Application of the Kusuoka approximation with a tree-based branching algorithm to the pricing of interest-rate derivatives under the HJM model

Ninomiya, Mariko

doi:10.1112/s146115700800048x

Cited by 7 publications

(6 citation statements)

References 8 publications

(11 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…While there, the focus was on space-time white noise driving the system, we consider only finite-dimensional noise, and can obtain the same rate of convergence as in the finite-dimensional setting with bounded and smooth vector fields. Contrary to [36], our model is inherently infinite-dimensional and does not allow a reduction to a low-dimensional stochastic differential equation.…”

Section: Integration Errormentioning

confidence: 99%

Efficient Simulation and Calibration of General HJM Models by Splitting Schemes

Dörsek¹,

Teichmann²

2013

SIAM J. Finan. Math.

View full text Add to dashboard Cite

We introduce efficient numerical methods for generic HJM equations of interest rate theory by means of high-order weak approximation schemes. These schemes allow for QMC implementations due to the relatively low dimensional integration space. The complexity of the resulting algorithm is considerably lower than the complexity of multi-level MC algorithms as long as the optimal order of QMC-convergence is guaranteed. In order to make the methods applicable to real world problems, we introduce and use the setting of weighted function spaces, such that unbounded payoffs and unbounded characteristics of the equations in question are still allowed. We also provide an implementation, where we efficiently calibrate an HJM equation to caplet data.

show abstract

Section: Integration Errormentioning

confidence: 99%

Efficient Simulation and Calibration of General HJM Models by Splitting Schemes

Dörsek¹,

Teichmann²

2013

SIAM J. Finan. Math.

View full text Add to dashboard Cite

show abstract

“…In this section, we introduce the TBBA (Crisan and Lyons 2002) and its efficient implementation for our problem. The TBBA was applied to the weak approximation problem of SDEs in (Ninomiya 2003b(Ninomiya , 2010Crisan and Ortiz-Latorre 2013).…”

Section: Tbbamentioning

confidence: 99%

“…When we use these methods iteratively along the time steps, the support of the intermediate measures grows exponentially as the number of partitions increases. To overcome this problem, the TBBA (Crisan and Lyons 2002) was applied to these methods in (Ninomiya 2003b;Ninomiya and Mitsuzono 2004;Ninomiya 2010;Crisan and Ortiz-Latorre 2013). On the other hand, using the framework of KLNVscheme and the Gaussian random variables, the Ninomiya-Victoir (N-V) (Ninomiya and Victoir 2008) and Ninomiya-Ninomiya (N-N) (Ninomiya and Ninomiya 2009) methods have been proposed as practically feasible second-order methods, and the Q ð7;2Þ ðsÞ method (Shinozaki 2016(Shinozaki , 2017 as a third order method.…”

Section: Introductionmentioning

confidence: 99%

Higher-order Discretization Methods of Forward-backward SDEs Using KLNV-scheme and Their Applications to XVA Pricing

Ninomiya

Shinozaki

2019

Applied Mathematical Finance

View full text Add to dashboard Cite

This study proposes new higher-order discretization methods of forward-backward stochastic differential equations. In the proposed methods, the forward component is discretized using the Kusuoka-Lyons-Ninomiya-Victoir scheme with discrete random variables and the backward component using a higher-order numerical integration method consistent with the discretization method of the forward component, by use of the tree based branching algorithm. The proposed methods are applied to the XVA pricing, in particular to the credit valuation adjustment. The numerical results show that the expected theoretical order and computational efficiency could be achieved.

show abstract

“…This problems has a great deal in various areas including mathematical finance. In [7,8,9,10,12,13], theory and notion of higher-order approximation are introduced as well as its applicability. We call this scheme Kusuoka approximation in this paper.…”

Section: Introductionmentioning

confidence: 99%

Application of the Kusuoka approximation to pricing barrier options

Kusuoka

Ninomiya

2016

Stochastic Systems Theory and its Applications (SSS)

Self Cite

View full text Add to dashboard Cite

The main theme of this research is numerical verification of applicability of a higher-order approximation to pricing barrier options, which is a both mathematically and practically important path-dependent type problem in mathematical finance. The authors successfully extend two types of algorithms called NV and NN. Both algorithms are based on a higher-order approximation scheme called Kusuoka approximation and have been shown to attain second-order approximation of stochastic differential equations as long as applied to European-type problems. In extending the algorithms, the authors apply a function representing the probability of hitting a boundary. In the numerical experiments, these two algorithms are compared with the Euler-Maruyama scheme which is one of the most popular first-order approximation schemes. As a result, it is demonstrated that the speed of calculation of these two algorithms could be much higher than that of the Euler-Maruyama scheme extended by the same way. It is concluded that one of the keys to improvement of the results is the construction of the function for calculation of the probability of hitting a boundary.

show abstract

Application of the Kusuoka approximation with a tree-based branching algorithm to the pricing of interest-rate derivatives under the HJM model

Cited by 7 publications

References 8 publications

Efficient Simulation and Calibration of General HJM Models by Splitting Schemes

Efficient Simulation and Calibration of General HJM Models by Splitting Schemes

Higher-order Discretization Methods of Forward-backward SDEs Using KLNV-scheme and Their Applications to XVA Pricing

Application of the Kusuoka approximation to pricing barrier options

Contact Info

Product

Resources

About