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

2010 ◽  
Vol 13 ◽  
pp. 208-221 ◽  
Author(s):  
Mariko Ninomiya
Keyword(s):  
Interest Rate ◽  
Random Variables ◽  
Factor Models ◽  
Higher Order ◽  
Weak Approximation ◽  
Interest Rate Derivatives ◽  
Hjm Model ◽  
Discrete Random Variables

AbstractThis paper demonstrates the application of a new higher-order weak approximation, called the Kusuoka approximation, with discrete random variables to non-commutative multi-factor models. Our experiments show that using the Heath–Jarrow–Morton model to price interest-rate derivatives can be practically feasible if the Kusuoka approximation is used along with the tree-based branching algorithm.

scholarly journals Improving multilevel Monte Carlo for stochastic differential equations with application to the Langevin equation

2015 ◽  
Vol 471 (2176) ◽  
pp. 20140679 ◽  
Author(s):  
Eike H. Müller ◽  
Rob Scheichl ◽  
Tony Shardlow
Keyword(s):  
Monte Carlo ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Langevin Equation ◽  
Operator Splitting ◽  
Random Variables ◽  
Weak Approximation ◽  
Multilevel Monte Carlo ◽  
Discrete Random Variables ◽  
Modified Equations

This paper applies several well-known tricks from the numerical treatment of deterministic differential equations to improve the efficiency of the multilevel Monte Carlo (MLMC) method for stochastic differential equations (SDEs) and especially the Langevin equation. We use modified equations analysis as an alternative to strong-approximation theory for the integrator, and we apply this to introduce MLMC for Langevin-type equations with integrators based on operator splitting. We combine this with extrapolation and investigate the use of discrete random variables in place of the Gaussian increments, which is a well-known technique for the weak approximation of SDEs. We show that, for small-noise problems, discrete random variables can lead to an increase in efficiency of almost two orders of magnitude for practical levels of accuracy.

scholarly journals Apreçamento de Opções Asiáticas de Taxa de Juros através de um Modelo HJM de Três Fatores

2010 ◽  
Vol 8 (1) ◽  
pp. 9
Author(s):  
Claudio Henrique Barbedo ◽  
Octávio Bessada Lion ◽  
Jose Valentim Machado Vicente
Keyword(s):  
Interest Rate ◽  
Standard Procedure ◽  
Over The Counter ◽  
Interest Rate Derivatives ◽  
Market Participants ◽  
Hjm Model ◽  
Derivative Instruments ◽  
Pricing Error ◽  
Risk Managers

Pricing interest rate derivatives is a challenging task that has attracted the attention of many researchers in recent decades. Portfolio and risk managers, policymakers, traders and more generally all market participants are looking for valuable information from derivative instruments. We use a standard procedure to implement the HJM model and to price IDI options. We intend to assess the importance of the principal components of pricing and interest rate hedging derivatives in Brazil, one of the major emerging markets. Our results indicate that the HJM model consistently underprices IDI options traded in the over-the-counter market while it overprices long-term options traded in the exchange studied. We also find a direct relationship between time to maturity and pricing error and a negative relation with moneyness.

A multi-factor Markovian HJM model for pricing American interest rate derivatives

2007 ◽  
Vol 31 (4) ◽  
pp. 359-378 ◽  
Author(s):  
Marat V. Kramin ◽  
Saikat Nandi ◽  
Alexander L. Shulman
Keyword(s):  
Interest Rate ◽  
Interest Rate Derivatives ◽  
Hjm Model ◽  
American Interest
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