• Selected
• Entire List

Abstract:
This article develops and empirically implements a stock valuation model. The model makes three assumptions: (i) dividend equals a fixed fraction of net earnings-per-share plus noise; (ii) the economy's pricing kernel is consistent with the Vasicek term structure of interest rates; and (iii) the expected earnings growth rate follows a mean-reverting stochastic process. Our parameterization of the earnings process distinguishes long-run earnings growth from current growth and separately measures the characteristics of the firm's business cycle. The resulting stock valuation formula has three variables as input: net earnings-per-share, expected earnings growth and interest rate. Using a sample of individual stocks, our empirical exercise leads to the following conclusions: (1) the derived valuation formula produces significantly lower pricing errors than existing models both in-and out-of-sample; (2) modeling earnings growth dynamics properly is the most crucial for achieving better performance, while modeling the discounting dynamics properly also makes a significant difference; (3) our model's pricing errors are highly persistent over time and correlated across stocks, suggesting the existence of factors that are important in the market's valuation but missing from our model. In addition to pricing stocks, we can apply the model to back out market expectations about the firm's future from its stock price, allowing us to recover the relevant information embedded in the stock price.

Abstract:
From a credit risk perspective, little is known about the distress factors - economy-wide or firm-specific - that are important in explaining variations in defaultable coupon yields. This paper proposes and empirically tests a family of credit risk models. Empirically, we find that firm-specific distress factors play a role (beyond treasuries) in explaining defaultable coupon bond yields. Credit risk models that take into consideration leverage and book-to-market are found to reduce out-of-sample yield fitting errors (for the majority of firms). Moreover, the empirical evidence suggests that interest rate risk may be of first-order prominence for pricing and hedging. Measured by both out-of-sample pricing and hedging errors, the credit risk models perform relatively better for high grade bonds. Controlling for credit rating, the model performance is generally superior for longer maturity bonds compared to its shorter maturity counterparts. Using equity as an instrument reduces hedging errors. This paper provides an empirical investigation of credit risk models using observable economic factors.

Abstract:
This article presents a framework for studying the role of recovery on defaultable debt prices (for a wide class of processes describing recovery rates and default probability). These debt models have the ability to differentiate the impact of recovery rates and default probability, and can be utilized to invert the market expectation of recovery rates implicit in bond prices. Empirical implementation of these models suggests two central findings. First, the recovery concept that specifies recovery as a fraction of the discounted par value has broader empirical support. Second, parametric debt valuation models can provide a useful assessment of recovery rates embedded in bond prices. This article has attempted to model recovery and comprehend their impact on debt values.

Abstract:
The fundamental valuation equation of Cox, Ingersoll and Ross was expressed in terms of the indirect utility of wealth function. As closed-form solution for the indirect utility is generally
unobtainable when investment opportunities are stochastic, existing contingent claims models involving general stochastic processes were almost all derived under the restrictive log utility assumption. An alternative valuation equation is proposed here that depends only on the direct utility function. This alternative valuation approach is applied to derive closed-form
solutions for bonds, bond options, individual stocks, and stock options under both power utility and exponential utility functions. Allowable processes for aggregate output, firms' dividends, and state variables are quite general and empirically plausible. The resulting interest rate and stock price dynamics have many empirically plausible properties. Our bond and stock option pricing models with stochastic volatility and stochastic interest rates have most existing models nested. The stock option pricing model is also shown to have the ability to reconcile certain puzzling empirical regularities such as the volatility smile.

Abstract:
How do risk-neutral return skews evolve over time and in the cross-section of individual stocks? We document the differential pricing of individual equity options versus the market index, and relate it to variations in the skew. The change-of-measure induced by marginal-utility tilting of the physical density can introduce skews in the risk-neutral return density. We derive the skew laws that decompose individual return skewness into a systematic skewness component and an idiosyncratic skewness component. Our empirical analysis of OEX options and 30 of its individual components demonstrates that individual risk-neutral distributions differ from that of the market index by being far less negatively skewed, and substantially more volatile.

risk neutral skews, option pricing, individual stock options

Abstract:
This study formalizes the departure between risk-neutral and physical index return volatilities, termed volatility spreads. Theoretically, the departure between risk neutral and physical index volatility is connected to the higher-order physical return moments and the parameters of the pricing kernel process. This theory predicts positive volatility spreads when investors are risk averse, and when the physical index distribution is negatively skewed and leptokurtic. Our empirical evidence is supportive of the theoretical implications of risk aversion, exposure to tail events, and fatter left-tails of the physical index distribution in markets where volatility is traded.

