The ANZIAM journal最新文献_第7页

AN ANALYTICAL APPROXIMATION FORMULA FOR THE PRICING OF CREDIT DEFAULT SWAPS WITH REGIME SWITCHING 带制度转换的信用违约互换定价的解析近似公式

The ANZIAM journal Pub Date : 2021-04-01 DOI: 10.1017/S1446181121000274

Xin‐Jiang He, Sha Lin

引用次数: 1

EDITORIAL: SPECIAL ISSUE ON FINANCIAL MATHEMATICS AND QUANTITATIVE FINANCE 社论:金融数学与定量金融专刊

The ANZIAM journal Pub Date : 2021-04-01 DOI: 10.1017/S1446181121000304

Song‐Ping Zhu, Xiaoping Lu, Xin‐Jiang He

引用次数: 0

ANZ VOLUME 63 ISSUE 2 COVER AND FRONT MATTER 澳新银行第63卷第2期封面和封面

The ANZIAM journal Pub Date : 2021-04-01 DOI: 10.1017/s1446181121000158

引用次数: 0

SPECTRALLY ACCURATE OPTION PRICING UNDER THE TIME-FRACTIONAL BLACK–SCHOLES MODEL 时间分数black-scholes模型下频谱精确期权定价

The ANZIAM journal Pub Date : 2021-04-01 DOI: 10.1017/S1446181121000286

G. Tour, N. Thakoor, D. Tangman

{"title":"SPECTRALLY ACCURATE OPTION PRICING UNDER THE TIME-FRACTIONAL BLACK–SCHOLES MODEL","authors":"G. Tour, N. Thakoor, D. Tangman","doi":"10.1017/S1446181121000286","DOIUrl":"https://doi.org/10.1017/S1446181121000286","url":null,"abstract":"Abstract We propose a Legendre–Laguerre spectral approximation to price the European and double barrier options in the time-fractional framework. By choosing an appropriate basis function, the spectral discretization is used for the approximation of the spatial derivatives of the time-fractional Black–Scholes equation. For the time discretization, we consider the popular \u0000$L1$\u0000 finite difference approximation, which converges with order \u0000$mathcal {O}((Delta tau )^{2-alpha })$\u0000 for functions which are twice continuously differentiable. However, when using the \u0000$L1$\u0000 scheme for problems with nonsmooth initial data, only the first-order accuracy in time is achieved. This low-order accuracy is also observed when solving the time-fractional Black–Scholes European and barrier option pricing problems for which the payoffs are all nonsmooth. To increase the temporal convergence rate, we therefore consider a Richardson extrapolation method, which when combined with the spectral approximation in space, exhibits higher order convergence such that high accuracies over the whole discretization grid are obtained. Compared with the traditional finite difference scheme, numerical examples clearly indicate that the spectral approximation converges exponentially over a small number of grid points. Also, as demonstrated, such high accuracies can be achieved in much fewer time steps using the extrapolation approach.","PeriodicalId":74944,"journal":{"name":"The ANZIAM journal","volume":"10 1","pages":"228 - 248"},"PeriodicalIF":0.0,"publicationDate":"2021-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85341799","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

LOCALIZED RADIAL BASIS FUNCTIONS FOR NO-ARBITRAGE PRICING OF OPTIONS UNDER STOCHASTIC ALPHA–BETA–RHO DYNAMICS 随机动力学下期权无套利定价的局部径向基函数

The ANZIAM journal Pub Date : 2021-04-01 DOI: 10.1017/S1446181121000237

N. Thakoor

{"title":"LOCALIZED RADIAL BASIS FUNCTIONS FOR NO-ARBITRAGE PRICING OF OPTIONS UNDER STOCHASTIC ALPHA–BETA–RHO DYNAMICS","authors":"N. Thakoor","doi":"10.1017/S1446181121000237","DOIUrl":"https://doi.org/10.1017/S1446181121000237","url":null,"abstract":"Abstract Closed-form explicit formulas for implied Black–Scholes volatilities provide a rapid evaluation method for European options under the popular stochastic alpha–beta–rho (SABR) model. However, it is well known that computed prices using the implied volatilities are only accurate for short-term maturities, but, for longer maturities, a more accurate method is required. This work addresses this accuracy problem for long-term maturities by numerically solving the no-arbitrage partial differential equation with an absorbing boundary condition at zero. Localized radial basis functions in a finite-difference mode are employed for the development of a computational method for solving the resulting two-dimensional pricing equation. The proposed method can use either multiquadrics or inverse multiquadrics, which are shown to have comparable performances. Numerical results illustrate the accuracy of the proposed method and, more importantly, that the computed risk-neutral probability densities are nonnegative. These two key properties indicate that the method of solution using localized meshless methods is a viable and efficient means for price computations under SABR dynamics.","PeriodicalId":74944,"journal":{"name":"The ANZIAM journal","volume":"11 1","pages":"203 - 227"},"PeriodicalIF":0.0,"publicationDate":"2021-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85460639","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

FINITE MATURITY AMERICAN-STYLE STOCK LOANS WITH REGIME-SWITCHING VOLATILITY 具有制度转换波动性的有限期限美式股票贷款

The ANZIAM journal Pub Date : 2021-04-01 DOI: 10.1017/S1446181121000250

Xiaoping Lu, E. R. Putri

引用次数: 0

ANZ VOLUME 63 ISSUE 2 COVER AND BACK MATTER 澳新银行第63卷第2期封面和封底

The ANZIAM journal Pub Date : 2021-04-01 DOI: 10.1017/s144618112100016x

引用次数: 0

OPTION PRICING UNDER THE FRACTIONAL STOCHASTIC VOLATILITY MODEL 分数阶随机波动率模型下的期权定价

The ANZIAM journal Pub Date : 2021-04-01 DOI: 10.1017/S1446181121000225

Y. Han, Z. Li, C. Liu

引用次数: 4