1,602 research outputs found
Echinoderes dalzottoi Grzelak & Sørensen 2022, sp. nov.
No full textEchinoderes dalzottoi sp. nov. urn:lsid:zoobank.org:act: CFE372C3-2BAF-4A6B-B3C4-A0A14551747F Figs 8–10; Tables 6–7 Diagnosis Echinoderes with spines in middorsal position on segments 4 and 6, and spines in lateroventral positions on segments 6 to 9. Tubes present in subdorsal, sublateral (might be missing in some specimens) and ventrolateral positions on segment 2, lateroventral positions on segment 5, sublateral positions on segment 8, and laterodorsal positions on segment 9. Sexually dimorphic tubes furthermore present in laterodorsal positions on segment 10 in males; females with fringe-like structure in midlateral positions. Minute scales present on segments 2 to 10, but regular cuticular hairs absent throughout trunk Etymology The species is named after Dr Matteo Dal Zotto in recognition of his contributions to kinorhynch taxonomy and ecology. Material examined Holotype NEW ZEALAND • ♀; Pahaua Canyon, stn TAN1004/31; 41.4962° S, 175.6828° E; 730 m b.s.l.; Apr. 2010; NIWA TAN1004 Voyage; soft sediment; NIWA-159403. Mounted for LM in Fluoromount G on HS slide. Paratypes NEW ZEALAND • 1 ♂; Pahaua Canyon, stn TAN1004/27; 41.4983° S, 175.7043° E; 1013 m b.s.l.; Apr. 2010; NIWA TAN1004 Voyage; soft sediment; NHMD-917147. Mounted as holotype • 1 ♂; Honeycomb Canyon, stn TAN1004/58; 41.4080° S, 175.8977° E; 670 m b.s.l.; Apr. 2010; NIWA TAN1004 Voyage; soft sediment; NIWA-159404. Mounted as holotype. Additional material NEW ZEALAND • 1 ♂; same collection data as for holotype; personal reference collection of MVS. Mounted for SEM • 1 ♂; Pahaua Canyon, stn TAN1004/27; 41.4983° S, 175.7043° E; 1013 m b.s.l.; Apr. 2010; NIWA TAN1004 Voyage; soft sediment; personal reference collection of MVS. Mounted for SEM • 1 ♀; Honeycomb Canyon, stn TAN1004/58; 41.4080° S, 175.8977° E; 670 m b.s.l.; Apr. 2010; NIWA TAN1004 Voyage; soft sediment; personal reference collection of MVS. Mounted for SEM. Description GENERAL. Adults with head, neck and eleven trunk segments (Figs 8–10). Overview of measurements and dimensions in Table 6. Distribution of cuticular structures, i.e., sensory spots, glandular cell outlets, spines and tubes, summarized in Table 7. Head morphology could not be examined in detail in any of available specimens. NECK. Consists of 16 placids. Midventral placid broadest, 13 µm in width and 15 µm in length, whereas all others narrower, measuring 7 µm in width at their bases (Fig. 8). The trichoscalid plates are well developed (Fig. 9D). SEGMENT 1. Consists of complete cuticular ring. Sensory spots present in subdorsal, laterodorsal and ventromedial positions. Sensory spots relatively large and without marginal hairs, located on anterior half of segment (Figs 8A–B, 9C–D, 10B–C, E). Glandular cell outlet type 1 present in middorsal position and in ventrolateral positions. Cuticular hairs or perforation sites not present. Posterior segment margin almost straight, forming pectinate fringe with short, sawtooth-like fringe tips (Fig. 10B–C). SEGMENT 2. Consists of complete cuticular ring, with tubes located in subdorsal, sublateral and ventrolateral positions (Figs 8A–B, 9C–D, 10B–C, E); sublateral tubes missing in one paratype and two SEM specimens; no sexual or developmental differences explain presence or absence of tubes. Sensory spots of similar sizes as on preceding segment, present in middorsal, laterodorsal and ventromedial positions; ventromedial ones with long marginal hair. Unpaired glandular cell outlet type 1 present in middorsal position and as pair in ventromedial positions. Pachycyclus of anterior segment margin of regular thickness, interrupted in middorsal position. Secondary pectinate fringe present near anterior segment margin of this and following segments, but usually covered by preceding segment. This and following nine segments completely hairless. Cuticular hairs reduced to minute scales distributed around segment (Fig. 10B–C, E–H), emerging through perforation sites; perforation sites easily visible in LM (Fig. 9C–K). Posterior segment margin almost straight, but with rounded midventral extension (Fig. 10D–E); pectinate fringe tips as on preceding