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Abstract:
We present evidence that the equity premium and the premium of value stocks over growth stocks are consistent in the 1982-96 period with a stochastic discount factor calculated as the weighted average of individual households' marginal rate of substitution with low and economically plausible values of the relative risk aversion coefficient. Since these premia are not explained with an SDF calculated as the per capita marginal rate of substitution with low value of the RRA coefficient, the evidence supports the hypothesis of incomplete consumption insurance. We also present evidence is that an SDF calculated as the per capita marginal rate of substitution is better able to explain the equity premium and does so with a lower value of the RRA coefficient, as the definition of asset holders is tightened to recognize the limited participation of households in the capital market.

Abstract:
We present evidence that the equity premium and the premium of value stocks over growth stocks are explained in the 1982 1996 period with a stochastic discount factor (SDF) calculated as the weighted average of individual households' marginal rate of substitution with low and economically plausible values of the relative risk aversion (RRA) coefficient. Household consumption of non-durables and services is reconstructed from the CEX database. Since the above premia are not explained with a SDF calculated as the per capita marginal rate of substitution with low value of the RRA coefficient, the evidence supports the hypothesis of incomplete consumption insurance. We also present evidence is that a SDF calculated as the per capita marginal rate of substitution is better able to explain the equity premium and does so with a lower value of the RRA coefficient, as the definition of asset holders is tightened to recognize the limited participation of households in the capital market.

Abstract:
The Euler equations of consumption are tested on the household consumption of non-durables and services, reconstructed from the CEX database. The estimated relative risk aversion coefficient of the representative household decreases, and the estimated unexplained mean equity premium decreases, as infra marginal asset holders are eliminated from the sample. These results provide evidence of limited capital market participation. The estimated unexplained mean equity premium decreases when the assumption of complete consumption insurance is relaxed. The estimated correlation between the equity premium and the cross-sectional variance of the households' consumption growth is negative, as required, if the relaxation of market completeness is to contribute towards the explanation of the premium. The overall evidence from asset prices in favor of relaxing the assumption of complete consumption insurance is weak. An extensive Monte Carlo investigation highlights the relationship between the economic implications of limited participation and the resulting statistical properties of commonly used test statistics. The simulation results provide direct evidence relating observation error in consumption.

Abstract:
Ongoing questions on the historical mean and standard deviation of the return on equities and bonds and on the equilibrium demand for these securities are addressed in the context of a stationary, overlapping-generations economy in which consumers are subject to a borrowing constraint. The key feature captured by the OLG economy is that the bulk of the future income of the young agents is derived from their wages forthcoming in their middle age, while the bulk of the future income of the middle-aged agents is derived from their savings in equity and bonds. The young would like to borrow and invest in equity, but the borrowing constraint prevents them from doing so. The middle-aged choose to hold a diversified portfolio that includes positive holdings of bonds, and this explains the demand for bonds. Without the borrowing constraint, the young borrow and invest in equity, thereby decreasing the mean equity premium and increasing the rate of interest.

Abstract:
Ongoing questions on the historical mean and standard deviation of the return on equities and bonds and on the equilibrium demand for these securities are addressed in the context of a stationary, overlapping-generations economy in which consumers are subject to a borrowing constraint. The key feature captured by the OLG economy is that the bulk of the future income of the young agents is derived from their wages forthcoming in their middle age, while the bulk of the future income of the middle-aged agents is derived from their savings in equity and bonds. The young would like to borrow and invest in equity but the borrowing constraint prevents them from doing so. The middle-aged choose to hold a diversified portfolio that includes positive holdings of bonds and this explains the demand for bonds. Without the borrowing constraint the young borrow and invest in equity, thereby decreasing the mean equity premium and increasing the rate of interest.

