Pricing Options under Heston’s Stochastic Volatility Model via Accelerated Explicit Finite Differencing Methods

We present an acceleration technique, effective for explicit finite difference schemes describing diffusive processes with nearly symmetric operators, called Super-Time-Stepping (STS). The technique is applied to the two-factor problem of option pricing under stochastic volatility. It is shown to significantly reduce the severity of the stability constraint known as the Courant-Friedrichs-Lewy condition whilst retaining the simplicity of the chosen underlying explicit method. For European and American put options under Heston’s stochastic volatility model we demonstrate degrees of acceleration over standard explicit methods sufficient to achieve comparable, or superior, efficiencies to a benchmark implicit scheme. We conclude that STS is a powerful tool for the numerical pricing of options and propose them as the method-of-choice for exotic financial instruments in two and multi-factor models.

Significant factors affecting the forced-air cooling process of polylined horticultural produce : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Food Technology at Massey University, Palmerston North, New Zealand

New Zealand is the world’s third biggest producer of kiwifruit, with 94 % of the kiwifruit produced exported (NZ $ 1.0 bn in 2014). Forced-air cooling of the produce (from the harvest temperature of about 20 °C to near storage temperature of 0 °C) immediately after harvest improves storage potential and maintains produce quality before transportation to market. The design of the kiwifruit packaging system influences the rate of cooling and temperature achieved, mainly by affecting the airflow within and throughout the package. The typical kiwifruit package contains 10.5 kg of fruit and consists of a cardboard box and polyliner bag to prevent the loss of moisture and fruit shrivelling. Individual boxes are assembled onto pallets (10 boxes to a pallet layer, 10 layers high) Open areas or vents (in the box) facilitate cooling by allowing cool air to enter and circulate throughout the package. In forced-air cooling pallets are assembled into double rows with an aisle between the rows. Cool air is sucked through the pallets by a fan in the aisle, cooling the fruit and warming the air. The air is then either blown or ducted to the refrigeration system to be re-cooled. The polyliner keeps the local humidity high near the fruit, preventing weight loss due to evaporative cooling, but, as a barrier to direct fruit to air contact, slows the cooling rate. This project investigated the impact of operating conditions and package design on the cooling performance in such systems. A numerical model was developed (a CFD model implemented using the Fluent CFD software) that describes and predicts the temperature profiles of palletised kiwifruit packages undergoing forced-air cooling. The capability of the model to predict the fruit temperatures in each package was quantitatively validated against experimental data. The numerical model was able to predict temperature profiles within experimental error bars over 14 h of cooling. The numerical model was used to determine the operating point (in terms of pressure drop and flowrate across the pallet) to ensure rapid cooling of the produce without incurring excessive operational costs due to the power requirements. Results from both experimental work and the numerical model informed that there was an effective limit to the volumetric flowrate of 0.243 L kg-1 s-1: flowrates in excess of the limit had no or little effective benefit. This threshold flowrate is below the typical range recommended in industry for the forced-air cooling of non-polylined horticultural produce, which is 0.5 – 2.0 L kg-1 s-1. The numerical model demonstrated that the overall cooling performance (cooling rate, uniformity, power consumption and pallet throughput per week) can be improved by controlling the airflow distribution between the fastest and slowest cooling kiwifruit packages. An alternative design that channels cool air through the pallet towards the slowest cooling packages, located at the back of the pallet, by using two package designs in the same pallet, was presented. At 0.243 L kg-1 s-1 it was found that the pressure drop and power required to achieve equivalent cooling rates with the new design was reduced (by 24 % each) compared to the conventional design. Additionally, at the half-cooling time the cooling uniformity was improved by 19 %. The key features of the new design can be expected to be applicable for the cooling of horticultural produce involving an inner packaging liner

Dying for the bonds of marriage: Forced marriages as a weapon of genocide

‘Forced marriages’ involve a woman or girl being abducted and declared the ‘wife’ of her captor without her consent or her family’s consent. The practice generally occurs during wartime and the ‘wife’ is normally subjected to rape, forced impregnation and sexual slavery. Moreover, she is coerced into an intimate relationship with a man who is often the perpetrator of crimes against her and her community. While forced marriages have recently been recognised as a crime against humanity, this Article contends that this does not constitute full recognition of the destructive nature of forced marriages. Instead, this Article mirrors and extends the Akayesu decision that rape can be used as a tool of genocide and maintains that forced marriages can also be a form of genocide