segment, except midventral area with slightly narrower fringe tips. SEGMENT 3. Present segment, and eight remaining ones, consist of one tergal and two sternal plates (Figs 8A–B, 9A, D). Sensory spots present in subdorsal and midlateral positions. Sensory spots on this and following segments smaller than on preceding segments, all with one long marginal hair. Glandular cell outlets type 1 as on preceding segment. Perforation sites appear as band around segment, interrupted in middorsal and laterodorsal areas and in central part of sternal plate on this and following five segments (Figs 8A–B, 9C–D, F–G, 10F–G). Posterior segment margin straight, terminating in pectinate fringe with slightly more slender fringe tips along ventral margin than on preceding segments, otherwise as on preceding segment. SEGMENT 4. With spine in middorsal position; spine relatively long (51 µm), reaching posterior margin of segment 5 (Figs 8A, 10A, F). Glandular cell outlets type 1 present in paradorsal and ventromedial positions. No other traits observed. Segment otherwise as segment 3. SEGMENT 5. With tubes in lateroventral positions (Figs 8B, 9D, 10G). Sensory spots present in subdorsal, midlateral and ventromedial positions (Figs 8A–B, 9C, 10F). Glandular cell outlets type 1 present in middorsal and ventromedial positions. Perforation sites, secondary fringe and posterior segment margin as on preceding segment. SEGMENT 6. With spines in middorsal and lateroventral positions (Fig. 8A–B). Middorsal spine, as on segment 4, relatively long (99 µm), reaching well beyond posterior segment margin of segment 8 (Fig. 10A, I). Sensory spots present in paradorsal, subdorsal, midlateral and ventromedial positions (Figs 8A–B, 10F–G). Glandular cell outlets type 1 present in paradorsal and ventromedial positions. Segment otherwise as segment 5. SEGMENT 7. With spines in lateroventral positions, and sensory spots in paradorsal, midlateral and ventromedial positions (Figs 8A–B, 9G, 10F–G). Glandular cell outlets type 1 present in middorsal position and as pair in ventromedial positions. Tips of pectinate fringe of posterior segment margin slightly shorter and more slender than on preceding segments. Segment otherwise as segment 6. SEGMENT 8. With spines in lateroventral positions, and tubes in sublateral positions (Figs 8A–B, 9E, 10H). Sensory spots present in paradorsal and subdorsal positions. Glandular cell outlets type 1 present in paradorsal and ventromedial positions. Band of perforation site patches interrupted in subdorsal area instead of laterodorsally as on preceding segments. Segment otherwise as segment 7. SEGMENT 9. With spines in lateroventral positions. Tubes present in laterodorsal positions, but very close to midlateral line (Figs 8A, 9E, 10H–I). Sensory spots located in paradorsal, subdorsal and ventrolateral positions (Figs 8A–B, 9J, 10I). Glandular cell outlets type 1 present paradorsally and ventromedially. Small, rounded sieve plates located in sublateral positions (Fig. 9K). Perforation sites, secondary fringe and posterior segment margin as on preceding segment. SEGMENT 10. With well-developed laterodorsal tubes, present in males only, located near posterior segment margin and close to midlateral line (Figs 8C, 9H, 10K). Females without tubes, but with fringelike structures present in midlateral positions (Figs 8A, 10J). Sensory spots present in subdorsal and ventrolateral positions (Figs 8A–B, 10J–K); subdorsal pair located rather close to paradorsal area. Glandular cell outlets type 1 present as middorsal one, and in ventromedial positions. Perforation sites restricted to paradorsal area, lateral sides of tergal plate, and lateral halves of sternal plates. Posterior segment margin of tergal plate straight, without fringe tips (Fig. 10J–K); margins of sternal plates concave, reaching posterior margin of terminal segment, with short and narrow fringe tips. SEGMENT 11. With lateral terminal spines (Figs 8A–B, 9A, 10D). Females with lateral terminal accessory spines (Figs 8A–B, 9I, 10A, D); males with three penile spines (Fig. 10K). Dorsal and ventral penile spines slender and tubular, with dorsal ones much longer than ventral; median spines very stout, coneshaped (Figs 8C, 10K). Sensory