-White asset dynamics. We discuss the potential of an efficient and adaptive Monte Carlo approach, the Stochastic Grid Bundling Method}(SGBM), which employs the techniques of simulation, regression and bundling. Greeks of the exposure profiles can be calculated in the same backward iteration with little extra effort. Assuming independence between default event and exposure profiles, we give examples of calculating exposure, CVA and Greeks for Bermudan and barrier options.","PeriodicalId":197400,"journal":{"name":"arXiv: Computational Finance","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115019223","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: 4
High-order compact schemes for Black-Scholes basket options 布莱克-斯科尔斯篮子期权的高阶紧凑方案
arXiv: Computational Finance Pub Date : 2014-06-09 DOI: 10.1007/978-3-319-23413-7_152
Bertram During, Christof Heuer
{"title":"High-order compact schemes for Black-Scholes basket options","authors":"Bertram During, Christof Heuer","doi":"10.1007/978-3-319-23413-7_152","DOIUrl":"https://doi.org/10.1007/978-3-319-23413-7_152","url":null,"abstract":"","PeriodicalId":197400,"journal":{"name":"arXiv: Computational Finance","volume":"109 4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129060587","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: 1
The least squares method for option pricing revisited 回顾了期权定价的最小二乘方法
arXiv: Computational Finance Pub Date : 2014-04-07 DOI: 10.4064/AM2354-2-2018
M. Klimek, Marcin Pitera
{"title":"The least squares method for option pricing revisited","authors":"M. Klimek, Marcin Pitera","doi":"10.4064/AM2354-2-2018","DOIUrl":"https://doi.org/10.4064/AM2354-2-2018","url":null,"abstract":"It is shown that the the popular least squares method of option pricing converges even under very general assumptions. This substantially increases the freedom of creating different implementations of the method, with varying levels of computational complexity and flexible approach to regression. It is also argued that in many practical applications even modest non-linear extensions of standard regression may produce satisfactory results. This claim is illustrated with examples.","PeriodicalId":197400,"journal":{"name":"arXiv: Computational Finance","volume":"191 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132886677","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: 4
Extrapolating the term structure of interest rates with parameter uncertainty 具有参数不确定性的利率期限结构的外推
arXiv: Computational Finance Pub Date : 2013-12-18 DOI: 10.2139/ssrn.2369208
Anne G. Balter, A. Pelsser, P. Schotman
{"title":"Extrapolating the term structure of interest rates with parameter uncertainty","authors":"Anne G. Balter, A. Pelsser, P. Schotman","doi":"10.2139/ssrn.2369208","DOIUrl":"https://doi.org/10.2139/ssrn.2369208","url":null,"abstract":"Pricing extremely long-dated liabilities market consistently deals with the decline in liquidity of financial instruments on long maturities. The aim is to quantify the uncertainty of rates up to maturities of a century. We assume that the interest rates follow the affine mean-reverting Vasicek model. We model parameter uncertainty by Bayesian distributions over the parameters. The cross-sectional and time series parameters are obtained via the restricted bivariate VAR(1) model. The empirical example shows extremely low confidence in long term extrapolations due to the accumulated effect of the mean-reversion`s behaviour close to the unit root.","PeriodicalId":197400,"journal":{"name":"arXiv: Computational Finance","volume":"48 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132386430","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 pricing with Gamma processes and their extensions Gamma过程及其扩展的精确模拟定价
arXiv: Computational Finance Pub Date : 2013-10-24 DOI: 10.21314/JCF.2013.259
Lancelot F. James, Dohyun Kim, Zhiyuan Zhang
{"title":"Exact simulation pricing with Gamma processes and their extensions","authors":"Lancelot F. James, Dohyun Kim, Zhiyuan Zhang","doi":"10.21314/JCF.2013.259","DOIUrl":"https://doi.org/10.21314/JCF.2013.259","url":null,"abstract":"Exact path simulation of the underlying state variable is of great practical importance in simulating prices of financial derivatives or their sensitivities when there are no analytical solutions for their pricing formulas. However, in general, the complex dependence structure inherent in most nontrivial stochastic volatility (SV) models makes exact simulation difficult. In this paper, we present a nontrivial SV model that parallels the notable Heston SV model in the sense of admitting exact path simulation as studied by Broadie and Kaya. The instantaneous volatility process of the proposed model is driven by a Gamma process. Extensions to the model including superposition of independent instantaneous volatility processes are studied. Numerical results show that the proposed model outperforms the Heston model and two other L'evy driven SV models in terms of model fit to the real option data. The ability to exactly simulate some of the path-dependent derivative prices is emphasized. Moreover, this is the first instance where an infinite-activity volatility process can be applied exactly in such pricing contexts.","PeriodicalId":197400,"journal":{"name":"arXiv: Computational Finance","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133484004","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: 3
Multilevel Monte Carlo methods for applications in finance 多层蒙特卡罗方法在金融中的应用
arXiv: Computational Finance Pub Date : 2012-12-01 DOI: 10.1201/9781315372006-7
M. Giles, L. Szpruch
{"title":"Multilevel Monte Carlo methods for applications in finance","authors":"M. Giles, L. Szpruch","doi":"10.1201/9781315372006-7","DOIUrl":"https://doi.org/10.1201/9781315372006-7","url":null,"abstract":"Since Giles introduced the multilevel Monte Carlo path simulation method [18], there has been rapid development of the technique for a variety of applications in computational finance. This paper surveys the progress so far, highlights the key features in achieving a high rate of multilevel variance convergence, and suggests directions for future research.","PeriodicalId":197400,"journal":{"name":"arXiv: Computational Finance","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115203539","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: 34
Application of simplest random walk algorithms for pricing barrier options 最简单随机游走算法在障碍期权定价中的应用
arXiv: Computational Finance Pub Date : 2012-11-24 DOI: 10.1142/9789814436434_0011
M. Krivko, M. Tretyakov
{"title":"Application of simplest random walk algorithms for pricing barrier options","authors":"M. Krivko, M. Tretyakov","doi":"10.1142/9789814436434_0011","DOIUrl":"https://doi.org/10.1142/9789814436434_0011","url":null,"abstract":"We demonstrate effectiveness of the first-order algorithm from [Milstein, Tretyakov. Theory Prob. Appl. 47 (2002), 53-68] in application to barrier option pricing. The algorithm uses the weak Euler approximation far from barriers and a special construction motivated by linear interpolation of the price near barriers. It is easy to implement and is universal: it can be applied to various structures of the contracts including derivatives on multi-asset correlated underlyings and can deal with various type of barriers. In contrast to the Brownian bridge techniques currently commonly used for pricing barrier options, the algorithm tested here does not require knowledge of trigger probabilities nor their estimates. We illustrate this algorithm via pricing a barrier caplet, barrier trigger swap and barrier swaption.","PeriodicalId":197400,"journal":{"name":"arXiv: Computational Finance","volume":"57 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114937142","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
A New Kind of Finance 一种新的金融
arXiv: Computational Finance Pub Date : 2012-10-04 DOI: 10.1007/978-3-642-35482-3_8
Philip Z. Maymin
{"title":"A New Kind of Finance","authors":"Philip Z. Maymin","doi":"10.1007/978-3-642-35482-3_8","DOIUrl":"https://doi.org/10.1007/978-3-642-35482-3_8","url":null,"abstract":"","PeriodicalId":197400,"journal":{"name":"arXiv: Computational Finance","volume":"46 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130653303","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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