SIAM Journal on Optimization

10.1137/siopt ◽  
2014 ◽  
Keyword(s):  
Siam Journal

Special issue on semantics and program schemas SIAM journal on computing

1974 ◽  
Vol 6 (4) ◽  
pp. 32-32
Author(s):  
Robert Constable ◽  
David Park
Keyword(s):  
Special Issue ◽  
Siam Journal

scholarly journals COLLOCATING VOLATILITY: A COMPETITIVE ALTERNATIVE TO STOCHASTIC LOCAL VOLATILITY MODELS

2020 ◽  
Vol 23 (06) ◽  
pp. 2050038
Author(s):  
ANTHONIE W. VAN DER STOEP ◽  
LECH A. GRZELAK ◽  
CORNELIS W. OOSTERLEE
Keyword(s):  
Differential Equations ◽  
Scientific Computing ◽  
Collocation Methods ◽  
Heston Model ◽  
Stochastic Collocation ◽  
Exotic Options ◽  
Siam Journal ◽  
Local Volatility ◽  
Volatility Models ◽  
Stochastic Local Volatility

We discuss a competitive alternative to stochastic local volatility models, namely the Collocating Volatility (CV) framework, introduced in [L. A. Grzelak (2019) The CLV framework — A fresh look at efficient pricing with smile, International Journal of Computer Mathematics 96 (11), 2209–2228]. The CV framework consists of two elements, a “kernel process” that can be efficiently evaluated and a local volatility function. The latter, based on stochastic collocation — e.g. [I. Babuška, F. Nobile & R. Tempone (2007) A stochastic collocation method for elliptic partial differential equations with random input Data, SIAM Journal on Numerical Analysis 45 (3), 1005–1034; B. Ganapathysubramanian & N. Zabaras (2007) Sparse grid collocation schemes for stochastic natural convection problems, Journal of Computational Physics 225 (1), 652–685; J. A. S. Witteveen & G. Iaccarino (2012) Simplex stochastic collocation with random sampling and extrapolation for nonhypercube probability spaces, SIAM Journal on Scientific Computing 34 (2), A814–A838; D. Xiu & J. S. Hesthaven (2005) High-order collocation methods for differential equations with random inputs, SIAM Journal on Scientific Computing 27 (3), 1118–1139] — connects the kernel process to the market and allows the CV framework to be perfectly calibrated to European-type options. In this paper, we consider three different kernel process choices: the Ornstein–Uhlenbeck (OU) and Cox–Ingersoll–Ross (CIR) processes and the Heston model. The kernel process controls the forward smile and allows for an accurate and efficient calibration to exotic options, while the perfect calibration to liquid market quotes is preserved. We confirm this by numerical experiments, in which we calibrate the OU-CV, CIR-CV and Heston-CV frameworks to FX barrier options.

A CONIC AFFINE SCALING DOGLEG METHOD FOR NONLINEAR OPTIMIZATION WITH BOUND CONSTRAINTS

2013 ◽  
Vol 30 (03) ◽  
pp. 1340011 ◽  
Author(s):  
LIJUAN ZHAO ◽  
WENYU SUN
Keyword(s):  
Quadratic Model ◽  
Affine Scaling ◽  
Bound Constraints ◽  
Siam Journal ◽  
Standard Testing ◽  
Conic Model ◽  
Mild Conditions ◽  
Numerical Tests ◽  
Collinear Scalings ◽  
Conic Approximations

The conic model proposed by Davidon (1980) [Davidon, WC (1980). Conic approximations and collinear scalings for optimizers. SIAM Journal on Numerical Analysis, 17, 268–281.] is an extension of quadratic model incorporating more information than quadratic model. In this paper, we propose a conic affine scaling dogleg method for bound constrained optimization. Under some mild conditions, the sequence generated by our algorithm converges to a stationary point. Numerical tests on a series of standard testing problems confirm the efficiency of the method.

scholarly journals GENERATING FUNCTIONS AND SHORT RECURSIONS, WITH APPLICATIONS TO THE MOMENTS OF QUADRATIC FORMS IN NONCENTRAL NORMAL VECTORS

2013 ◽  
Vol 30 (2) ◽  
pp. 436-473 ◽  
Author(s):  
Grant Hillier ◽  
Raymond Kan ◽  
Xiaolu Wang
Keyword(s):  
Generating Functions ◽  
Quadratic Forms ◽  
Symmetric Functions ◽  
Statistical Computing ◽  
Invariant Polynomials ◽  
Zonal Polynomials ◽  
Siam Journal ◽  
Computing Power ◽  
Normal Vectors ◽  
Recursive Relations

Recursive relations for objects of statistical interest have long been important for computation, and they remain so even with hugely improved computing power. Such recursions are frequently derived by exploiting relations between generating functions. For example, the top-order zonal polynomials that occur in much distribution theory under normality can be recursively related to other (easily computed) symmetric functions (power-sum and elementary symmetric functions; Ruben, 1962, Annals of Mathematical Statistics 33, 542–570; Hillier, Kan, and Wang, 2009, Econometric Theory 25, 211–242). Typically, in a recursion of this type the kth object of interest, dk, say, is expressed in terms of all lower order dj’s. In Hillier et al. (2009) we pointed out that, in the case of top-order zonal polynomials and other invariant polynomials of multiple matrix argument, a fixed length recursion can be deduced. We refer to this as a short recursion. The present paper shows that the main results in Hillier et al. (2009) can be generalized and that short recursions can be obtained for a much larger class of objects/generating functions. As applications, we show that short recursions can be obtained for various problems involving quadratic forms in noncentral normal vectors, including moments, product moments, and expectations of ratios of powers of quadratic forms. For this class of problems, we also show that the length of the recursion can be further reduced by an application of a generalization of Horner’s method (cf. Brown, 1986, SIAM Journal on Scientific and Statistical Computing 7, 689–695), producing a super-short recursion that is significantly more efficient than even the short recursion.

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