spots present in subdorsal positions. Glandular cell outlet type 1 present middorsally. Segment devoid of characteristic perforation site patches, but very short cuticular hair-like structures covering paradorsal area. Very short fringes covering margins of tergal and sternal plates. Tergal extensions triangular (Figs 8A, C, 10J). Sternal extensions rounded, not extending beyond tergal extensions (Figs 8B, D, 9K). Distribution Canyons: Pahaua, Honeycomb, 670–1013 m b.s.l. See Fig. 1 for a geographic overview of stations and Table 1 for station and specimen information. Taxonomic remarks on Echinoderes dalzottoi sp. nov. See taxonomic remarks for E. dalzottoi sp. nov. below, together with remarks for E. leduci sp. nov.Published as part of Grzelak, Katarzyna & Sørensen, Martin V., 2022, Echinoderes (Kinorhyncha: Cyclorhagida) from the Hikurangi Margin, New Zealand, pp. 1-108 in European Journal of Taxonomy 844 on pages 25-31, DOI: 10.5852/ejt.2022.844.1949, http://zenodo.org/record/722215
Echinoderes blazeji Grzelak & Sørensen 2022, sp. nov.
No full textEchinoderes blazeji sp. nov. urn:lsid:zoobank.org:act: 38F17023-13B9-487F-AF98-9F44AE186815 Figs 2–4; Tables 2–3 Diagnosis Echinoderes with a very minute spine in middorsal position on segment 4 and in lateral accessory positions on segment 7. Tubes present in lateroventral positions on segment 5, sublateral positions on segment 8 and laterodorsal positions on segment 10; tubes on segment 10 well-developed in males, whereas much smaller in females. Glandular cell outlet type 2 present in midlateral positions on segment 8. Large, elongate sieve plates located midlaterally on segment 9. Lateral terminal spines twice as long in males as in females. Etymology The species is named after Blazej, the son of the first author – for his love of all dragons. Material examined Holotype NEW ZEALAND • ♂; Pahaua Canyon, stn TAN1004/27; 41.4983° S, 175.7043° E; 1013 m b.s.l.; Apr. 2010; NIWA TAN1004 Voyage; soft sediment; NIWA-159400. Mounted for LM in Fluoromount G on HS slide. Paratypes NEW ZEALAND • 1 ♀; same collection data as for holotype; NHMD-917223 • 1 ♂; same collection data as for holotype; NIWA-159401. Mounted as holotype. Additional material NEW ZEALAND • 1 ♂; same collection data as for holotype; personal reference collection of MVS. Mounted for SEM • 3 ♀♀, 1 ♂; Honeycomb Canyon, stn TAN1004/58; 41.4080° S, 175.8977° E; 670 m b.s.l.; Apr. 2010; NIWA TAN1004 Voyage; soft sediment; personal reference collection of MVS. Mounted for SEM • 1 ♂; Honeycomb Canyon, stn TAN1004/62; 41.4760° S, 175.9477° E; 1171 m b.s.l.; Apr. 2010; NIWA TAN1004 Voyage; soft sediment; personal reference collection of MVS. Mounted for SEM. Description GENERAL. Adults with head, neck and eleven trunk segments (Figs 2–4). Overview of measurements and dimensions in Table 2. Distribution of cuticular structures, i.e., sensory spots, glandular cell outlets, spines and tubes, summarized in Table 3. The head morphology could not be examined in detail in any of the available specimens. NECK. Consists of 16 placids. Midventral placid broadest, 11 µm in width and 12 µm in length, whereas all others narrower, measuring 7 µm in width at bases (Fig. 2). Trichoscalid plates well developed (Fig. 3B). SEGMENT 1. Consists of complete cuticular ring. Subdorsal and laterodorsal sensory spots present, situated on anterior half of segment. Sensory spots on this and following segments droplet-shaped, consisting of central pore surrounded by micropapillae (Fig. 4C, E, G). Glandular cell outlet type 1 not observed. Cuticular hairs arising from rounded perforation sites, distributed evenly around segment except in anterior part. Segment terminates in pectinate fringe with relatively long fringe tips (Fig. 4C). SEGMENT 2. Consists of complete cuticular ring with sensory spots present in middorsal, laterodorsal, midlateral and ventromedial positions (Figs 2A–B, 3B, 4B–C). Glandular cell outlet type 1 present in middorsal position and as a pair in ventromedial positions. Pachycyclus of anterior segment margin of regular thickness, interrupted in middorsal position on this and following segments. Cuticular hairs densely covering entire segment. Perforation sites on this and