Eliezer Z. Prisman

There have been numerous historical claims by First Nations across Canada for damages resulting from the taking of land and the resulting loss of use of such land. Many of these cases have come before the courts. Generally in such cases, there is agreement that either the Federal Government and/or a provincial government has not fulfilled its fiduciary duty. Hence, the disputes before the courts usually pertain to valuing the losses of the First Nation(s) who is (are) the Plaintiff(s) in these cases. Since the original taking of the lands occurred many decades in the past, the court is challenged with difficult valuation issues, which are complicated by a lack of historical data and transaction records. Hence, even if the parties agree on the methodology for valuing the losses and on an annual lease rate, they still need to determine the annual price of the land. A common practice for generating a price trajectory for the land is to use a very small sample of land prices, and interpolate between these prices to estimate the intervening land prices. This practice does not generate the expected trajectory given the known observations. It implicitly assumes a deterministic price process with an annual fixed appreciation of the asset throughout the period. These assumptions are inconsistent both with realistic price movements and the literature modeling asset price processes. Consequently this practice can, and mostly does, generate a very significant bias in the value of the loss. This paper suggests a loss of use valuation method that is based on a land price process consistent with the literature modeling asset price processes.

In a regulated market, such as automobile insurance (AI), regulators set the return on equity that insurers are allowed to achieve. Most insurers are engaged in a variety of insurance lines of business, and thus the full information beta methodology (FIB) is commonly employed to estimate the AI beta. The FIB uses two steps: first, the beta of each insurer is estimated, and then the beta of each line of business is estimated, as the beta of an insurer is a weighted average of the betas of the lines of business. When there are a sufficient number of public companies, company and market returns are used. Otherwise, researchers have resorted to using accounting data in the FIB. Theoretically, the two steps are not separable and the estimation should be done with one step. We introduce the one‐step methodology in our article. The one‐step and two‐step methodologies are compared empirically for the Ontario market of AI. Insurers in Ontario are predominantly private companies; thus, accounting data are used to estimate the AI beta. We show that a significant bias is introduced by the traditional, two‐step FIB methodology in estimating the betas for different lines of business, while insurers’ betas are very similar under both methods. This has a significant application to the estimation of betas of “pure players” in classic corporate finance. It implies that their betas and hence the resulting, required rates of return used in the net present value calculations should be estimated based on the one‐step method that we develop in this article.

An economic setting of ancient Jewish law is analyzed and reinterpreted in light of a modern formal financial model. Certain real estate transactions in ancient Israel, as stipulated in the Bible, involved embedded financial options that seem to have been overlooked by the commentators. This article interprets, utilizing modern financial theory, the biblical text and sheds light on a phrase used in stipulating these rules that has puzzled some commentators. The option’s value and the complexity of the pricing system that would have been needed in order to capture true market prices of these assets are demonstrated.

This paper describes and validates a stochastic model (Ornstein–Uhlenbeck process) for parathyroid hormone (PTH) levels. Rapid intraoperative parathyroid hormone assay supports the emergence of a minimally invasive approach to unilateral parathyroid exploration in the surgical treatment of hyperparathyroidism. The model’s goal is to verify whether a cure has been attained with excision of abnormal parathyroid tissue, based on intraoperative measurements, sparing the need for a bilateral exploration. The scarcity of PTH observations renders the classical methods of goodness-of-fit tests (GoFT) and cure criteria inadmissible or numerically challenging. The paper suggests a new approach to accomplish these goals given limited data. The GoFT strongly supports the model and consequently the induced cure criterion. This model will clarify the confusion in the literature regarding the required PTH decay representing a high likelihood of cure from hyperparathyroidism.

The ideas presented in this paper are those of the authors and not necessarily reflect the views of the National bank of Canada. Both authors thank the National Bank of Canada and the SSHRC of Canada for their help. Thanks are also due to Professor Y. Tian for his comments, and for participating, together with students of the Financial Engineering program at York University, in the data preparation and the execution of the Matlab programs. In this paper, we propose a necessary and sufficient condition for bid and ask prices of European options to be free of arbitrage, and derive from it an efficient numerical methodology to determine its satisfaction by a given set of prices. If the bid and ask prices satisfy the no-arbitrage (NA) condition, our methodology produces a vector of NA prices that lie between the bid and ask prices. Otherwise, our methodology generates a vector of arbitrage-free prices that is as close as possible, in some sense, to the bid–ask strip. The arbitrage-free prices detected by our methodology render the commonly used practice of using mid-points and then ‘cleaning’ arbitrage from them as unnecessary. Moreover, a vector of ‘cleaned’ prices obtained from mid-point prices may be outside the bid–ask spread even in an arbitrage-free market and, hence, in this case will not be representative of the current market. A new procedure of estimating implied valuation operators is also suggested here. This procedure is rooted in the economic properties of put and call prices and is based on Phillips and Taylor’s approximation of a convex function. This approach is superior to common estimation techniques in that it produces an analytical expression for the implied valuation operator and is not data intensive as some other studies. Empirical findings for the new methods are documented and their economic implications are discussed.

Legal disputes over compensation paid almost a century ago in lieu of a cash flow stream spanning a few decades present a number of challenges. These difficulties involve interrelated conceptual issues as well as technical obstacles. The re-evaluation of the compensation, in terms of dollars of the compensation time, requires knowledge of the yield curve at that time. However, the kept records of historical yield, is of only one rate: the long term spot rate. The rate was recorded and kept for the first business day of each month. Furthermore, the evaluation in today’s dollars requires present/future value calculations spanning over thirty years while yields for such a long duration are not observable. The paper offers a conceptual overview, proposes a methodology to overcome the technical difficulties, and exemplifies the implementation process.

The S&P/Case-Shiller® Home Price Indices are designed to measure change in the total value of all existing single-family housing stocks. This paper utilizes duality in linear programming to explore a close connection between the methodology of the indices and the classic no-arbitrage (NA) condition in financial markets. In essence, the interpretation of the NA is the “dual” problem to the primal minimization problem by which a regression is used to estimate the indices. The variables of the duality of the NA maximization problem present a term structure of discount factors, the reciprocal of which are backward-looking indices. The insight induces a new methodology for appraising single-family housing and exposes its connection to the commonly-used appraisal method. It is well known that the pricing of derivative securities is based on arbitrage arguments. In view of the index family being the underlying asset of the recent home price derivatives, the intimate connection between its estimation methodology and the classical definition of the NA condition is a point of interest.

Legal disputes over compensation paid almost a century ago in lieu of a cash flow stream spanning a few decades present a number of challenges. These difficulties involve interrelated conceptual issues as well as technical obstacles. The re-evaluation of the compensation, in terms of dollars of the compensation time, requires knowledge of the yield curve at that time. However, the kept records of historical yield, is of only one rate: the long term spot rate. The rate was recorded and kept for the first business day of each month. Furthermore, the evaluation in today’s dollars requires present/future value calculations spanning over thirty years while yields for such a long duration are not observable. The paper offers a conceptual overview, proposes a methodology to overcome the technical difficulties, and exemplifies the implementation process.