Heterogeneous Agents and the Indifference Pricing of Property Index Linked Swaps

Swap spreads predicted by the traditional risk-neutral valuation models are much lower than the quoted market spreads for property index linked swaps (Patel and Pereira, Journal of Real Estate Finance and Economics, 36:5–21, 2008). This paper attempts to develop a utility indifference-based model for evaluating the reservation spreads of swap receivers and payers based on the principle of expected wealth utility equivalence rather than the traditional risk-neutral argument. Under the proposed model framework, this paper addresses the determination of the swap spreads. When the incompleteness of real estate markets and heterogeneity of representative agents are taken into consideration, it is shown that the agents’ risk preferences and heterogeneous beliefs about expected future property returns are the remarkable determinants for the swap spreads. Our model also identifies market power and the settlement rules in the event of counterparty default as important factors in determining the swap spreads. Our model provides a possible interpretation for the difference between the spreads predicted by the traditional models and the actual market spreads.     

Distressed debt prices and recovery rate estimation

This paper has two purposes. First, it uses distressed debt prices to estimate recovery rates at default. In this regard, estimates are obtained for three recovery rate models: recovery of face value, recovery of Treasury, and recovery of market value. We show that identifying the “economic” default date, as distinct from the recorded default date, is crucial to obtaining unbiased estimates. The economic default date is defined to be the first date when the market prices the firm’s debt as if it has defaulted. An implication is that the standard industry practice of using 30-day post default prices to compute recovery rate yields biased estimates. Second, we construct and estimate a distressed debt pricing model. We use this model to implicitly estimate the parameters of the embedded recovery rate process and to price distressed debt. Our distressed debt pricing model fits market prices well, with an average pricing error of less than one basis point.      

Insider trading in an equilibrium model with default: a passage from reduced-form to structural modelling

We study, in the framework of Back [Rev. Financial Stud. 5(3), 387–409 (1992)], an equilibrium model for the pricing of a defaultable zero coupon bond issued by a firm. The market consists of a risk-neutral informed agent, noise traders, and a market maker who sets the price using the total order. When the insider does not trade, the default time possesses a default intensity in the market’s view as in reduced-form credit risk models. However, we show that, in equilibrium, the modelling becomes structural in the sense that the default time becomes the first time that some continuous observation process falls below a certain barrier. Interestingly, the firm value is still not observable. We also establish the no expected trade theorem that the insider’s trades are inconspicuous.      

The Current State of the Arbitrage Pricing Theory

This paper provides a simple proof of a recent theorem presented by Reisman (1992) , concerning the use of proxies for the factors in the return-generating process of the arbitrage pricing theory (APT). In the single-factor case, the theorem asserts that any variable correlated with the factor can serve as the benchmark in an approximate APT expected return relation. The significance of this result is considered and a new direction for empirical work on “arbitrage pricing” is outlined.     

A Pricing Model for Residential Homes with Poisson Arrivals and a Sales Deadline

We introduce a pricing model for single-family residences on the real estate market. The model considers purchase offers that arrive according to a Poisson process. The homeowner’s problem is to set a price that will maximize his net profit. The selling agent suggests a price to the homeowner that will maximize her net profit, which consists of her sales commission minus her costs. Our model accounts for a deadline to sell the home, a common feature of the housing market, beyond which fixed and variable penalty costs accrue to both the homeowner and selling agent. We demonstrate the behavior of the model and show under what conditions the owner’s and agent’s incentives are aligned. Our computational results suggest, in most circumstances, that agents should not pressure owners to substantially lower their asking prices in the presence of a deadline.     

Pricing catastrophe risk in life (re)insurance

What is the catastrophe risk a life insurance company faces? What is the correct price of a catastrophe cover? During a review of the current standard model, due to Strickler, we found that this model has some serious shortcomings. We therefore present a new model for the pricing of catastrophe excess of loss cover (Cat XL). The new model for annual claim cost C is based on a compound Poisson process of catastrophe costs. To evaluate the distribution of the cost of each catastrophe, we use the Peaks Over Threshold model for the total number of lost lives in each catastrophe and the beta binomial model for the proportion of these corresponding to customers of the insurance company. To be able to estimate the parameters of the model, international and Swedish data were collected and compiled, listing accidents claiming at least twenty and four lives, respectively. Fitting the new model to data, we find the fit to be good. Finally we give the price of a Cat XL contract and perform a sensitivity analysis of how some of the parameters affect the expected value and standard deviation of the cost and thus the price.     

