Pricing Annuity Guarantees Under a Regime-Switching Model

Abstract

We consider the pricing problem of equity-linked annuities and variable annuities under a regimeswitching model when the dynamic of the market value of a reference asset is driven by a generalized geometric Brownian motion model with regime switching. In particular, we assume that regime switching over time according to a continuous-time Markov chain with a finite number state space representing economy states. We use the Esscher transform to determine an equivalent martingale measure for fair valuation in the incomplete market setting. The paper is complemented with some numerical examples to highlight the implications of our model on pricing these guarantees.     

Diagnosing Asset Pricing Models Using the Distribution of Asset Returns

This paper develops a set of diagnostic tests which can shed light on why a particular model is failing and indicate what steps might be taken to make the model consistent with asset returns. Theoretical bounds on the moments of a stochastic discount factor are derived as a function of the moments of observed asset returns. Particular attention is paid to restrictions on moments other than the variance. These bounds can also be used to measure the information about the distribution of the discount factor contained in the moments of various asset returns. As an application of this methodology, bounds on the discount factor are estimated using size-based portfolios, and the results are used to analyze the small firm effect. Empirical results indicate, for the period 1926–1975, that moments of the returns of small firms contain information about the discount factor that is not contained in the moments of the returns of large firms and/or a proxy of the aggregate wealth portfolio. However, this difference disappears when more recent data is included.     

Trading Volume: Implications of an Intertemporal Capital Asset Pricing Model

We derive an intertemporal asset pricing model and explore its implications for trading volume and asset returns. We show that investors trade in only two portfolios: the market portfolio, and a hedging portfolio that is used to hedge the risk of changing market conditions. We empirically identify the hedging portfolio using weekly volume and returns data for U.S. stocks, and then test two of its properties implied by the theory: Its return should be an additional risk factor in explaining the cross section of asset returns, and should also be the best predictor of future market returns.     

Using Expectations to Test Asset Pricing Models

Asset pricing models generate predictions relating assets' expected rates of return and their risk attributes. Most tests of these models have employed realized rates of return as a proxy for expected return. We use analysts' expected rates of return to examine the relation between these expectations and firm attributes. By assuming that analysts' expectations are unbiased estimates of market-wide expected rates of return, we can circumvent the use of realized rates of return and provide evidence on the predictions emanating from traditional asset pricing models. We find a positive, robust relation between expected return and market beta and a negative relation between expected return and firm size, consistent with the notion that these are risk factors. We do not find that high book-to-market firms are expected to earn higher returns than low book-to-market firms, inconsistent with the notion that book-to-market is a risk factor.     

Decimal Pricing and Information-Based Trading: Tick Size and Informational Efficiency of Asset Price

Abstract:  In this study we analyze the effect of tick size on information-based trading. Although prior studies provide extensive evidence on the effect of tick size on market quality measures such as spreads, depths, and return volatility, there is little evidence as to the effect of tick size on the informational efficiency of asset price. Our results indicate that the probability of information-based trading during the post-decimal period is significantly greater than the corresponding figure during the pre-decimal period. We also show that the increase in information-based trading after decimalization cannot be attributed to concurrent changes in stock attributes. We interpret our findings as evidence that the smaller tick size under penny pricing encourages information-based trading and thereby raises the informational efficiency of asset price.     

The US Housing Market: Asset Pricing Forecasts Using Time Varying Coefficients

The US housing market has experienced significant cyclical volatility over the last twenty-five years due to major structural changes and economic fluctuations. In addition, the housing market is generally considered to be weak form inefficient. Houses are relatively illiquid, exceptionally heterogeneous, and are associated with large transactions costs. As such, past research has shown that it is possible to predict, at least partially, the time path of housing prices. The ability to predict housing prices is important such that investors can make better asset allocation decisions, including the pricing and underwriting of mortgages. Most of the prior studies examining the US housing market have employed constant coefficient approaches to forecast house price movements. However, this approach is not optimal as an examination of data reveals substantial sub-sample parameter instability. To account for the parameter instability, we employ alternative estimation methodologies where the estimated parameters are allowed to vary over time. The results provide strong empirical evidence in favor of utilizing the rolling Generalized Autoregressive Conditional Heteroskedastic (GARCH) Model and the Kalman Filter with an Autoregressive Presentation (KAR) for the parameters time variation. Lastly, we provide out-of-sample forecasts and demonstrate the precision of our approach.     

Coordination of Expectations in Asset Pricing Experiments

We investigate expectation formation in a controlled experimentalenvironment. Subjects are asked to predict the price in a standardasset pricing model. They do not have knowledge of the underlyingmarket equilibrium equations, but they know all past realizedprices and their own predictions. Aggregate demand for the riskyasset depends upon the forecasts of the participants. The realizedprice is then obtained from market equilibrium with feedbackfrom six individual expectations. Realized prices differ significantlyfrom fundamental values and typically exhibit oscillations around,or slow convergence to, this fundamental. In all groups participantscoordinate on a common prediction strategy.     