following eight segments appear as band around segment, easily visible in LM (Fig. 3B–C, E–I). Posterior segment margin straight along dorsal edge, but markedly extended posteriorly in midventral position (Fig. 4C). Primary pectinate fringe with tips similar to those of preceding segment in middorsal to ventrolateral position and smaller and thinner tips in ventromedial and paraventral positions (Figs 2A–B, 4B–C). SEGMENT 3. Present segment, and eight remaining ones, consist of one tergal and two sternal plates (Figs 2A–B, 3A–D). Sensory spots present in subdorsal and sublateral positions (Fig. 3B–C). Glandular cell outlets type 1 located in middorsal and ventromedial positions. Cuticular hairs on this and following seven segments densely covering entire segment, except for narrow area in laterodorsal position (Fig. 2A). Posterior segment margin straight, terminating in pectinate fringe with relatively long and uniform fringe tips along entire segment margin. SEGMENT 4. With minute (~10 µm) middorsal spine (Figs 3B, 4E). Sensory spots located subdorsally (Figs 3B, 4B). Glandular cell outlet type 1 present in subdorsal and ventromedial positions (Fig. 3B–C). Segment otherwise as segment 3. SEGMENT 5. With tubes in lateroventral positions (Figs 2B, 3C, 4F). Sensory spots present in subdorsal, midlateral and ventromedial positions (Figs 2A–B, 4E–F). Glandular cell outlets type 1 present in subdorsal and ventromedial positions. Cuticular hair covering as on preceding segment except for hairless paraventral area. Secondary fringe and posterior segment margin as on preceding segment. SEGMENT 6. With sensory spots present in subdorsal, sublateral and ventromedial positions (Figs 2A–B, 3E, 4E–F). Glandular cell outlets type 1 as on preceding segment. Cuticular hair covering and secondary pectinate fringe as on segment 5. SEGMENT 7. With minute spines (<10 µm) in lateral accessory positions (Figs 2B, 3F, 4F); spines hardly visible in both LM and SEM due to dense cuticular hairs covering and their inconspicuous appearance. Sensory spots located in subdorsal, midlateral, and ventromedial positions. Glandular cell outlets type 1 present in subdorsal and ventromedial positions. Segment otherwise as segment 6. SEGMENT 8. With tubes in sublateral positions and glandular cell outlets type 2 located in midlateral positions (Figs 2A–B, 3E–F, 4G–H). Sensory spots present in subdorsal, laterodorsal and ventromedial positions; subdorsal pair located closer to paradorsal line than on preceding segments. Glandular cell outlets type 1 present in subdorsal and ventromedial positions. Pectinate fringe tips slightly shorter than on preceding segments. SEGMENT 9. Without spines or tubes. Sensory spots located in subdorsal, laterodorsal, midlateral and ventrolateral positions (Figs 2A–B, 4G). Pair of sieve plates, composed of large, elongated sieve area located anterior to rounded areas with central pore, located in sublateral positions (Figs 2A, 3F–I). Glandular cell outlets type 1, cuticular hair covering and posterior segment margin as on preceding segment. SEGMENT 10. With laterodorsal tubes, located near posterior segment margin. In males, tubes long (~15 µm) (Figs 2A, 3H, 4I–J). In females, tubes much shorter (~6 µm) and more flexible (Figs 2C, 4K), without basal part characteristic for tubes in males as well as for tubes described on segments 5 and 8. Sensory spots present in subdorsal and ventrolateral positions. Glandular cell outlets type 1 present as middorsal one, and as pair in ventromedial positions. Posterior segment margin of tergal plate straight, while margins of sternal plates concave, reaching posterior margin of terminal segment. Pectinate fringe tips significantly shorter and narrower than on preceding segment. SEGMENT 11. With lateral terminal spines; in males, lateral terminal spines twice long as in females (Figs 2, 3A, D, 4A, D; Table 2). Females with short and relatively thin lateral terminal accessory spines (Figs 2C–D, 3I, 4K); males with three penile spines, two of them flexible and elongated, one short and stout (Figs 2A–B, 3H, 4I–J).Additionally, one female specimen shows pair of fringed tubes-like structures on ventral side (Fig. 4K); examination of ventral side