The Effect of Listing Price Strategy on Transaction Selling Prices

While true underlying home values are expected to be randomly distributed, actual residential listing prices tend to be highly clustered. Particularly, more than 75 % of the homes in our sample are associated with a round or “just below” round asking price. This study provides a theoretical and empirical examination of how the thousands digit in a home’s asking price is related to the final transaction price relative to its true underlying value. Our findings suggest that, on average, homes listed using a “just below” pricing strategy are associated with the greatest discount negotiated relative to the asking price. However, the higher initial degree of list overpricing reflected in “just below” pricing compared with other strategies more than offsets the greater discount. Therefore, “just below” is the most effective pricing strategy for the seller in terms of a greater dollar yield relative to value. These empirical findings have economic significance and are robust across both “buyer” and “seller” housing markets, new versus existing homes, and across multiple home price ranges.     

Fast accurate binomial pricing

We discuss here an alternative interpretation of the familiar binomial lattice approach to option pricing, illustrating it with reference to pricing of barrier options, one- and two-sided, with fixed, moving or partial barriers, and also the pricing of American put options. It has often been observed that if one tries to price a barrier option using a binomial lattice, then one can find slow convergence to the true price unless care is taken over the placing of the grid points in the lattice; see, for example, the work of Boyle & Lau [2]. The placing of grid points is critical whether one uses a dynamic programming approach, or a Monte Carlo approach, and this can make it difficult to compute hedge ratios, for example. The problems arise from translating a crossing of the barrier for the continuous diffusion process into an event for the binomial approximation. In this article, we show that it is not necessary to make clever choices of the grid positioning, and by interpreting the nature of the binomial approximation appropriately, we are able to derive very quick and accurate pricings of barrier options. The interpretation we give here is applicable much more widely, and helps to smooth out the ‘odd-even’ ripples in the option price as a function of time-to-go which are a common feature of binomial lattice pricing.     

Investment guarantees in unit-linked life insurance from the customer perspective

Interest rate guarantees are a typical contract feature in unit-linked-life insurance products. As the financial crisis of 2007/2008 has shown, these guarantees can be of substantial value for policyholders since they ensure that at least a minimum amount will be paid back even if the mutual fund value falls below a specific guaranteed level. However, from the insurance company’s view, these guarantees can be costly—especially in highly volatile markets—due to the required risk management measures which must be undertaken to secure the guarantees promised to the customers. Thus, the aim of this paper is to investigate whether customers really value these guarantees and if their willingness to pay (WTP) is sufficient to cover the guarantee costs. To elicit customer WTP, we use an online questionnaire and compare these results to the actual guarantee costs calculated with the Black and Scholes option pricing formula. One main finding is that even though most of the participants in the online questionnaire work in the financial industry, subjective prices are difficult to derive and are lower, on average, than the prices obtained using a financial pricing model. However, many participants are still willing to pay a substantially higher price.     

The pricing of Bermudan-style options on correlated assets

In this paper, we present a methodology for approximating a correlated multivariate-lognormal process with a recombining or “simple” multivariate-binomial process. The method represents an extension and implementation of previous work by Nelson and Ramaswamy (1990) and Ho, Stapleton and Subrahmanyam (1995) on diffusion approximation. The general method is illustrated by pricing a Bermudan-style put option on the minimum of three asset prices, and by pricing Bermudan-style options on bonds, where the value of the bond at a point in time depends upon the interest rate in two currencies and the foreign exchange rate. This type of structure, known as the “Power Reverse Dual” is a popular product in the case of Japanese Yen-US Dollar currencies. This revised version was published online in June 2006 with corrections to the Cover Date.     

Analysis of efficient markets

A simple trading model is presented in which Bayes’ rule is used to aggregate traders’ forecasts about risky assets’ future returns. In this financial market, Bayes’ rule operates like an omnipotent market-maker performing functions that in 1776 Adam Smith attributed to an “invisible hand.” We have analyzed two distinct cases: in the first scenario, the traders’ forecast errors are uncorrelated, and in the second scenario, the traders’ forecast errors are correlated. The contribution of our paper is fourfold: first, we prove that the “efficient market” mean-return can be expressed as a complex linear combination of the traders’ forecasts. The weights depend on the forecast variances, as well as on the correlations among the traders’ forecasts. Second we show that the “efficient” variance is equal to the inverse of the sum of the traders’ precision errors, and is also related to the correlations among the traders’ forecast errors. Third, we prove that the efficient market return is the best linear minimum variance estimator (BLMVE) of the security’s mean return (in the sense that it minimizes the sum of the traders’ mean squared forecast errors). Thus, an efficient market aggregates traders’ heterogeneous information in an optimal way. Fourth, we prove that an efficient market produces a mean return (price) as a Blackwell sufficient (most informative) experiment among all possible aggregated expected return (price) forecasts.     