Abstract:
We document widespread violations of stochastic dominance by one-month S&P 500 index call options market over 1986-2006. These violations imply that a trader can improve her expected utility by engaging in a zero-net-cost trade. We allow the market to be incomplete and also imperfect by introducing transaction costs and bid-ask spreads. Even though pre-crash option prices conform to the Black-Scholes-Merton model reasonably well, they are incorrectly priced if the distribution of the index return is estimated from time-series data even with a variety of statistical adjustments. Even though there are fewer violations by OTM calls than by ITM calls, there are still substantial violations by OTM calls, contradicting the inference drawn from the observed implied volatility smile that the problem primarily lies with the left-hand tail of the index return distribution. Most of the violations by post-crash options are not due to the smile being too steep: options are underpriced over 1988-1995 and overpriced over 1997-2006. The decrease in violations over the post-crash period 1988-1995 is followed by a substantial increase in violations over 1997-2006. These results do not support the hypothesis that the options market is becoming more rational over time.

Derivative pricing; volatility smile, incomplete markets, transaction costs; index options; stochastic dominance bounds

Abstract:
The observed discrepancies of derivative prices from their theoretical, arbitrage-free values are examined in the presence of proportional transaction costs. Analytic upper and lower bounds on the reservation write and purchase prices, respectively, are obtained when an investor's preferences exhibit constant relative risk aversion between zero and one. The economy consists of multiple primary securities with the stationary returns, a constant rate of interest, and any number of American or European derivatives with path-dependent arbitrary payoffs. The price processes of the primary securities are modelled either as jump/diffusions in a continuous-time framework, or as arbitrary processes in a discrete-time framework.

derivative pricing, transaction costs, multi-securities, american claims, exotic options, utility maximization, volatility smile.

Abstract:
The Bansal and Yaron (2004) model of long-run risks (LRR) in aggregate consumption and dividend growth and its cointegrated extension are tested on a cross-section of assets and rejected over 1930-2006. Reversal of earlier conclusions is due to the increased power of the tests resulting from two observations under the null: the latent state variables and, therefore, the pricing kernel are known affine functions of observables; and, the unconditional moments of the time series processes impose constraints in addition to the pricing constraints. The models perform better in postwar subperiods, consistent with evidence of structural-breaks.

Long Run Risks, Equity Premium, Cross-Section of Asset Returns, Cointegration, Latent State Variables

Abstract:
By applying stochastic dominance arguments, upper bounds on the reservation write price of European calls and puts and lower bounds on the reservation purchase price of these derivatives are derived in the presence of proportional transaction costs incurred in trading the underlying security. The primary contribution is the derivation of bounds when intermediate trading in the underlying security is allowed over the life of the option. A tight upper bound is derived on the reservation write price of a call and a tight lower bound is derived on the reservation purchase price of a put. These results jointly impose tight upper and lower bounds on the implied volatility.

Abstract:
By applying stochastic dominance arguments, upper bounds on the reservation write price of calls and puts and lower bounds on the reservation purchase price of these derivatives are derived in the presence of proportional transaction costs incurred in trading the underlying security. The primary contribution of this paper is the derivation of bounds in the case that intermediate trading in the underlying security is allowed over the life of the option. Numerical examples illustrate that a tight bound is imposed on the reservation write price of a call option.

Abstract:
American call and put options on the S&P 500 index futures that violate the stochastic dominance bounds of Constantinides and Perrakis (2007) over 1983-2006 are identified as potentially profitable investment opportunities. Call bid prices more frequently violate their upper bound than put bid prices do, while evidence of underpriced calls and puts over this period is scant. In out-of-sample tests, the inclusion of short positions in such overpriced calls, puts, and, particularly, straddles in the market portfolio is shown to increase the expected utility of any risk averse investor and also increase the Sharpe ratio, net of transaction costs and bid-ask spreads. The results are strongly supportive of mispricing.

option mispricing, futures options, derivatives pricing, stochastic dominance, transaction costs, market efficiency