Networks in Production: Asset Pricing Implications

In this paper, I examine asset pricing in a multisector model with sectors connected through an input‐output network. Changes in the network are sources of systematic risk reflected in equilibrium asset prices. Two characteristics of the network matter for asset prices: network concentration and network sparsity. These two production‐based asset pricing factors are determined by the structure of the network and are computed from input‐output data. Consistent with the model predictions, I find return spreads of 4.6% and ?3.2% per year on sparsity and concentration beta‐sorted portfolios, respectively.     

An Empirical Investigation of CDS Spreads Using a Regime-Switching Default Risk Model

Default risk in equity returns can be measured by structural models of default. In this article we propose a credit warning signal (CWS) based on the Merton Default Risk (MDR) model and a Regime-Switching Default Risk (RSDR) model. The RSDR model is a generalization of the MDR model, comprises regime-switching asset distribution dynamics, and thus produces more realistic default probability estimates in cases of deteriorating credit quality. Alternatively, it reduces to the MDR model. Using a dataset of U.S. credit default swap (CDS) contracts around the 2007-8 crisis we construct rating-based indices to investigate the MDR and RSDR implied probabilities of default in relation to the market-observed CDS spreads. The proposed CWS measure indicates an increase in implied default probabilities several months ahead of notable increases in CDS spreads.     

An Investigation of Commodity Futures Prices Using the Consumption-Based Intertemporal Capital Asset Pricing Model

In this paper we extend the multigood futures pricing model of Grauer and Litzenberger 9 to a dynamic discrete time setting. We then test the model using data on futures prices for corn, wheat, and soybeans. The parameter estimates we obtain are similar to those obtained by other researchers using stock return data. The model itself is rejected and we offer some suggestions as to which assumption may be violated. We also give an interpretation to the Hansen-Singleton nonlinear instrumental variables estimation technique used in our empirical work.     

On a Simple Econometric Approach for Utility-Based Asset Pricing Model

The Journal of Finance has published an important paper entitled A Simple Econometric Approach for Utility-Based Asset Pricing Model by Brown and Gibbon (1985). The main purpose of this paper is to extend the research of Brown and Gibbons (1985) and Karson, Cheng and Lee (1995) in estimating the relative risk aversion (RRA) parameter in utility-based asset pricing model. First, we review the distributions of RRA parameter estimate . Then, a new method to the distribution of is derived, and a Bayesian approach for the inference of is proposed. Finally, empirical results are presented by using market rate of return and riskless rate data during the period December 1925 through December 2001.     

Generalised Sharpe Ratios and Asset Pricing in Incomplete Markets

The paper presents an incomplete market pricingmethodology generating asset pricebounds conditional on the absence of attractiveinvestment opportunities in equilibrium.The paper extends and generalises the seminal article ofCochrane and Saá-Requejowho pioneered option pricing based on the absenceof arbitrage and high Sharpe Ratios. Ourcontribution is threefold:We base the equilibrium restrictions on an arbitrary utility function, obtaining theCochrane and Saá-Requejo analysis as a special case with truncated quadratic utility. We extend the definition of Sharpe Ratio from quadratic utility to the entire family of CRRA utility functions and restate the equilibrium restrictions in terms ofGeneralised Sharpe Ratios which, unlike the standard Sharpe Ratio, provide aconsistent ranking of investment opportunities even when asset returns are highlynon-normal. Last but not least, we demonstrate that for Itô processes theCochrane and Saá-Requejo price bounds are invariant to the choice of the utilityfunction, and that in the limit they tend to a unique price determined by theminimal martingale measure.     

Dynamic Spanning in the Consumption-Based Capital Asset Pricing Model

Under the assumptions of the Consumption-based Capital Asset Pricing Model (CCAPM), Pareto optimal consumption allocations are characterized by each agent's consumption process being adapted to the filtration generated by the aggregate consumption process of the economy. The wealth processes of the agents, however, are adapted to the finer filtration generated by aggregate consumption and the conditional distribution of future aggregate consumption. Therefore, in order to achieve Pareto optimal consumption allocations, a sufficiently varied set of assets must exist such that any wealth process adapted to this finer filtration can be implemented by dynamically trading in that set of assets. We provide sufficient conditions for the existence of such a set of assets based on dynamically trading contingent claims on aggregate consumption. In addition, we give sufficient conditions for the existence of equilibria in a dynamically effectively complete market in which agents are only able to trade in contingent claims on aggregate consumption, the market portfolio of firms, and a (numeraire) zero-coupon bond. We demonstrate the role of short- and long-term contingent claims on aggregate consumption for the implementation of Pareto optimal allocations in the presence of short- andlong-term risks. In addition, in the presence of personal risks, we demonstrate the role of insurance contracts.     