risk-neutral volatility, physical volatility, pricing kernels, risk aversion, fat-tails

Abstract:
This article develops a family of stock valuation models that are based on book values and earnings. The modeling approach can be consistent with a large class of allowable dividend policies and does not require an explicit forecast of future book values. Reconciling empirical evidence, the model determined expected rate of return is related to book-to-market and earnings yield. Model implementation using S&P 500 stocks yields several empirical results. First, the performance yardsticks indicate that the models show promise in explaining market valuations. Second, both book and earnings considerations are crucial in stock valuation. Finally, zero-dividend and negative earnings stocks present no particular valuation hurdles with reasonable goodness-of-fit statistics.

Abstract:
This paper proposes a methodology for the valuation of contingent securities. In particular, it establishes how the characteristic function (of the future uncertainty) is basis augmenting and spans the payoff universe of most, if not all, derivative assets. In one specific application, from the characteristic function of the state-price density, it is possible to analytically price options on any arbitrary transformation of the underlying uncertainty. By differentiating (or translating) the characteristic function, limitless pricing and/or spanning opportunities can be designed. As made lucid via example contingent claims, by exploiting the unifying spanning concept, the valuation approach affords substantial analytical tractability. The strength and versatility of the methodology is inherent when valuing (1) Average-interest options; (2) Correlation options; and (3) Discretely-monitored knock-out options. For each option-like security, the characteristic function is strikingly simple (although the corresponding density is unmanageable/indeterminate). This article provides the economic foundations for valuing derivative securities.

Abstract:
This paper shows that a continuum of options and a continuum of characteristic functions are equivalent classes of spanning securities, for a wide class of payoff functions. In particular, it establishes how the characteristic function (of the future uncertainty) is basis augmenting and spans the payoff universe of most, if not all, derivative assets. In one specific application, from the characteristic function of the state-price density, it is possible to analytically price options on any arbitrary transformation of the underlying uncertainty. By differentiating (or translating) the characteristic function, limitless pricing and/or spanning opportunities can be designed. The strength and versatility of the methodology is inherent when valuing (1) average-interest options, (2) correlation options, and (3) discretely-monitored knock-out options. Possible extensions to our work include the pricing of American options from the characteristic function, and the recovery of the risk-neutral density from the continuum of out-of-money calls and puts. We provide the economic foundations for valuing derivative securities.

Abstract:
Distinct from the market-index, most individual firms' risk-neutral return distributions share three characteristics: they are far more volatile, substantially less negatively-skewed, and more leptokurtotic. But, what are the implications of these properties for models of individual equity options? We present and empirically investigate a double-jump option-pricing model that allows for stochastic volatility, return-jumps, volatility-jumps, and admits many existing models as special cases. Using a sample of 100 most active firms on the CBOE, we find that (i) the double-jump process is the least misspecified and the least demanding in fitting the tail-size and tail-asymmetry of the individual return distributions; (ii) the double-jump model improves pricing performance beyond return-jumps absent volatility-jumps, and beyond volatility-jumps absent return-jumps; and (iii) between return-jumps and volatility-jumps, the former is empirically more relevant than the latter for pricing options. The inverse link between volatility-jumps and return-jumps is instrumental for reconciling the valuation of deep out-of-money options. Compared to risk-neutral skewness, the excess kurtosis is, by far, a more crucial determinant of the cross-section of pricing-errors, especially for puts.

risk-neutral kurtosis, return-jumps, volatility-jumps, stochastic volatility, individual equity option-models, option-implied return distributions

Abstract:
This article investigates, both theoretically and empirically, the economics of stock market crashes. Using more than 100 years of daily data on the DJIA (and shorter series on NASDAQ, IBM, and Caterpillar), we first document empirically that (a) the probability of a daily stock market decline in excess of 5% is non-negligible (about 0.25%); (b) stock market crashes are not only relatively more likely to occur than rallies (higher crash arrival rates), but substantially more brutal; (c) the pre-1945 crash valuation measures depart radically from the post-1945 counterpart with the left tail decaying to zero much slower than the right tail; and (d) the motion of large percentage price declines and rises conforms closely with the characteristics of the Frechet distribution (asymptotically). To realistically model the empirical properties of crashes and extremes, we propose a family of Markov processes for which the density of the maximum percentage price drop can also be derived. The objective probability of the crash is found to be related, in an intuitive manner, to higher order moments of the return distribution. Examination of this model suggests that the implied probabilities are not at odds with the empirical counterparts. To assess the implications of our findings for real-life investment analysis, we generated buy/sell signals contingent on the crash probability. Investment trading rules relying on the model's prediction outperform traditional ones (e.g., buy and hold). Our implementation methods are sufficiently versatile to discover crash/rally information embedded in option markets. Exploiting more than 17,000 out-of-money option prices, the framework quantifies three dimensions of crash discovery (i) time-variations in Arrow-Debreu security price on the extreme, (ii) the structure of jump-fear levels, and (iii) the term structure of forward jump-risks. This paper provides a unified treatment for discovering crashes in stock and option markets.