Abstract:
The central premise of the Black and Scholes [Black, F., Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy 81, 637-659] and Merton [Merton, R. (1973). Theory of rational option pricing. Bell Journal of Economics and Management Science 4, 141-184] option pricing theory is that there exists a self-financing dynamic trading policy of the stock and risk free accounts that renders the market dynamically complete. This requires that the market be complete and perfect. In this essay, we are concerned with cases in which dynamic trading breaks down either because the market is incomplete or because it is imperfect due to the presence of trading costs, or both. Market incompleteness renders the risk-neutral probability measure non unique and allows us to determine the option price only within a range. Recognition of trading costs requires a refinement in the definition and usage of the concept of a risk-neutral probability measure. Under these market conditions, a replicating dynamic trading policy does not exist. Nevertheless, we are able to impose restrictions on the pricing kernel and derive testable restrictions on the prices of options.We illustrate the theory in a series of market setups, beginning with the single period model, the two-period model and, finally, the general multiperiod model, with or without transaction costs.We also review related empirical results that document widespread violations of these restrictions.

Abstract:
We document that the leverage-adjusted returns on S&P 500 index calls and puts are decreasing in their strike-to-price ratio over 1986-2007, contrary to the prediction of the Black-Scholes-Merton model; and the leverage-unadjusted returns on S&P 500 index calls are decreasing in their strike-to-price ratio, contrary to the prediction and empirical results of Coval and Shumway (2001). Several factor models are tested and fail to explain the cross-section of option returns. Two option-specific factors, the change in monthly OTM put volume and the change in the VIX index, have some explanatory power when the factor premia are estimated from the universe of options but large alphas remain when the premia are estimated from equities. The three Fama-French factors leave large alphas even when the premia are estimated from options.

index options, option mispricing, derivatives, risk premia, market efficiency

Abstract:
American call and put options on the S&P 500 index futures that violate the stochastic dominance bounds of Constantinides and Perrakis (2007) over 1983-2006 are identified as potentially profitable investment opportunities. Call bid prices more frequently violate their upper bound than put bid prices do, while evidence of under priced calls and puts over this period is scant. In out-of-sample tests, the inclusion of short positions in such overpriced calls, puts, and, particularly, straddles in the market portfolio is shown to increase the expected utility of any risk averse investor and also increase the Sharpe ratio, net of transaction costs and bid-ask spreads.

option mispricing, futures options, derivatives pricing, stochastic dominance, transaction costs, market efficiency

Abstract:
The mean, covariability, and predictability of the return of different classes of financial assets challenge the rational economic model for an explanation. The unconditional mean aggregate equity premium is almost seven percent per year and remains high after adjusting downwards the sample mean premium by introducing prior beliefs about the stationarity of the price-dividend ratio and the (non)forecastability of the long-term dividend growth and price-dividend ratio. Recognition that idiosyncratic income shocks are uninsurable and concentrated in recessions contributes toward an explanation. Also borrowing constraints over the investors' life cycle that shift the stock market risk to the saving middle-aged consumers contribute toward an explanation.

Abstract:
The mean, co-variability, and predictability of the return of different classes of financial assets challenge the rational economic model for an explanation. The unconditional mean aggregate equity premium is almost seven percent per year and remains high after adjusting downwards the sample mean premium by introducing prior beliefs about the stationarity of the price-dividend ratio and the (non) forecastability of the long-term dividend growth and price-dividend ratio. Recognition that idiosyncratic income shocks are uninsurable and concentrated in recessions contributes toward an explanation. Also borrowing constraints over the investors' life cycle that shift the stock market risk to the saving middle-aged consumers contribute toward an explanation.

Abstract:
Habit persistence in consumption preferences and durability of consumption goods are two hypotheses which imply time-nonseparability in the derived utility for consumption expenditures. We study a simple model with both effect, in which lagged consumption expenditures enter the Euler equation. Habit persistence implies that the coefficients on the lagged expenditures are negative, while durability implies positive coefficients. If both effects are present, then estimating the sign of the coefficients addresses the question as to which of the two effects is dominant. Earlier empirical work on monthly data supported the durability of consumption expenditures. We estimate and test the Euler equation using monthly, quarterly and annual data and find evidence that habit persistence dominates the effect of durability.

