Present Value Price Research Articles

Intertemporal Emission Trading with a Dominant Agent: How does a Restriction on Borrowing Affect Efficiency?

In this paper we analyze how restricting intertemporal trading by prohibiting borrowing of emissions permits affects the ability of a dominant agent to exploit its market power. We show that the monopolist could take advantage of the constraint on borrowing by not distributing the sale of permits cost-effectively across periods. Furthermore, we show that a constant present-value price over time does not imply a cost- effective distribution of abatement (permit sales) across periods.

A class of complete benchmark models with intensity-based jumps

This paper proposes a class of complete financial market models, the benchmark models, with security price processes that exhibit intensity-based jumps. The benchmark or reference unit is chosen to be the growth-optimal portfolio. Primary security account prices, when expressed in units of the benchmark, turn out to be local martingales. In the proposed framework an equivalent risk-neutral measure need not exist. Benchmarked fair derivative prices are obtained as conditional expectations of future benchmarked prices under the real-world probability measure. This concept of fair pricing generalizes the classical risk-neutral approach and the actuarial present-value pricing methodology.

A class of complete benchmark models with intensity-based jumps

This paper proposes a class of complete financial market models, the benchmark models, with security price processes that exhibit intensity-based jumps. The benchmark or reference unit is chosen to be the growth-optimal portfolio. Primary security account prices, when expressed in units of the benchmark, turn out to be local martingales. In the proposed framework an equivalent risk-neutral measure need not exist. Benchmarked fair derivative prices are obtained as conditional expectations of future benchmarked prices under the real-world probability measure. This concept of fair pricing generalizes the classical risk-neutral approach and the actuarial present-value pricing methodology.

Stock and Bond Pricing in an Affine Economy

This article provides a stochastic valuation framework for bond and stock returns that builds on three different pricing traditions: affine models of the term structure, present-value pricing of equities, and consumption-based asset pricing. Our model provides a more general application of the affine framework in that both bonds and equities are priced in a consistent fashion. This pricing consistency implies that term structure variables help price stocks while stock price fundamentals help price the term structure. We illustrate our model by considering three examples that are similar in spirit to well-known pricing models that fall within our general framework: a Mehra and Prescott (1985) economy, a present value model similar to Campbell and Shiller (1988b), and a model with stochastic risk aversion similar to Campbell and Cochrane (1998). The empirical performance of our models is explored, with a particular emphasis on return predictability.

A generalization of the Cairns–Krautkraemer model and the optimality of the mining rule

There exists a rule of thumb of mines, which decides how the cut-off grade (the lowest grade of extracted ore) should change in response to a change in the price of the metal. It requires that the cut-off grade should decrease (increase) when the present value price of metal increases (decreases). In this paper, the optimality of the rule will be examined by generalizing the Cairns–Krautkraemer model under the perfect foresight assumption.

The grade selection rule of the metal mines; an empirical study on copper mines

There exists a rule of thumb of mines, which requires that the cut-off grade, that is the lowest grade of extracted ore, should decrease (increase) when the present value price of metal increases (decreases). Theoretically, it was shown that the mining rule is optimal, if the deposit has a disorderly ore quality distribution. Conversely, if the deposit has an orderly ore quality distribution, the reverse rule is optimal, where the reverse rule requires that the cut-off grade should increase (decrease) when the present value price of metal increases (decreases). In this paper, the theoretical results are tested empirically from the data of 51 copper mines during 1970–1992. It is found that they are supported by the data.

Testing the Present Value Relation for Housing Prices: Should I Leave My House in San Francisco?

We examine the efficiency of residential housing markets by examining price, rent, and cost of capital indices generated from a transactions level data base for Alameda and San Francisco Counties in Northern California. We can reject both constant and nonconstant discount rate versions of the housing price present value relation in the short run. Long-run results are consistent with the housing price present value relation when we adjust the discount factor for changes in both tax rates and borrowing costs that characterize our 1970–1988 sample period. Our preferred explanation for the short-run rejection of, but long-run consistency with, the present value model is the high transaction costs that characterize the housing market. However, we cannot rule out the possibility that deviations of actual and present value price are due to asset market bubbles or nonrational expectations.

Price expectations, ore quality selection, and the supply of a nonrenewable resource

Economic models of depletion imply that the present value price of a resource and the quality of extracted ore should be directly related. The empirical evidence is that, in the short run, the average quality of extracted ore and, in some cases, metal output decline in response to a price increase. This paper examines a model of extraction with heterogeneous ore quality within a deposit and revised price expectations in which this seemingly paradoxical supply response is rationalized as the outcome of ore quality selection which maximizes the present value of the mine.

The Cut-Off Grade and the Theory of Extraction

The cutoff grade problem arises when technological infeasibility or high cost prevents an extractive firm from exploiting a heterogeneous deposit in strict sequence. The optimal cutoff grade varies directly with anticipated changes in present value price. A stochastic price path induces a higher (lower) initial cutoff grade if the marginal profit function is concave (convex). The optimal response to an unanticipated price change depends on the difference between the rates of change in price along the new and original price paths and whether or not the firm can increase extractive capacity, including the life of the mine.