of segment 11 not possible in other specimens; therefore, we cannot conclude whether it is a sexually dimorphic character or not. Sensory spots present in subdorsal positions. Unpaired glandular cell outlet type 1 present middorsally. Segment devoid of cuticular hairs, but very short cuticular hair-like structures covering tergal extensions and posterior parts of sternal plates. Very short fringes covering margins of tergal and sternal plates. Tergal extensions elongated and triangular (Figs 2A, C, 4J). Sternal extensions slightly extended posteriorly, not extending beyond tergal extensions (Fig. 2B, D). Distribution Canyons: Pahaua, Honeycomb, 670–1171 m b.s.l. See Fig. 1 for a geographic overview of stations and Table 1 for station and specimen information. Taxonomic remarks on Echinoderes blazeji sp. nov. The arrangement of spines and tubes, with a minute middorsal spine on segment 4, minute lateral spines on segment 7 only and lateral tubes on segments 5 and 8, is not present in any other species of Echinoderes. These characters, combined with the large sieve plates and dense cuticular hairs, make E. blazeji sp. nov. even more distinctive and narrow the number of potential congeners down to species belonging to the so-called Echinoderes coulli -group (following the diagnosis of Yamasaki & Fujimoto 2014). Currently, this group accommodates 17 species (Randsø et al. 2019; Yamasaki et al. 2020a; Cepeda et al. 2022; Kennedy et al. 2022) that share a number of morphological characters and habitat preferences. Echinoderes blazeji sp. nov. can easily be distinguished from all other E. coulli -group congeners by its presence of lateral spines only on segment 7. The group is suggested to share morphological features such as absence of middorsal spines or, if present, on segment 4 only; lateral spines absent or very minute and restricted to segments 6 and 7; presence of lateral tubes on segments 5 and 8; and female lateral terminal accessory spines being either poorly-developed or absent (Yamasaki & Fujimoto 2014). Therefore, the possession of only one pair of lateral spines makes E. blazeji unique among all other species of this group. Nevertheless, it should be stressed that these spines are extremely minute and might easily be overlooked due to the dense cuticular hair covering, especially during LM examination. But even if the presence of lateral spines on segment 7 had gone unnoticed among the nine species of the E. coulli group with a middorsal spine on segment 4 (i.e., E. annae Sørensen et al., 2016, E. cyaneafictus Cepeda et al., 2022, E. maxwelli (Omer-Cooper, 1957), E. ohtsukai Yamasaki & Kajihara, 2012, E. parthenope Cepeda et al., 2022, E. regina Yamasaki, 2016, E. rex Lundbye et al., 2011, E. serratulus Yamasaki, 2016 and E. teretis Brown, 1999 in Adrianov & Malakhov 1999), only E. annae shows the absence of lateral spines (Omer-Cooper 1957; Adrianov & Malakhov 1999; Lundbye et al. 2011; Yamasaki & Kajihara 2012; Sørensen et al. 2016a; Yamasaki 2016; Cepeda et al. 2022). However, other conditions in E. annae make this species easily distinguishable from E. blazeji. In contrast to the new species, which has only one pair of relatively big glandular cell outlets type 2 on segment 8, E. annae possesses numbers of minute glands distributed over several segments. Moreover, the latter species is characterized by the presence of midlateral tubes on segment 9, which are absent in E. blazeji, and by very short and stout lateral terminal spines, which cannot be confused with the longer and thinner lateral spines in E. blazeji. Furthermore, the lateral terminal spines themselves seem to represent another characteristic feature for the new species, since they are twice as long in males as in females (♂ LTS =104 µm vs ♀ LTS =50 µm, respectively). Echinoderid sexual dimorphism is usually displayed in the female presence of lateral terminal accessory spines, in the appearance of the laterodorsal tubes on segment 10 (i.e., Sørensen 2006; Pardos et al. 2016a; Grzelak & Sørensen 2018; present study) or presence of papillae/pores on the ventral side in females (Sørensen et al. 2020). Having sexual dimorphism expressed in lateral terminal spine lengths is a rather unusual trait