Abstract:
Proposals that portion of the Social Security Trust Fund assets be invested in equities entail the possibility that a severe decline in equity prices renders the Fund assets insufficient to provide the currently mandated level of benefits. In this event, existing taxpayers may be compelled to act as insurers of last resort. The cost to taxpayers of such an implicit commitment equals the value of a put option with payoff equal to the benefit's shortfall. We calibrate an OLG model that generates realistic equity premia and value the put. With 20 percent of the Fund assets invested in equities, the highest level currently under serious discussion, we value a put that guarantees the currently mandated level of benefits at one percent of GDP, or a temporary increase in Social Security taxation of at most 25 percent. We value a put that guarantees 90 percent of benefits at merely .03 percent of GDP. In contrast to earlier literature, our results account for the significant changes in the distribution of security returns resulting from Trust Fund purchases. We also explore the inter-generational welfare implications of the guarantee.

Abstract:
The tax law confers upon the investor a timing option--to realize capital losses and defer capital gains. With the tax rate on long term capital gains and losses being about half the short term rate, the tax law provides a second timing option--to realize capital losses short term and realize capital gains long term, if at all. Our theory and simulation with actual stock prices over the 1962-1977 period establish that the second timing option is extremely valuable: Taxable investors should realize their long term capital gains in high variance stocks and repurchase the same or similar stock, in order to reestablish the short-term status and realize potential future losses short term.Tax trading does not explain the positive abnormal returns of small firms. In the presence of transactions costs, tax trading predicts that the volumeof tax-loss selling increases from January to December and ceases inthe first few days of January. The trading volume seasonal maps into a stockprice seasonal only if tax-loss sellers are assumed irrational or ignorant of the price seasonality.

Abstract:
Several empirical regularities in the prices of financial assets are at odds with the predictions of standard economic theory. I address these regularities and explore the extent to which they are resolved in the context of two markets organized in very different ways. The first setting is a neoclassical economy with incomplete markets and heterogeneous agents. Market incompleteness naturally arises because of the non-existence of markets in which consumers or households can co-insure idiosyncratic income shocks for obvious moral hazard reasons. The second setting is an overlapping generations economy with three generations in which the young generation is constrained from borrowing and investing in equities. The borrowing constraints naturally arise because human capital alone does not collateralize major loans in modern economies for reasons of moral hazard and adverse selection.

Abstract:
We explore the consequences for asset pricing of admitting a bequest motive into an otherwise standard overlapping generations model where agents trade equity and perpetual debt securities. Prices of securities are seen to be approximately 50% higher in an economy with bequests as compared to an otherwise identical one where bequests are absent. Robust estimates of the equity premium are obtained in several cases where the desire to leave bequests is modest relative to the desire for old age consumption.

Abstract:
The assumption that bondholders follow either a buy-and-hold or a continuous realization trading policy, rather than the optimal trading policy,is at variance with reality and, as we demonstrate, may seriously bias the estimation of the yield curve and the implied tax bracket of the marginal investor. Tax considerations which govern a bondholder`s optimal trading policy include the following: realization of capital losses, short term if possible; deferment of the realization of capital gains, especially if they are short term; changing the holding period status from long term to short term by sale of the bond and repurchase, so that future capital losses may be realized short term; and raising the basis through sale of the bond and repurchase in order to deduct from ordinary income the amortized premium. Because of the interaction of these factors, no simple characterization of the optimal trading policy is possible. We can say, however, that it differs substantially from the buy-and-hold policy irrespective of whether the bondholder is a bank, a bond dealer, or an individual. We obtain these strong results even when we allow for transactions costs and explicitly consider numerous IRS regulations designed to curtail tax avoidance.

Abstract:
The Bansal and Yaron (2004) model of long-run risks (LRR) in aggregate consumption and dividend growth and its cointegrated extension are tested on a cross-section of assets and rejected over 1930-2006. Reversal of earlier conclusions is due to the increased power of the tests resulting from two observations under the null: the latent state variables and, therefore, the pricing kernel are known affine functions of observables; and, the unconditional moments of the time series processes impose constraints in addition to the pricing constraints. The models perform better in postwar subperiods, consistent with evidence of structural-breaks.