Trading and Pricing in Upstairs and Downstairs Stock Markets

We provide empirical evidence on the economic benefits of negotiatingtrades in the upstairs trading room of brokerage firms relativeto the downstairs market. Using Helsinki Stock Exchange data,we find that upstairs trades tend to have lower informationcontent and lower price impacts than downstairs trades. Thisis consistent with the hypotheses that the upstairs market isbetter at pricing uninformed liquidity trades and that upstairsbrokers can give better prices to their customers if they knowthe unexpressed demands of other customers. We find that theseeconomic benefits depend on price discovery occurring in thedownstairs market.     

Some Tests of the Risk-Return Relationship Using Alternative Asset Pricing Models and Observed Expected Returns

This study examines the performance of three asset pricing models: the CAPM, the APT and the UAPT using observed expected returns from a three-phase dividend discount model with Value Line analyst estimates of future company-level earnings, dividends and growth rates. Our study is the first we know of to test the three major asset pricing models using observed expected returns. Our results are similar to prior research using ex post (realized) returns in that we find that the UAPT using macroeconomic factors is the best performing model, followed by the APT and the CAPM. However, our results also suggest that the importance of macroeconomic factors is much greater to expected returns than to realized returns, and the corresponding R2 values for models using expected returns are much higher than for models using realized returns. Combining our results for the UAPT with those of Marston and Harris (1993) for the CAPM suggests that these models are more successful in tests using observed expected returns than in tests using realized returns as proxies for expected returns. Unit root tests suggest that monthly observed expected returns follow the classic random walk without drift model while monthly realized returns do not.     

Dynamic Spanning in the Consumption-Based Capital Asset Pricing Model

Under the assumptions of the Consumption-based Capital AssetPricing Model (CCAPM), Pareto optimal consumption allocationsare characterized by each agent's consumption process beingadapted to the filtration generated by the aggregate consumptionprocess of the economy. The wealth processes of the agents,however, are adapted to the finer filtration generated by aggregateconsumption and the conditional distribution of future aggregateconsumption. Therefore, in order to achieve pareto optimal consumptionallocations, a sufficiently varied set of assets must existsuch that any wealth process adapted to this finer filtrationcan be implemented by dynamically trading in that set of assets.We provide sufficient conditions for the existence of such aset of assets based on dynamically trading contingent claimson aggregate consumption. In addition, we give sufficient conditionsfor the existence of equilibria in a dynamically effectivelycomplete market in which agents are only able to trade in contingentclaims on aggregate consumption, the market portfolio of firms,and a (numeraire) zero-coupon bond. We demonstrate the roleof short- and long-term contingent claims on aggregate consumptionfor the implementation of Pareto optimal allocations inthe presenceof short- and long-term risks. In addition, in the presenceof personal risks, we demonstrate the role of insurance contracts.JEL Classification: G13.     

Examination of Conditional Asset Pricing in UK Stock Returns

I examine the empirical performance of various specifications of the capital asset pricing model (CAPM) in UK stock returns, using the stochastic discount framework. When the proxy for the market portfolio includes a proxy for labor income growth in addition to the stock market index, the performance of the CAPM improves. The improvement in performance shows in the magnitude and significance of the pricing errors and in the reduced impact of asset characteristics and other factors in the pricing of assets. There is further improvement when I use conditional versions of the models.     

Estimation and Test of a Simple Model of Intertemporal Capital Asset Pricing

A simple valuation model with time‐varying investment opportunities is developed and estimated. The model assumes that the investment opportunity set is completely described by the real interest rate and the maximum Sharpe ratio, which follow correlated Ornstein–Uhlenbeck processes. The model parameters and time series of the state variables are estimated using U.S. Treasury bond yields and expected inflation from January 1952 to December 2000, and as predicted, the estimated maximum Sharpe ratio is related to the equity premium. In cross‐sectional asset‐pricing tests, both state variables have significant risk premia, which is consistent with Merton's ICAPM.     

Tests of the Relations Among Marketwide Factors,Firm-Specific Variables,and Stock Returns Using a Conditional Asset Pricing Model

In this article we generalize Harvey's (1989) empirical specification of conditional asset pricing models to allow for both time-varying covariances between stock returns and marketwide factors and time-varying reward-to-covariabilities. The model is then applied to examine the effects of firm size and book-to-market equity ratios. We find that the traditional asset pricing model with commonly used factors can only explain a small portion of the stock returns predicted by firm size and book-to-market equity ratios. The results indicate that allowing time-varying covariances and time-varying reward-to-covariabilities does little to salvage the traditional asset pricing models.     

Capital Share Risk in U.S. Asset Pricing

A single macroeconomic factor based on growth in the capital share of aggregate income exhibits significant explanatory power for expected returns across a range of equity characteristic portfolios and nonequity asset classes, with risk price estimates that are of the same sign and similar in magnitude. Positive exposure to capital share risk earns a positive risk premium, commensurate with recent asset pricing models in which redistributive shocks shift the share of income between the wealthy, who finance consumption primarily out of asset ownership, and workers, who finance consumption primarily out of wages and salaries.