Quantitative Finance Lab

We propose a pricing method for derivatives modeled by a set of stochastic differential equations with the objective of reducing the computing time. The speed up observed in our numerical implementation can be as large as 50. The method is based on a joint use of Monte-Carlo simulations and PDE or analytical formulas. The method is tested Read the rest of this entry »

The pricing equations derived from uncertain volatility models in finance are often cast in the form of nonlinear partial differential equations. Implicit timestepping leads to a set of nonlinear algebraic equations which must be solved at each timestep. To solve these equations, an iterative approach is employed. In this paper, we prove the convergence of a particular iterative scheme for one factor uncertain volatility models. We also demonstrate how Read the rest of this entry »

Many problems in Finance can be posed in terms of an optimal stochastic control. Some well-known examples include transaction cost/uncertain volatility models, passport options, unequal borrowing/lending costs in option pricing, risk control in reinsurance, optimal withdrawals in variable annuities, optimal execution of trades, and asset allocation. These optimal stochastic control problems can be formulated as nonlinear Hamilton-Jacobi-Bellman (HJB) partial differential equations (PDEs). In general, especially in realistic situations where the controls are constrained (e.g. in the case of asset allocation, we may require that trading must cease upon insolvency, that short positions are not allowed, or that position limits are imposed), there are no analytical solutions to the HJB PDEs. At first glance Read the rest of this entry »