Abstract:
Widespread violations of stochastic dominance by 1-month S&P 500 index call options over 1986-2006 imply that a trader can improve expected utility by engaging in a zero-net-cost trade net of transaction costs and bid-ask spread. Although precrash option prices conform to the Black-Scholes-Merton model reasonably well, they are incorrectly priced if the distribution of the index return is estimated from time-series data. Substantial violations by postcrash OTM calls contradict the notion that the problem lies primarily with the left-hand tail of the index return distribution and that the smile is too steep. The decrease in violations over the postcrash period of 1988-1995 is followed by a substantial increase over 1997-2006, which may be due to the lower quality of the data but, in any case, does not provide evidence that the options market is becoming more rational over time.

G10, G13

Abstract:
Widespread violations of stochastic dominance by one-month S&P 500 index call options over 1986-2006 imply that a trader can improve expected utility by engaging in a zero-net-cost trade net of transaction costs and bid-ask spread. Although pre-crash option prices conform to the Black-Scholes-Merton model reasonably well, they are incorrectly priced if the distribution of the index return is estimated from time-series data. Substantial violations by post-crash OTM calls contradict the notion that the problem primarily lies with the left-hand tail of the index return distribution and that the smile is too steep. The decrease in violations over the post-crash period 1988-1995 is followed by a substantial increase over 1997-2006 which may be due to the lower quality of the data but, in any case, does not provide evidence that the options market is becoming more rational over time.

Abstract:
We study consumption-based asset pricing models which allow for both habit persistence and durability of consumption goods, using quarterly consumption and asset return data for six countries. We estimate the parameters representing habit persistence or durability, risk aversion and time preference for each of the countries. We find that time-nonseparable preferences improve the fit of the model. When the nonseparability parameter is statistically significant, its magnitude indicates that the effect of habit persistence dominates the effect of durability in consumption expenditures. However, the international evidence for habit persistence is weaker than it is for the United States. The results indicate that the simple model of time nonseparability does not provide a satisfactory explanation of consumption and asset returns.

Abstract:
We present evidence that the equity premium and the premium of value stocks over growth stocks are explained in the 1982-1996 period with a stochastic discount factor (SDF) calculated as the weighted average of individual households' marginal rate of substitution with low and economically plausible values of the relative risk aversion (RRA) coefficient. Household consumption of non-durables and services is reconstructed from the CEX database. Since the above premia are not explained with a SDF calculated as the per capita marginal rate of substitution with low value of the RRA coefficient, the evidence supports the hypothesis of incomplete consumption insurance. We also present evidence is that a SDF calculated as the per capita marginal rate of substitution is better able to explain the equity premium and does so with a lower value of the RRA coefficient, as the definition of asset holders is tightened to recognize the limited participation of households in the capital market.

Equity premium, Incomplete consumption insurance, Heterogeneous consumers, Limited capital market participation

Abstract:
Analytic bounds on the reservation write price of European-style contingent claims are derived in the presence of proportional transaction costs in a model which allows for intermediate trading. The option prices are obtained via a utility maximization approach by comparing the maximized utilities with and without the contingent claim. The mathematical tools come mainly from the theories of singular stochastic control and viscosity solutions of nonlinear partial differential equations.

Abstract:
Empirical difficulties encountered by representative-consumer models are resolved in an economy with heterogeneity in the form of uninsurable, persistent, and heteroscedastic labor income shocks. Given the joint process of arbitrage-free asset prices, dividends, and aggregate income, satisfying a certain joint restriction, it is shown that this process is supported in the equilibrium of an economy with judiciously modeled income heterogeneity. The Euler equations of consumption in a representative-agent economy are replaced by a set of Euler equations that depend not only on the per capita consumption growth but also on the cross-sectional variance of the individual consumers' consumption growth.

Abstract:
Proportional transaction costs are considered as a possible explanation of the volatility smile of index options. A tight upper bound on the call option price is derived in the presence of proportional transaction costs by extending stochastic dominance arguments. A tight and novel lower bound on the call option price is derived by imposing a plausible upper bound on the investor's relative risk aversion coefficient. The bounds are sufficiently tight to reject the hypothesis that transaction costs can account for the volatility smile in an otherwise Black-Scholes market environment.