Lie Symmetry Analysis of the Black-Scholes-Merton Model for European Options with Stochastic Volatility

We perform a classification of the Lie point symmetries for the Black--Scholes--Merton Model for European options with stochastic volatility, $\sigma$, in which the last is defined by a stochastic differential equation with an Orstein--Uhlenbeck term. In this model, the value of the option is given by a linear (1 + 2) evolution partial differential equation in which the price of the option depends upon two independent variables, the value of the underlying asset, $S$, and a new variable, $y$. We find that for arbitrary functional form of the volatility, $\sigma(y)$, the (1 + 2) evolution equation always admits two Lie point symmetries in addition to the automatic linear symmetry and the infinite number of solution symmetries. However, when $\sigma(y)=\sigma_{0}$ and as the price of the option depends upon the second Brownian motion in which the volatility is defined, the (1 + 2) evolution is not reduced to the Black--Scholes--Merton Equation, the model admits five Lie point symmetries in addition to the linear symmetry and the infinite number of solution symmetries. We apply the zeroth-order invariants of the Lie symmetries and we reduce the (1 + 2) evolution equation to a linear second-order ordinary differential equation. Finally, we study two models of special interest, the Heston model and the Stein--Stein model.Comment: Published version, 14pages, 4 figure

Biomarkers of environmental contaminants in field population of green mussel (Perna viridis) from Karnataka-Kerala coast (South West coast of India)

The green mussel Perna viridis was sampled from relatively clean and contaminated sites along the Kartanata-Kerala coast (south west coast of India) to study the tissue concentration of trace metals and biological responses to stress (biomarkers) such as sister chromatid exchange (SCE), chromosomal aberration, micronucleus (MN) test, hemic neoplasia (HN), Chromotest (Ames test) and comet assay

Heavy metal distribution in the biotic and abiotic matrices along Karnataka coast, west coast of India

Sediment and soft tissue of bivalve samples collected from various sites of Karnataka coast were analysed for the estimation of the nanaal and anthropogenic heavy metal fluxes. Seasonal variations of heavy metals in sediment and bivalves collected from selected hot spots from Binage, Karwar and Thannirbavi, Mangalore were monitored. High concentrations of Hg was observed in the environment near' the vicinity of a caustic soda plant at Binage, Karwar, indicating Hg pollution. Total Hg concentration in the tissue of oysters sampled from a contaminated stream from the above site, exceeded the safe limit of 0.5 ilg g.1 wet weight. The base-line heavy metal concentrations in sediment and bivalves from selected sites of coastal Karnataka are presented

Accumulation of trace metals in green mussel Perna viridis in the shellfish harvesting environment along southern Karnataka coast

The levels of trace metals, Cd, Pb, Cu, Zn, Ni and Fe in seawater and their bioaccumulation in green mussel Perna viridis were examined in two shellfish harvesting environments, Someshwara and Surathkal, along the southern Karnataka coast. In seawater, the concentration of trace metals analysed were below the levels causing harmful effects on the larvae and adult mussels, set by the European Council Directive 79/923/EEC. The Fe, Ni, Cd and Zn levels in mussel tissue from Surathkal were relatively higher when compared to that of mussel tissue samples from Someshwara while Cu and Pb levels were lower. The mean tissue concentrations of trace metals in the soft tissue of P. viridis from shellfish waters were found to be safe and below the permissible concentrations for seafood (US FDA and WHO) as well as EU limits in marine products

On two finless porpoise Neophocaena phocaenoides landed at Malpe Fishing Harbour, Udupi district, Karnataka.

Two finless porposies Neophocaenan phocaenoides were caught by purseseine and landed at Malpe Fishing Harbour On 06-11-2003. Both the animals were auctioned for Rs. 660.Enquiries with the purseseiner which brought the porposies, revealed that they were caught from a depth of 15 m along with the catch of sardine, mackerel and rainbow sardine. The mesh size of the purseseine was 18 mm

Influence of Environmental Factors on Growth Rate of Crassostrea madrasensis (Preston) in Suspended Culture

Growth response of Crassostrea madrasensis to varying environmental factors in the Mulki estuary of Karnataka was investigated from April 2004 to March 2005. Temperature, salinity, pH, particulate organic matter (POM), particulate inorganic matter (PIM), total particulate matter (TPM) and chlorophyll a (Chl a) levels were correlated with growth in shell length. Marked seasonal patterns in growth rate were observed in relation to changes in environmental factors. Growth curve indicated a rapid phase (16.21±1.2 mm month-1) initially (May-June) followed by a slow phase (0.8±0.52 mm month-1) coinciding with the drop in salinity (August-September). Considering the temporal variations of environmental factors, their influence on growth rate was analysed seasonally. The growth rate was significantly correlated with Chl a concentrations in all the seasons. A pronounced seasonal cycle was noticed in Chl a levels resulting from blooms in pre-monsoon (April-May) and post-monsoon (October) seasons

Heavy metal concentration in sea water, sediment and bivalves off Tuticorin

Concentration of heavy metals Cd, Cu, Fe, Mn, Ni, Pb and Zn in sea water, sediment and bivalve samples from three stations was studied for one year along Tuticorin coast. The concentration was in the order of Fe>Mn>Zn>Cu>Pb>Cd>Ni. Generally the concentration of Fe was very high in the sediment and bivalves when compared to earlier studies from other areas along the Indian coast. High concentration of Fe, Mn, Cu, Pb and Zn was observed during monsoon season. One way ANOVA indicated statistically significant differences (p<0.01) among the samples in the concentration of Cu, Fe, Mn, Pb and Zn. Except for Cd and Cu, no significant difference was noticed in the seasonal variation of other metals

Timing Offset Calibration of CZTI instrument aboard ASTROSAT

The radio as well as the high energy emission mechanism in pulsars is yet not understood properly. A multi-wavelength study is likely to help in better understanding of such processes. The first Indian space-based observatory, ASTROSAT, has five instruments aboard, which cover the electromagnetic spectrum from infra-red (1300 $\AA$) to hard X-ray (380 KeV). Cadmium Zinc Telluride Imager (CZTI), one of the five instruments is a hard X-ray telescope functional over an energy range of 20-380 KeV. We aim to estimate the timing offset introduced in the data acquisition pipeline of the instrument, which will help in time alignment of high energy time series with those from two other ground-based observatories, viz. the Giant Meterwave Radio Telescope (GMRT) and the Ooty Radio Telescope (ORT). PSR B0531+21 is a well-studied pulsar with nearly aligned radio and hard X-ray pulse profiles. We use simultaneous observations of this pulsar with the ASTROSAT, the ORT and the GMRT. The pulsar was especially observed using the ORT with almost daily cadence to obtain good timing solutions. We also supplement the ORT data with archival FERMI data for estimation of timing noise. The timing offset of ASTROSAT instruments was estimated from fits to arrival time data at the ASTROSAT and the radio observatories. We estimate the offset between the GMRT and the ASTROSAT-CZTI to be -4716 $\pm$ 50 $\mu s$. The corresponding offset with the ORT was -29639 $\pm$ 50 $\mu s$. The offsets between the GMRT and Fermi-LAT -5368 $\pm$ 56 $\mu s$. (Abridged)Comment: 6 pages, 5 figures, 2 tables, Revised and Updated, accepted for publication in A&