Assessing populations of the major cereal pathogens for reduced sensitivity to MBC, DMI and Strobilurin fungicides

End of project reportStudies of eyespot populations in winter wheat crops in the period 2001 to 2003 showed that the R type (Tapesia acuformis) is the dominant strain comprising 77% of isolates. Over 90% of isolates were resistant to MBC fungicides, 53% showed reduced sensitivity to prochloraz and 22% reduced sensitivity to cyprodinil. A study of winter wheat crops in February and March 2003 showed that resistance to strobilurin fungicides was widespread in Mycosphaerella graminicola (Septoria tritici) populations. Resistance was found in all but one of 21 crops sampled, at levels ranging from 9% to 84% with an average of 48%. Subsequent studies of 27 crops over the summer of 2003 showed that strobilunin resistance increased from an average of 31% before the application of the second (T2) spray to an average of 73%, three to four weeks after the application of the final (T3) spray. Strobilurin resistance in M. graminicola remained high in 2004, ranging from 50% to 100% with an average of 83% in populations in winter wheat crops sampled in March. The effect of different fungicide programmes on resistance was studied during summer 2003 at two experimental sites. Levels of strobilurin resistance in M. graminicola populations increased during the summer, in unsprayed plots and plots treated with triazole fungicides as well as in those treated with strobiurin fungicides at both sites. M. graminicola populations in winter wheat crops sampled in 2003 and 2004 were predominantly resistant to MBC-generating fungicides and sensitive to the triazole-based fungicides. Studies of the barley leaf blotch pathogen Rhynchosporium secalis showed that resistance to MBC fungicides occurred in 20% of isolates collected from crops from 2001 to 2003, but all isolates were sensitive to triazole and strobilurin fungicides

A class of high-order Runge-Kutta-Chebyshev stability polynomials

The analytic form of a new class of factorized Runge-Kutta-Chebyshev (FRKC) stability polynomials of arbitrary order $N$ is presented. Roots of FRKC stability polynomials of degree $L=MN$ are used to construct explicit schemes comprising $L$ forward Euler stages with internal stability ensured through a sequencing algorithm which limits the internal amplification factors to $\sim L^2$. The associated stability domain scales as $M^2$ along the real axis. Marginally stable real-valued points on the interior of the stability domain are removed via a prescribed damping procedure. By construction, FRKC schemes meet all linear order conditions; for nonlinear problems at orders above 2, complex splitting or Butcher series composition methods are required. Linear order conditions of the FRKC stability polynomials are verified at orders 2, 4, and 6 in numerical experiments. Comparative studies with existing methods show the second-order unsplit FRKC2 scheme and higher order (4 and 6) split FRKCs schemes are efficient for large moderately stiff problems.Comment: 24 pages, 5 figures. Accepted for publication in Journal of Computational Physics, 22 Jul 2015. Revise

Runge-Kutta-Gegenbauer explicit methods for advection-diffusion problems

In this paper, Runge-Kutta-Gegenbauer (RKG) stability polynomials of arbitrarily high order of accuracy are introduced in closed form. The stability domain of RKG polynomials extends in the the real direction with the square of polynomial degree, and in the imaginary direction as an increasing function of Gegenbauer parameter. Consequently, the polynomials are naturally suited to the construction of high order stabilized Runge-Kutta (SRK) explicit methods for systems of PDEs of mixed hyperbolic-parabolic type. We present SRK methods composed of $L$ ordered forward Euler stages, with complex-valued stepsizes derived from the roots of RKG stability polynomials of degree $L$. Internal stability is maintained at large stage number through an ordering algorithm which limits internal amplification factors to $10 L^2$. Test results for mildly stiff nonlinear advection-diffusion-reaction problems with moderate ($\lesssim 1$) mesh P\'eclet numbers are provided at second, fourth, and sixth orders, with nonlinear reaction terms treated by complex splitting techniques above second order.Comment: 20 pages, 7 figures, 3 table