Abstract:
We develop models of stochastic discount factors in international economies that produce stochastic risk premiums and stochastic skewness in currency options. We estimate the models using time-series returns and option prices on three currency pairs that form a triangular relation. Estimation shows that the average risk premium in Japan is larger than that in the US or the UK, the global risk premium is more persistent and volatile than the country-specific risk premiums, and investors respond differently to different shocks. We also identify high-frequency jumps in each economy, but find that only downside jumps are priced. Finally, our analysis shows that the risk premiums are economically compatible with movements in stock and bond market fundamentals.

Stochastic discount factors, international economy, stochastic risk premium

Abstract:
We investigate whether the volatility risk premium is negative by examining the statistical properties of delta-hedged option portfolios (buy the option and hedge with stock). Within a stochastic volatility framework, we demonstrate a correspondence between the sign and magnitude of the volatility risk premium, and the mean delta-hedged portfolio return. Using a sample of S&P 500 index options, we provide empirical tests that have the following general results. First, the delta-hedged strategy underperforms zero. Second, the documented underperformance is less for options away from the money. Third, the underperformance is greater at times of higher volatility. Fourth, the volatility risk premium significantly affects delta-hedged gains even after accounting for jump fears. Our evidence is supportive of a negative market volatility risk premium.

Option pricing, stochastic volatility, volatility risk premium, delta-hedged gains

Abstract:
We investigate whether the volatility risk premium is negative by examining the statistical properties of delta-hedged option portfolios (buy the option and hedge with stock). Within a stochastic volatility framework, we demonstrate a correspondence between the sign and magnitude of the volatility risk premium and the mean delta-hedged portfolio returns. Using a sample of S&P 500 index options, we provide empirical tests that have the following general results. First, the delta-hedged strategy underperforms zero. Second, the documented underperformance is less for options away from the money. Third, the underperformance is greater at times of higher volatility. Fourth, the volatility risk premium significantly affects delta-hedged gains even after accounting for jump-fears. Our evidence is supportive of a negative market volatility risk premium.

Abstract:
This paper examines higher-moment market risks in the cross-section of hedge fund returns to make several contributions. First, it is shown that hedge funds, but not mutual funds, are substantially exposed to volatility, skewness, and kurtosis risks. We find significant cross-sectional variation in the intensity of higher-moment exposures across hedge fund styles and across hedge funds within a particular style, suggesting potential for neutralizing higher-moment risks. Corroborating this result, when funds of hedge funds are investigated as a separate investment category they do not show aggressive loading on higher-moment risks. Second, we provide evidence on economically significant premiums being embedded in hedge fund returns on account of their exposures to higher-moment risks. Third, we uncover a set of higher-moment factors that are not strongly associated with factors in benchmark models that are currently used for evaluating hedge fund performance. Finally, the addition of higher-moment factors to benchmark models can better explain the behavior of hedge fund returns. Bearing on issues of practical consequence, benchmark models augmented with higher-moment factors can considerably alter the hedge funds' alpha-based rankings.

volatility risk, skewness risk, kurtosis risk, higher moments, exposures, hedge funds, alphas

Abstract:
The treatment of this article renders closed-form density approximation feasible for univariate continuous-time models. Implementation methodology depends directly on the parametric-form of the drift and the diffusion of the primitive process and not on its transformation to a unit-variance process. Offering methodological convenience, the approximation method relies on numerically evaluating one-dimensional integrals and circumvents existing dependence on intractable multidimensional integrals. Density-based inferences can now be drawn for a broader set of models of equity volatility. Our empirical results provide insights on crucial outstanding issues related to the rank-orderings of continuous-time stochastic volatility models, the absence/presence of non-linearities in the drift function, and the desirability of pursuing more flexible diffusion function specifications.

