A dimension and variance reduction Monte-Carlo method for option pricing under jump-diffusion models

We develop a highly efficient MC method for computing plain vanilla European option prices and hedging parameters under a very general jump-diffusion option pricing model which includes stochastic variance and multi-factor Gaussian interest short rate(s). The focus of our MC approach is variance reduction via dimension reduction. More specifically, the option price is expressed as an expectation of a unique solution to a conditional Partial Integro-Differential Equation (PIDE), which is then solved using a Fourier transform technique. Important features of our approach are (1) the analytical tractability of the conditional PIDE is fully determined by that of the Black–Scholes–Merton model augmented with the same jump component as in our model, and (2) the variances associated with all the interest rate factors are completely removed when evaluating the expectation via iterated conditioning applied to only the Brownian motion associated with the variance factor. For certain cases when numerical methods are either needed or preferred, we propose a discrete fast Fourier transform method to numerically solve the conditional PIDE efficiently. Our method can also effectively compute hedging parameters. Numerical results show that the proposed method is highly efficient.     

Synthesis, Characterization, and Activity of Yttrium(III) Nitrate Complexes Bearing Tripodal Phosphine Oxide and Mixed Phosphine-Phosphine Oxide Ligands

A series of four tripodal phosphine oxide ligands, (OPR(2))(2)CHCH(2)POR(2) (1a-1d), and four mixed phosphine-phosphine oxide ligands, (OPR(2))(2)CHCH(2)PR(2) (3a-3d), were synthesized and coordinated to yttrium to produce Y(NO(3))(3)[(OPR(2))(2)CHCH(2)POR(2)] (2a-2d) and Y(NO(3))(3)[(OPR(2))(2)CHCH(2)PR(2)](OPPh(3)) (4a-4d) complexes. The previously reported ligand 1a and unknown phosphine oxide ligands 1b-1d were generated in an unprecedented trisubstitution reaction of bromoacetaldehyde diethyl acetal, while the novel partially reduced ligands 3a-3d were synthesized from 1a-1d according to a known literature protocol for the selective monoreduction of bisphosphine oxides. The neutral yttrium complexes 2a-2d are nine-coordinate and display a tricapped trigonal-prismatic geometry. Complexes 4a-4d are also neutral, nine-coordinate species and have a pendant phosphine functionality, which provides the potential to form bimetallic early-late transition-metal complexes. Additionally, yttrium complexes 2a-2d were activated with base and tested for the ring-opening polymerization of ε-caprolactone, but the results showed that base by itself was significantly more effective than the yttrium species investigated.     

HARVESTING ECONOMIC MODELS AND CATCH‐TO‐BIOMASS DEPENDENCE: THE CASE OF SMALL PELAGIC FISH

Abstract In the case of small pelagic fish, it seems reasonable to consider harvest functions depending nonlinearly on fishing effort and fish stock. Indeed, empirical evidence about these fish species suggests that marginal catch does not necessarily react in a linear way neither to changes in fishing effort nor in fish stock levels. This is in contradiction with traditional fishery economic models where catch‐to‐input marginal productivities are normally assumed to be constant. While allowing for nonlinearities in both catch‐to‐effort and catch‐to‐stock parameters, this paper extends the traditional single‐stock harvesting economic model by focusing on the dependence of the stationary solutions upon the nonlinear catch‐to‐stock parameter. Thus, we analyze equilibrium responses to changes in this parameter, which in turn may be triggered either by climatic or technological change. Given the focus in this study on the case of small pelagic fish, the analysis considers positive but small values for the catch‐to‐stock parameter.