in Echinoderes. Differences in length of lateral terminal spines expressed as sexual dimorphism have been observed for E. aquilonius Higgins & Kristensen, 1988 and E. lusitanicus Neves et al., 2016 (Higgins & Kristensen 1988; Neves et al. 2016), but more interestingly, also in E. coulli Higgins, 1977 – a species closely related with E. blazeji sp. nov. Higgins (1977) described two forms of females in E. coulli: one form with lateral terminal spines similar to those in males, and a second form with short lateral terminal spines being half the length of those of males. The latter shortspined form was, however, more abundant in the population and constituted about half of all examined specimens. In our case, all examined females (4 out of 9 specimens in total) had markedly shorter lateral terminal spines than males, which suggests that we might have the same kind of female dimorphism in E. blazeji. Sexual dimorphism expressed in spine lengths has also been reported for E. levanderi Karling, 1954 and the Arctic population of E. pterus Yamasaki et al., 2018, but in these cases it was related to the length of lateroventral spines (Karling 1954; Sørensen 2018; Yamasaki et al. 2018a). In addition, the pattern of glandular cell outlets type 1 on the dorsal side appears to be uncommon for the new species. The taxonomic significance of the glandular cell outlet type 1 pattern, in contrast to glandular cell outlets type 2, is not yet well explored or understood. In fact, it was only quite recently that Sørensen et al. (2020) drew attention to its potential taxonomic significance. They showed that a majority of species of Echinoderes (for which we have sufficient data) show outlets on segments 4 to 9 in paradorsal or paradorsal and middorsal (depends on the segment) positions (Sørensen et al. 2020). The presence of glandular cell outlets type 1 in subdorsal positions on segments 4 to 9, as observed for E. blazeji sp. nov., has so far only been reported from ten other, putatively closely related species, all belonging to the E. dujardinii species group, and in E. worthingi Southern, 1914, a species also closely related to the E. dujardinii group (Southern 1914; Sørensen et al. 2020). Since E. blazeji cannot be considered as closely related with the E. dujardinii -group, our observation of glandular cell outlets type 1 in the new species thus indicates that this morphological trait may still hide some interesting aspects. Finally, the new species has been found in a habitat that is quite unusual for species of the E. coulli - group. The majority of these species have been recorded in intertidal marine or brackish water, with the exception of four species that inhabit subtidal, but yet shallow, marine waters (Lundbye et al. 2011; Yamasaki 2016; Kennedy et al. 2022). In this context, E. blazeji sp. nov. is unique within the species group, since it is so far the only species inhabiting deep-sea waters.Published as part of Grzelak, Katarzyna & Sørensen, Martin V., 2022, Echinoderes (Kinorhyncha: Cyclorhagida) from the Hikurangi Margin, New Zealand, pp. 1-108 in European Journal of Taxonomy 844 on pages 11-18, DOI: 10.5852/ejt.2022.844.1949, http://zenodo.org/record/722215
On cross-currency models with stochastic volatility and correlated interest rates
No full textWe construct multi-currency models with stochastic volatility and correlated stochastic interest rates with a full matrix of correlations. We frst deal with a foreign exchange (FX) model of Heston-type, in which the domestic and foreign interest rates are generated by the short-rate process of Hull-White [HW96]. We then extend the framework by modeling the interest rate by a stochastic volatility displaced-diffusion Libor Market Model [AA02], which can model an interest rate smile. We provide semi-closed form approximations which lead to effcient calibration of the multi-currency models. Finally, we add a correlated stock to the framework and discuss the construction, model calibration and pricing of equity- FX-interest rate hybrid payoffs.Foreign-exchange (FX); stochastic volatility; Heston model; stochastic interest rates; interest rate smile; forward characteristic function; hybrids; affne diffusion; effcient calibration.
