A snakes and ladders representation of stock prices and returns

Snakes and ladders is an ancient Indian game of chance that offers amusement as well as a metaphor for life’s many ups and downs. Games offer useful and fun ways of conveying ideas as well as solution techniques and this game has considerable mathematical tractability. This note shows how snakes and ladders can be used to represent the ups and downs of share ownership and solve for fair values of a multistage project that pays fixed dividends at uncertain completion times and has random returns

Chronology for climate change: Developing age models for the biogeochemical ocean flux study cores

We construct age models for a suite of cores from the northeast Atlantic Ocean by means of accelerator mass spectrometer dating of a key core, BOFS 5K, and correlation with the rest of the suite. The effects of bioturbation and foraminiferal species abundance gradients upon the age record are modeled using a simple equation. The degree of bioturbation is estimated by comparing modeled profiles with dispersal of the Vedde Ash layer in core 5K, and we find a mixing depth of roughly 8 cm for sand-sized material. Using this value, we estimate that age offsets between unbioturbated sediment and some foraminifera species after mixing may be up to 2500 years, with lesser effect on fine carbonate (<10 mu m) ages. The bioturbation model illustrates problems associated with the dating of ''instantaneous'' events such as ash layers and the ''Heinrich'' peaks of ice-rafted detritus. Correlations between core 5K and the other cores from the BOFS suite are made on the basis of similarities in the downcore profiles of oxygen and carbon isotopes, magnetic susceptibility, water and carbonate content, and via marker horizons in X radiographs and ash beds

Empirical pricing kernels obtained from the UK index options market

Empirical pricing kernels for the UK equity market are derived as the ratio between risk-neutral densities, inferred from FTSE 100 index options, and historical real-world densities, estimated from time series of the index. The kernels thus obtained are almost compatible with a risk averse representative agent, unlike similar estimates for the US market

Continuous Workout Mortgages

This paper models Continuous Workout Mortgages (CWMs) in an economic environment with refinancings and prepayments by employing a market-observable variable such as the house price index of the pertaining locality. Our main results include: (a) explicit modelling of repayment and interest-only CWMs; (b) closed form formulae for mortgage payment and mortgage balance of a repayment CWM; (c) a closed form formula for the actuarially fair mortgage rate of an interest-only CWM. For repayment CWMs we extend our analysis to include two negotiable parameters: adjustable "workout proportion" and adjustable "workout threshold." These results are of importance as they not only help understanding the mechanics of CWMs and estimating key contract parameters. These results are of importance as they not only help in the understanding of the mechanics of CWMs and estimating key contract parameters, but they also provide guidance on how to enhance the resilience of the financial architecture and mitigate systemic risk.Continuous Workout Mortgage (CWM), Repayment, Interest-only, House price index, Prepayment intensity, Cap and floor on continuous flow

Links between the local trade in natural products, livelihoods and poverty alleviation in a semi-arid region of South Africa

Can the local commercialization of natural products contribute to reduced poverty and vulnerability? Commentary on this issue is mixed, with some observers being quite optimistic, while others hold a counterview. This paper explores the poverty alleviation potential of four products traded in Bushbuckridge, South Africa—traditional brooms, reed mats, woodcraft, and “marula” beer. While key in enhancing the livelihood security of the poorest households, these products were unlikely to provide a route out of poverty for most, although there were exceptions. Incomes often surpassed local wage rates, and some producers obtained returns equivalent to the minimum wage. Non-financial benefits such as the opportunity to work from home were highly rated, and the trade was found to represent a range of livelihood strategies both within and across products