Continuous-time models, Maximum-likelihood estimation, Density approximation

Abstract:
This paper proposes and empirically investigates a family of credit risk models driven by a two-factor structure for the short-interest rate and an additional third factor for firm-specific distress, using the reduced-form framework of Duffie and Singleton (1999). The set of firm-specific distress factors analyzed in the study include leverage, book-to-market, profitability, equity-volatility, and distance-to-default. Our estimation approach and performance yardsticks show that interest rate risk is of first-order importance for explaining variations in single-name defaultable coupon bond yields and credit spreads. When applied to low-grade bonds, a credit risk model that takes leverage into consideration reduces absolute yield mispricing by as much as 30% relative to a competing model that ignores leverage. None of the distress factors improve performance for high-grade bonds. A strategy relying on traded Treasury instruments is surprisingly effective in dynamically hedging credit exposures for firms in our sample.

Default risk models, reduced-form, leverage, distance-to-default, hedging

Abstract:
This article provides several new insights into the economic sources of skewness. First, we document the differential pricing of individual equity options versus the market index, and relate it to variations in return skewness. Second, we show how risk aversion introduces skewness in the risk-neutral density. Third, we derive laws that decompose individual return skewness into a systematic component and an idiosyncratic component. Empirical analysis of OEX options and 30 stocks demonstrates that individual risk-neutral distributions differ from that of the market index by being far less negatively skewed. This paper explains the presence and evolution of risk-neutral skewness over time and in the cross-section of individual stocks.

Abstract:
This paper studies the equilibrium valuation of foreign exchange-contingent claims. The basic framework is the continuous-time counterpart of the classic Lucas (1982) two-country model, in which exchange rates, term structures of interest rates and, in particular, factor risk prices are all endogenously determined and empirically plausible. This endogenous nature guarantees the internal consistency of these price processes with a general equilibrium. In addition to
the domestic and foreign nominal interest rates, closed-form valuation formulas are presented for exchange rate options and exchange rate futures options. Common to these formulas is
that stochastic volatility and stochastic interest rates are admitted. Hedge ratios and other comparative statics are provided analytically. It is shown that most existing currency option
models are included as special cases.

Abstract:
This paper studies the equilibrium valuation of foreign exchange-contingent claims. The basic framework is the continuous-time counterpart of the classic Lucas (1982) two-country model, in which exchange rates, term structures of interest rates and, in particular, factor risk prices are all endogenously determined and empirically plausible. This endogenous nature guarantees the internal consistency of these price processes with a general equilibrium. In addition to the domestic and foreign nominal interest rates, closed-form valuation formulas are presented for exchange rate options and exchange rate futures options. Common to these formulas is that stochastic volatility and stochastic interest rates are admitted. Hedge ratios and other comparative statistics are provided analytically. It is shown that most existing currency option models are included as special cases.

Abstract:
This article studies the valuation of average-rate contingent claims (both arithmetic and geometric), whose importance in corporate risk management is increasing rapidly. Arbitrage--free characterizations are provided for such option--like Asian claims. When the spot price is governed by a one-dimensional Markov diffusion, we examine analytically the response of the average-rate option claim to a change in (i) the underlying spot price; (ii) the average-to-date price dependence; (iii) the riskiness of the asset; (iv) the strike price; (v) the interest rate; and (vi) the dividend/convenience yield. Our analysis yields the distinctive outcome that the upper bound on the average-rate call option delta can depart significantly from the classic unity. Depending on the structure of the risk-neutral density, a lower average-rate option premium (relative to the traditional option) is also internally consistent. Marking a sharp contrast from convention, the average-rate call can be decreasing in the interest rate. In extending the above general characterizations to higher dimensional contexts, we offer tractable valuation formulas for (1) options on the average interest rate with stochastic volatility; (2) catastrophe insurance option contract; and (3) options on the average commodity futures price [with stochastic convenience yield and stochastic interest rate]. Each valuation formula is rich in its economic content and yet amenable to empirical implementation. This paper has developed a cohesive framework for the valuation of average-rate contingent securities.

Abstract:
This article studies the valuation of options written on the average level of a Markov process. The general properties of such options are examined. We propose a closed-form characterization in which the option payoff is contingent on cumulative catastrophe losses. In our framework, the loss rate is a mean-reverting Markov process, with no continuous martingale component. The model supposes that high loss levels have lower arrival rates. We analytically derive the cumulative loss process and its characteristic function. The resulting option model is promising.

