1,478 research outputs found
Optimal Redeeming Strategy of Stock Loans
A stock loan is a loan, secured by a stock, which gives the borrower the
right to redeem the stock at any time before or on the loan maturity. The way
of dividends distribution has a significant effect on the pricing of the stock
loan and the optimal redeeming strategy adopted by the borrower. We present the
pricing models sub ject to various ways of dividend distribution. Since
closed-form price formulas are generally not available, we provide a thorough
analysis to examine the optimal redeeming strategy. Numerical results are
presented as well.Comment: 17 pages, 4 figure
Pricing European and American Options under Heston Model using Discontinuous Galerkin Finite Elements
This paper deals with pricing of European and American options, when the
underlying asset price follows Heston model, via the interior penalty
discontinuous Galerkin finite element method (dGFEM). The advantages of dGFEM
space discretization with Rannacher smoothing as time integrator with nonsmooth
initial and boundary conditions are illustrated for European vanilla options,
digital call and American put options. The convection dominated Heston model
for vanishing volatility is efficiently solved utilizing the adaptive dGFEM.
For fast solution of the linear complementary problem of the American options,
a projected successive over relaxation (PSOR) method is developed with the norm
preconditioned dGFEM. We show the efficiency and accuracy of dGFEM for option
pricing by conducting comparison analysis with other methods and numerical
experiments
A Parallel Algorithm for solving BSDEs - Application to the pricing and hedging of American options
We present a parallel algorithm for solving backward stochastic differential
equations (BSDEs in short) which are very useful theoretic tools to deal with
many financial problems ranging from option pricing option to risk management.
Our algorithm based on Gobet and Labart (2010) exploits the link between BSDEs
and non linear partial differential equations (PDEs in short) and hence enables
to solve high dimensional non linear PDEs. In this work, we apply it to the
pricing and hedging of American options in high dimensional local volatility
models, which remains very computationally demanding. We have tested our
algorithm up to dimension 10 on a cluster of 512 CPUs and we obtained linear
speedups which proves the scalability of our implementationComment: 25 page
Mathematical analysis and numerical methods for pricing pension plans allowing early retirement
In this paper, we address the mathematical analysis and numerical solution of a model for pricing a defined benefit pension plan. More precisely, the benefits received by the member of the plan depend on the average salary and early retirement is allowed. Thus, the mathematical model is posed as an obstacle problem associated to a Kolmogorov equation in the time region where the salary is being averaged. Previously to the initial averaging date, a nonhomogeneous one factor Black-Scholes equation is posed. After stating the model, existence and regularity of solutions are studied. Moreover, appropriate numerical methods based on a Lagrange-Galerkin discretization and an augmented Lagrangian active set method are proposed. Finally, some numerical examples illustrate the performance of the numerical techniques and the properties of the solution and the free boundary.retirement plans, options pricing, Kolmogorov equations, complementarity problem, numerical methods, augmented Lagrangian formulation
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