Application of the American Real Flexible Switch Options Methodology A Generalized Approach

The paper deals with the inclusion of flexibility in financial decision-making under risk. It describes the application of the real options methodology with the possibility of sequential multinomial decision-making. The basic intention is to describe and apply a generalized approach and methodology of the flexibility modeling and valuation based on multiple choices and non-symmetrical switching costs under risk. The stochastic dynamic Bellman optimization principle is explained and applied. The optimization criterion of the present expected value is derived and used. Likewise, an option valuation approach based on replication strategy and risk-neutral probability is applied. An illustrative example of the application of the real multinomial flexible non-symmetrical switch options methodology is presented for three chosen modes. The option flexible values are computed. The usefulness, effectiveness, and suitability of applying the generalized flexibility model in company valuation and project evaluation is verified and confirmed. The significance of applying the generalized methodology in transition market economies is discussed and verified.financial options; real options; Discrete Binomial Model; pricing; stochastic dynamic Bellman Optimization Principle; switch options

Optimal quantization for the pricing of swing options

In this paper, we investigate a numerical algorithm for the pricing of swing options, relying on the so-called optimal quantization method. The numerical procedure is described in details and numerous simulations are provided to assert its efficiency. In particular, we carry out a comparison with the Longstaff-Schwartz algorithm.Comment: 27

Pricing and Risk Management with High-Dimensional Quasi Monte Carlo and Global Sensitivity Analysis

We review and apply Quasi Monte Carlo (QMC) and Global Sensitivity Analysis (GSA) techniques to pricing and risk management (greeks) of representative financial instruments of increasing complexity. We compare QMC vs standard Monte Carlo (MC) results in great detail, using high-dimensional Sobol' low discrepancy sequences, different discretization methods, and specific analyses of convergence, performance, speed up, stability, and error optimization for finite differences greeks. We find that our QMC outperforms MC in most cases, including the highest-dimensional simulations and greeks calculations, showing faster and more stable convergence to exact or almost exact results. Using GSA, we are able to fully explain our findings in terms of reduced effective dimension of our QMC simulation, allowed in most cases, but not always, by Brownian bridge discretization. We conclude that, beyond pricing, QMC is a very promising technique also for computing risk figures, greeks in particular, as it allows to reduce the computational effort of high-dimensional Monte Carlo simulations typical of modern risk management.Comment: 43 pages, 21 figures, 6 table

Meshfree Approximation for Multi-Asset Options

We price multi-asset options by solving their price partial differential equations using a meshfree approach with radial basis functions under jump-diffusion and geometric Brownian motion frameworks. In the geometric Brownian motion framework, we propose an effective technique that breaks the multi-dimensional problem to multiple 3D problems. We solve the price PDEs or PIDEs with an implicit meshfree scheme using thin-plate radial basis functions. Meshfree approach is very accurate, has high order of convergence and is easily scalable and adaptable to higher dimensions and different payoff profiles. We also obtain closed form approximations for the option Greeks. We test the model on American crack spread options traded on NYMEX.Multi-asset options, radial basis function, meshfree approximation, collocation, multidimensional Lévy process, basket options, PIDE, PDE