Abstract:
This paper provides a closed-form density approximation when the underlying state variable is a one-dimensional diffusion. Building on Ait-Sahalia (2002), we show that our refinement is applicable under a wide class of drift and diffusion functions. In addition, it facilitates the maximum likelihood estimation of discretely sampled diffusion models of short interest-rate or stock volatility with unknown conditional densities. Our interest-rate examples demonstrate that the analytical approximation is accurate.

closed-form density approximation, one-dimensional diffusion, maximum-likelihood

Abstract:
The structural uncertainty model with Bayesian learning, advanced by Weitzman (AER 2007), provides a framework for gauging the effect of structural uncertainty on asset prices and risk premiums. This paper provides an operational version of this approach that incorporates realistic priors about consumption growth volatility, while guaranteeing finite asset pricing quantities. In contrast to the extant literature, the resulting asset pricing model with subjective expectations yields well-defined expected utility, finite moment generating function of consumption growth, and tractable expressions for equity premium and riskfree return. Our quantitative analysis reveals that explaining the historical equity premium and riskfree return, in the context of subjective expectations, requires implausible levels of structural uncertainty. Furthermore, these implausible prior beliefs result in consumption disaster probabilities that virtually coincide with those implied by more realistic priors. At the same time, the two sets of prior beliefs have diametrically opposite asset pricing implications: one asserting, and the other contradicting, the antipuzzle view.

subjective expectations; learning; structural uncertainty; priors; predictive density of consumption growth; equity premium; riskfree return

Abstract:
The structural uncertainty model with Bayesian learning, advanced by Weitzman (AER 2007), provides a framework for gauging the effect of structural uncertainty on asset prices and risk premiums. This paper provides an operational version of this approach that incorporates realistic priors about consumption growth volatility, while guaranteeing finite asset pricing quantities. In contrast to the extant literature, the resulting asset pricing model with subjective expectations yields well-defined expected utility, finite moment generating function of consumption growth, and tractable expressions for equity premium and riskfree return. Our quantitative analysis reveals that explaining the historical equity premium and riskfree return, in the context of subjective expectations, requires implausible levels of structural uncertainty. Furthermore, these implausible prior beliefs result in consumption disaster probabilities that virtually coincide with those implied by more realistic priors. At the same time, the two sets of prior beliefs have diametrically opposite asset pricing implications: one asserting, and the other contradicting, the antipuzzle view.

subjective expectations, learning, structural uncertainty, priors, predictive density of consumption growth, equity premium, riskfree return

Abstract:
The structural uncertainty model with Bayesian learning, advanced by Weitzman (2007), provides a framework for gauging the effect of structural uncertainty on asset prices and risk premiums, and has quite a few appealing attributes. In this paper, we provide an operational version of his approach that incorporates realistic priors about consumption growth volatility while guaranteeing finite asset pricing quantities. Our modification allows characterization of the predictive density for consumption growth that is virtually indistinguishable from the heavy-tailed t distribution, but importantly possesses a finite moment generating function. The resulting asset pricing model with subjective expectations yields bounded expected utility, well-specified intertemporal marginal rate of substitution, and expressions for equity premium and riskfree return. Applying economic theory in the context of subjective expectations reveals that explaining the historical equity premium and riskfree return requires implausible levels of structural uncertainty. Furthermore, these implausible prior beliefs share disaster probabilities that almost coincide with those implied by more realistic priors. At the same time, the two sets of prior beliefs have diametrically opposite asset pricing implications: one asserting, and the other contradicting, the antipuzzle view.

subjective expectations, learning, structural uncertainty, priors, predictive density of consumption growth, equity premium, riskfree return

Abstract:
This paper studies the structure of stock market crashes, rallies, their jump arrival rates, and extremes. Large market moves are characterized in a pure-jump modeling framework. Based on both raw and devolatized returns, it is shown empirically that crashes are more severe in intensity than rallies, and have higher arrival rates. At the same time, both left-tail and right-tail extreme events conform with Frechet limit laws. Pure-jump models which describe well the tail properties of market returns are identified via their Levy measures. The distribution of extreme events implied by our model's Levy measure is closer to the actual realization of extremes than those of competing models. Finally, there is information content in the Levy measure of pure-jump models for forward arrival rate of jumps.

jump structure, pure-jump price, crashes, arrival rate, extremes

Abstract:
The treatment of this article renders closed-form density approximation feasible for univariate continuous-time models. Implementation methodology depends directly on the parametric-form of the drift and the diffusion of the primitive process and not on its transformation to a unit-variance process. Offering methodological convenience, the approximation method relies on numerically evaluating one-dimensional integrals and circumvents existing dependence on intractable multidimensional integrals. Density-based inferences can now be drawn for a broader set of models of equity volatility. Our empirical results provide insights on crucial outstanding issues related to the rank-ordering of continuous-time stochastic volatility models, the absence/presence of nonlinearities in the drift function of equity volatility, and the desirability of pursuing more flexible diffusion function specifications.

