Download Affine Diffusions and Related Processes: Simulation, Theory by Aurélien Alfonsi PDF

By Aurélien Alfonsi

This ebook provides an outline of affine diffusions, from Ornstein-Uhlenbeck methods to Wishart procedures and it considers a few comparable diffusions akin to Wright-Fisher procedures. It makes a speciality of varied simulation schemes for those tactics, particularly second-order schemes for the vulnerable mistakes. It additionally provides a few versions, regularly within the box of finance, the place those equipment are correct and gives a few numerical experiments.

Show description

Read Online or Download Affine Diffusions and Related Processes: Simulation, Theory and Applications PDF

Similar counting & numeration books

Sparse Grid Quadrature in High Dimensions with Applications in Finance and Insurance

This booklet offers with the numerical research and effective numerical therapy of high-dimensional integrals utilizing sparse grids and different dimension-wise integration options with functions to finance and coverage. The e-book specializes in delivering insights into the interaction among coordinate changes, powerful dimensions and the convergence behaviour of sparse grid tools.

Applied Laplace Transforms and z-Transforms for Scientists and Engineers: A Computational Approach using a Mathematica Package

The idea of Laplace transformation is a crucial a part of the mathematical history required for engineers, physicists and mathematicians. Laplace transformation tools supply effortless and potent concepts for fixing many difficulties coming up in quite a few fields of technological know-how and engineering, specially for fixing differential equations.

Systems of Conservation Laws: Two-Dimensional Riemann Problems

This paintings may still function an introductory textual content for graduate scholars and researchers operating within the vital zone of partial differential equations with a spotlight on difficulties regarding conservation legislation. the one considered necessary for the reader is an information of the easy conception of partial differential equations.

Additional info for Affine Diffusions and Related Processes: Simulation, Theory and Applications

Example text

Rt /dt C Wt : 0 The parameters k; Â; and r0 are assumed to be positive. Â; 2k /. We know that r is a Gaussian process. This gives in particular that rt can take negative values with some positive probability, while interest rates are in practice usually positive. t/: Now, we would like to calculate the price of a floorlet. 45), it boils down to calculate the price of a call option on zero coupon bond. Without loss of generality, we assume that the current time is t D 0. rT0 ; T1 We now observe that the function r 7!

T t/ as a reward, where the rate X is fixed at time t. We exclude here and in the sequel any kind of default. The market practice is to quote the rate X which is fair for both parts. 43) Any other rate would give an arbitrage for the borrower or for the lender. T t// D 0: We now introduce some other standard products such as bonds, swaps, caps and floors. e. t Ä T0 . We consider a contract between two parts that is defined as follows. The borrower receives a unit of cash at time T0 , that he has to get back at time Tl .

Xtx ; t 2 Œ0; T /. Xtx ; t 2 Œ0; T /. Wt ; t 2 Œ0; T /, and we can define it intrinsically. XOt ; t 2 Œ0; T / matters. Getting accurate schemes for the weak error is then sufficient for this use. 2 Strong Approximations The main way to construct strong discretization schemes is to use iterated stochastic Taylor expansion. To fix the ideas, let us assume for a while that the dimension d D 1 and that the coefficients b and are smooth. 5) can be seen as the approximation where Xsx is replaced by Xtxi .

Download PDF sample

Rated 4.65 of 5 – based on 29 votes