C-CAPM Refinements and the Cross-Section of Returns

This paper studies if the consumption-based asset pricing model can explain the cross-section of expected returns. The CRRA model and several refinements (habit persistence and idiosyncratic shocks) all imply that the conditional expected return is linearly increasing in the asset’s conditional covariance with consumption growth. Results from quarterly data on the 25 Fama-French portfolios suggest that the model has serious problems: there are large and systematic pricing errors. In addition, the estimated time-varying effective risk aversion coefficients appear implausible and are unrelated with most candidates for habit persistence and idiosyncratic risk.     

Short note on inf-convolution preserving the Fatou property

We model agents’ preferences by cash-invariant concave functionals defined on L ^∞, and formulate the optimal risk allocation problem as their infimal-convolution. We study the case of agents whose choice functionals are law-invariant with respect to different probability measures and show how, in this case, the value function preserves a desirable dual representation (equivalent to the Fatou property). Financial support from the European Science Foundation (ESF) “Advanced Mathematical Methods for Finance” (AMaMeF) under the exchange grant 1192 is gratefully acknowledged.     

Information reduction via level crossings in a credit risk model

This paper provides an alternative credit risk model based on information reduction where the market only observes the firm’s asset value when it crosses certain levels, interpreted as changes significant enough for the firm’s management to make a public announcement. For a class of diffusion processes we are able to provide explicit expressions for the firm’s default intensity process and its zero-coupon bond prices.      

The two-fund separation theorem revisited

This paper resolves two issues regarding the traditional capital asset pricing model with one risk-free asset which seem to have been overlooked in the literature. First, it provides an elementary and complete proof of the two-fund separation theorem which accounts for the fact that asset demand may become undefined if the limiting slopes of the investor’s indifference curves are finite. Second, it shows that an additional limiting condition on investors’ risk aversions is generally necessary to guarantee existence of an equilibrium. Moreover, a generalized existence result is formulated which includes investors who in equilibrium may not invest in risky assets and a simple condition ensuring positive equilibrium asset prices is given.     

The cross-section of equity returns and assets’ fundamental cash-flow risk

The decomposition of consumption beta into a component driven by assets’ cash-flow news and one related to assets’ discount-rate news reveals that macroeconomic risks embodied in cash flows largely account for the cross-sectional dynamics of average stock returns. Empirically, we find that differences in expected excess returns between low book-to-market and high book-to-market portfolios are associated with differences in their cash-flow betas, and thus reflect macroeconomic, especially consumption-related risks. This result holds true for a broad set of consumption-based asset pricing models. In addition, the results indicate that the risk premium on equity markets is primarily driven by the exposure of assets’ cash-flow components to the cyclical variability of durable consumption goods.     

The Economics of Stock Exchange Listing Fees and Listing Requirements

This paper investigates the once and future role of listing fees. We consider the theory of listing fees and why such a pricing structure initially evolved. We show how capital market developments have changed the desirability, and even viability, of this pricing structure. We then analyze the economics of listing fees. While providing revenue to the exchange, listing fees impose large (opportunity) costs, and we analyze this trade-off, presenting evidence from the New York Stock Exchange. We also discuss what types of listing requirements make economics sense for exchanges (or perhaps regulators) to impose on companies. Finally we consider whether listing fees will continue to survive. Journal of Economic Literature Classification Numbers: G10, G18, K22, K23.     

水资源定价理论研究

本文对水资源定价理论研究的国内外进程和现状进行了分析,归纳出了未来水资源理论研究沿着定价理论、定价模型、水权交易和水价格弹性等四条主要路径进行,并探讨了国内外研究中存在的主要问题。     

Market Sentiments,Winner’s Curse and Bidding Outcome in Land Auctions

This paper empirically tests auction theory by examining how the stock market evaluates the outcome of open-bid English auctions of rights to develop residential real estate projects in Hong Kong. To do so, we deconstruct the complexity surrounding actual auction events, and empirically isolate the influence of conflicting auction theory predictions using data from expert opinion around auction events, actual auction event and outcome data, and stock market data. The empirical findings include (1) with increasing uncertainty bidders reduce bids, thus confirming predictions following the winner’s curse thesis; (2) joint bidding does not lead to increased bids based on pooled (“better”) information, but instead leads to reduced competition; while increased competition leads to increased prices at auction, as expected; (3) the market interprets auction outcomes as information events which function to signal developers’ expectations about future market prospects; but if the winning bid is considered too high, this interpretation is revised to that of the winner’s curse; (4) with joint bidding and winning, the market’s response to joint winners is better explained by concern for winner’s curse (despite supposed better informed bids) than the acquisition of a below cost development project following reduced competition at auction; and (5) the market interprets increased competition at auction as indicator of the future direction of property price movements in the secondary market—the more intense the competition, the more positive the future prospect of the property market are seen to be.