Approximate solution to a hybrid model with stochastic volatility: a singular-perturbation strategy
No full textWe study a hybrid model of Schobel-Zhu-Hull-White-type from a singular-perturbation-analysis perspective. The merit of the paper is twofold: On one hand, we find boundary conditions for the deterministic non-linear degenerate parabolic partial differential equation for the evolution of the stock price. On the other hand, we combine two-scales regular- and singular-perturbation techniques to find an approximate solution to the pricing PDE. The aim is to produce an expression that can be evaluated numerically very fast
Collocating volatility: a competative alternative to stochastic local volatility models
No full textWe discuss a competitive alternative to stochastic local volatility models, namely the Collocating Volatility (CV) framework, introduced in [L. A. Grzelak (2019) The CLV framework - A fresh look at efficient pricing with smile, International Journal of Computer Mathematics 96 (11), 2209-2228]. The CV framework consists of two elements, a "kernel process"that can be efficiently evaluated and a local volatility function. The latter, based on stochastic collocation - e.g. [I. Babuška, F. Nobile & R. Tempone (2007) A stochastic collocation method for elliptic partial differential equations with random input Data, SIAM Journal on Numerical Analysis 45 (3), 1005-1034; B. Ganapathysubramanian & N. Zabaras (2007) Sparse grid collocation schemes for stochastic natural convection problems, Journal of Computational Physics 225 (1), 652-685; J. A. S. Witteveen & G. Iaccarino (2012) Simplex stochastic collocation with random sampling and extrapolation for nonhypercube probability spaces, SIAM Journal on Scientific Computing 34 (2), A814-A838; D. Xiu & J. S. Hesthaven (2005) High-order collocation methods for differential equations with random inputs, SIAM Journal on Scientific Computing 27 (3), 1118-1139] - connects the kernel process to the market and allows the CV framework to be perfectly calibrated to European-type options. In this paper, we consider three different kernel process choices: the Ornstein-Uhlenbeck (OU) and Cox-Ingersoll-Ross (CIR) processes and the Heston model. The kernel process controls the forward smile and allows for an accurate and efficient calibration to exotic options, while the perfect calibration to liquid market quotes is preserved. We confirm this by numerical experiments, in which we calibrate the OU-CV, CIR-CV and Heston-CV frameworks to FX barrier options
A Fourier-based approach for valuing bonds with embedded options: an analysis of convolution- and cosine-based approximation methods using jump-diffusion models and extended with stochastic interest rates
No full textDue to their attractive characteristics, convertible and callable bonds became a more important class of fixed-income products within the financial market. Therefore, the need for fair and accurate pricing of convertible and callable bonds increases. Where the convertible option can be considered as a right for the bondholder, the callable option is a right assigned to the bond issuer. Moreover, due to the hybrid nature of a convertible bond, it both contains characteristics of fixed income and equity products. As a consequence, both the risk of default and the possible equity profits need to be taken into account when valuing convertible bonds. Furthermore, as many convertible bonds also include a call option, an extra early exercise feature due to this call option needs to be taken into account. This early exercise option further increases the complexity of the valuation problem, as a possible buyback of the bond before maturity needs to be considered in the value of the bond. Computing a fair and accurate price for convertible and callable bonds, therefore gives rise to a complex valuation problem which leads to the need for further research. In this thesis, a structural default model is used to value callable convertible bonds. Contrary to reduced-form models, structural default models are characterized by the rationale behind the default event. Due to the better rationale and new insights into possible better market fits, structural default models have gained new interest in academic research. Recent research is conducted on finding new numerical techniques used for approximating the prices of complex financial products. This thesis discussed different valuation methods as proposed by Longstaff and Schwartz, Lord et al. and Oosterlee and Grzelak applied to the valuation of callable convertible bonds. In particular, a convolution-based method (CONV) and a cosine-based (COS) method are discussed. Whereas the Monte Carlo methods and the CONV method are already used in different articles, the COS method was not yet applied to the callable convertible bond valuation. As the COS method has been proven to be an efficient algorithm for approximating the values of financial derivatives, this thesis uses the COS method to compare its convergence to seek more insights into the convergence of the CONV method. Monte Carlo methods are used to verify the obtained approximations. For the problem considered under constant interest rates, this thesis shows that the COS method can be derived and applied. For small values of the grid size, the COS method showed to converge much faster than the CONV method. For larger values of the grid size, the CONV method showed to catch