Continuous Workout Mortgages

This paper models Continuous Workout Mortgages (CWMs) in an economic environment with refinancings and prepayments by employing a market-observable variable such as the house price index of the pertaining locality. Our main results include: (a) explicit modelling of repayment and interest-only CWMs; (b) closed form formulae for mortgage payment and mortgage balance of a repayment CWM; (c) a closed form formula for the actuarially fair mortgage rate of an interest-only CWM. For repayment CWMs we extend our analysis to include two negotiable parameters: adjustable “workout proportion” and adjustable “workout threshold.” These results are of importance as they not only help understanding the mechanics of CWMs and estimating key contract parameters. These results are of importance as they not only help in the understanding of the mechanics of CWMs and estimating key contract parameters, but they also provide guidance on how to enhance the resilience of the financial architecture and mitigate systemic risk

Conceptualizing the human use of wild edible herbs for conservation in South African communal areas

The importance of wild edible herbaceous species to resource poor households in most rural economies within savannas has been little studied. This is because most of the herbs grow in impoverished species communities and lands, often referred to as ‘marginal lands’. The aim of this paper is to conceptualize how the economics of wild edible herbs to households can be used to add value to total livelihoods and conservation within traditional communal areas of South Africa. Analysis of the economics of the consumption of wild edible herbs in Thorndale (Bushbuckridge district) of the Limpopo province is presented. The majority of households consumed wild edible herbs, averaging 15.4 kg dried weight per household per year and valued at $167 per household. The herbs were mostly harvested from uncultivated areas of farms, and rangelands. There was little correlation between household characteristics and the dependence on wild herbs for food. The local people noted a decline in the availability of the species, although not much is known about attempts to cultivate them. The only reasons attributed to the decline were nutrient poor soils and insufficient rains. With this background, developing a local strategy to sustain the species through cultivation by households was found to be feasible. A multiple-use system for the herbs, their improvement and value addition towards commercialization and increased household usage may result in wider acceptance and subsequent cultivation. Species diversity will be enhanced whilst conserving the land on which they grow. This multiple use system may include species roles in soil and water conservation

Valuation of communal area livestock benefits, rural livelihoods and related policy issues

The multiple benefits from livestock production to rural households are evaluated in Thorndale, a communal area of the Limpopo Province South Africa. Monetary values of livestock products are presented. Values from most previous studies are static (and thus outdated), as a result of conceptual and methodological shifts. The net monetary value of the direct benefits from livestock was estimated as $656 per household/annum, excluding the holding of cattle for savings. The net value is equivalent to 22.7$33 per household/annum. Policy concerns are the provision of adequate market and pricing mechanisms for communal area livestock, tailored savings, investment support, credit schemes, and infrastructure. An appropriate multipurpose benefit production model, other than a commercialised model is suggested for the sector

Continuous Workout Mortgages

Continuous Workout Mortgage (CWM) balance and payments are indexed using market-observable house price index in an economic environment with prepayments. Our main results include: (a) explicit modelling of repayment and interest-only CWMs; (b) closed form formulas for mortgage payment and mortgage balance of a repayment CWM; (c) a closed form formula for the actuarially fair mortgage rate of an interest-only CWM. For repayment CWMs we extend our analysis to include two negotiable parameters: adjustable "workout proportion" and adjustable "workout threshold." These results are of importance as they not only help in the understanding of the mechanics of CWMs and estimating key contract parameters, but they also provide guidance on how to enhance the resilience of the financial architecture and mitigate systemic risk.

Holistic corpus-based dialectology

This paper is concerned with sketching future directions for corpus-based dialectology. We advocate a holistic approach to the study of geographically conditioned linguistic variability, and we present a suitable methodology, 'corpusbased dialectometry', in exactly this spirit. Specifically, we argue that in order to live up to the potential of the corpus-based method, practitioners need to (i) abandon their exclusive focus on individual linguistic features in favor of the study of feature aggregates, (ii) draw on computationally advanced multivariate analysis techniques (such as multidimensional scaling, cluster analysis, and principal component analysis), and (iii) aid interpretation of empirical results by marshalling state-of-the-art data visualization techniques. To exemplify this line of analysis, we present a case study which explores joint frequency variability of 57 morphosyntax features in 34 dialects all over Great Britain