up with the COS method to become almost equally accurate. The results also showed that, contrary to the COS method, the CONV method was robust under the choice of the hyper-parameter concerning the integration grid. For the COS method, it was shown that a bad choice of the hyper-parameter could lead to a bad approximation. Although the two-dimensional CONV method shows to converge to the value obtained under Monte Carlo simulation, the results are still off for grid sizes of intermediate size. Results seem to indicate that the amount of grid points is not sufficient for the proposed integration interval and that therefore more grid points are needed. A greater amount of grid points, however, will also indicate a requirement for a greater amount of resources which may not always be available. From the results of the zero-coupon case, the COS method showed a more rapid convergence towards the approximations obtained by the Monte Carlo methods than the approximations obtained using the CONV method. Furthermore, when taking the hyper-parameters into account, the CONV method showed less robust features than the COS method in the two-dimensional case. Only for a small range of the hyper-parameters convergence is obtained for the CONV method. On the other hand, the COS method clearly shows convergence for a much wider range of hyper-parameters.Applied Mathematic
Equity and Foreign Exchange Hybrid Models for Pricing Long-Maturity Financial Derivatives
No full textModelling derivative products in Finance usually starts with the specification of a system of Stochastic Differential Equations (SDEs), that corresponds to state variables like stock, interest rate, Foreign Exchange (FX) rate and volatility. By correlating the SDEs for the different asset classes one can define the hybrid models, and use them for pricing multi-asset derivatives. Even if each of the individual SDEs yields a closed-form solution, a non-zero correlation structure between the processes may cause difficulties for efficient product pricing. Typically, a closed-form solution of hybrid models is not known, and numerical approximation by means of Monte Carlo (MC) simulation or discretization of the corresponding Partial Differential Equations (PDEs) has to be employed for pricing. The speed of pricing European derivative products is crucial, especially for the calibration of the SDEs. Several theoretically attractive SDE models, that cannot fulfil the speed requirements, are not used in practice.Numerical AnalysisElectrical Engineering, Mathematics and Computer Scienc
Inny w Polsce. Komunikacja interkulturowa w państwie narodowym
No full textAutorka analizuje problem komunikacji między społeczeństwem dominującym a mniejszościami narodowymi i etnicznymi. Zwraca uwagę na kategorię swój /obcy regulującą relacje społeczne, ich zakorzenienie kulturowe i genezę polityczną . Ponadto definiuję na potrzeby wystąpienia, w oparciu o własne badania, pojęcie ‘państwo narodowe’. Kulturowe rozumienie inności omawia, przywołując cztery postawy: odrzucenie, nietolerancję, tolerancję i akceptację. Identyfikuje także bariery, utrudniające fortunną komunikację na granicy kultur, mające swą genezę w zmieniającym się układzie geopolitycznym. Stosunek do inności w Polsce ilustruje werbalnymi i niewerbalnymi zachowaniami komunikacyjnymi, poszukuje ich przyczyn w systemach praw-nym i edukacyjnym, które są dziedzictwem PRL-u. W swoich rozważaniach bierze pod uwagę czynniki, wpływające na kształtowanie relacji interkulturowych w Polsce po 1989 roku:– totalitaryzm utrwalony w pamięci społecznej,– zniesienia cenzury,– dynamikę procesów globalizacyjnych,– determinizm technologiczny relacji interpersonalnych i interkulturowych,– przeobrażenia aksjologiczne. Na zakończenie, na podstawie wyników badań, opisuje tendencje w zakresie omawianych relacji. The author analyses a problem of communication between a dominant society and national and ethnic minorities. She focuses on a category of one’s/ other that regulates social relations, their cultural roots and political origin. Additionally, for the purposes of the speech, the author defines ‘a national state’ term based on her own research in the field. Cultural understanding of otherness is explained based on four attitudes: rejection, intolerance, tolerance and acceptance. Barriers that hamper a fortunate communication on the edge of cultures and origin from a changing geopolitical system are identified. The author illustrates the attitude towards other-ness with verbal and nonverbal communicational behaviors, investigates their causes in legal and educational systems which are the heritage of Polish People’s Republic times. She considers the following aspects that have shaped intercultural relations in Poland after 1989:– totalitarianism imprinted in social memory of people,– abolition of censorship,– globalization processes dynamics,– technological determinism of interpersonal and intercultural relations,– axiological changes. Finally, the author describes the tendencies of the above relations based on the results of research
Pricing of Asian options on baskets of futures
No full textApplied MathematicsDelft Institute of Applied MathematicsElectrical Engineering, Mathematics and Computer Scienc
Correcting Non Positive Definite Correlation Matrices
No full textApplied mathematicsElectrical Engineering, Mathematics and Computer Scienc
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