Continuous-time models, Maximum-likelihood estimation, Density approximation, Market volatility dynamics

Abstract:
This paper provides a closed-form density approximation when the underlying state variable is a one-dimensional diffusion. Building on Ait-Sahalia (2002), we show that our refinement is applicable under a wide class of drift and diffusion functions. In addition, it facilitates the maximum likelihood estimation of discretely sampled diffusion models of short interest-rate or stock volatility with unknown conditional densities. Our interest-rate examples demonstrate that the analytical approximation is accurate.

Density approximation, one-dimensional diffusions

Abstract:
When the pricing kernel is U-shaped, then expected returns of claims with payout on the upside are negative for strikes beyond a threshold, determined by the slope of the U-shaped kernel in its increasing region, and have negative partial derivative with respect to strike in the increasing region of the kernel. Using returns of (i) S&P 500 index calls, (ii) calls on major international equity indexes, (iii) digital calls, (iv) upside variance contracts, and (v) a theoretical construct that we denote as kernel call, we find broad support for the implications of U-shaped pricing kernels. A possible theoretical reconciliation of our empirical findings is explored through a model that accommodates heterogeneity in beliefs about return outcomes and short-selling.

U-shaped pricing kernels, claims on the upside, negative call returns, short-selling, heterogeneity in beliefs

Abstract:
The research indicates that index option prices incorporate a negative volatility risk premium, thus providing a possible explanation of why Black-Scholes implied volatilities of index options on average exceed realized volatilities. This examination of the empirical implication of a market volatility risk premium on 25 individual equity options provides some new insights.

While the Black-Scholes implied volatilities from individual equity options are also greater on average than historical return volatilities, the difference between them is much smaller than for the market index. Like index options, individual equity option prices embed a negative market volatility risk premium, although much smaller than for the index option - and idiosyncratic volatility does not appear to be priced.

These empirical results provide a potential explanation of why buyers of individual equity options leave less money on the table than buyers of index options.

Abstract:
Do stocks with faster growth potential exhibit superior average returns? Exploiting a parameterized equity valuation model, we analytically solve for the expected rate of return. We develop theoretical restrictions under which growth outlook induces a higher expected rate of return. Empirically, we find that in certain cyclical segments of the market, stocks with higher (ex-ante) growth expectation perform better than their slower growing counterparts. Growth outlook also enhances the profitability of momentum strategies: Winners with accelerated earnings growth potential experience superior returns compared to winners with sluggish growth potential. Controlling for cross-sectional movements in earnings yield, higher growth outlook stocks tend to have more pronounced average returns. Intriguingly, small-cap stocks with low growth outlook outperform small-cap stocks with high growth outlook. Growth outlook has investment value beyond traditional strategy drivers (momentum, value and size).

Growth outlook, return cross-section, stock valuation, expected stock returns

Abstract:
This article empirically analyzes some properties shared by all one-dimensional diffusion option models. Using S&P 500 options, we find that when sampled intraday (or inter-day), (i) call (put) prices often go down (up) even as the underlying price goes up, and (ii) call and put prices often increase, or decrease, together. Our results are valid after controlling for time-decay and market microstructure effects. Therefore, one-dimensional diffusion option models cannot be completely consistent with observed option-price dynamics; options are not redundant securities, nor ideal hedging instruments---puts and the underlying asset prices may go down together.

Abstract:
This article offers a tractable monetary asset pricing model. In monetary economies, the price level, inflation, asset prices, and the real and nominal interest rates have to be determined simultaneously and in relation to each other. This link allows us to relate in closed form each of the dependent entities to the underlying real and monetary variables. Among other features of such economies, inflation can be partially non-monetary and the real and nominal term structures can depend on fundamentally different risk factors. In one extreme, the process followed by the real term structure is independent of that followed by its nominal counterpart.

Abstract:
Recent empirical studies find that once an option pricing model has incorporated stochastic volatility, allowing interest rates to be stochastic does not improve pricing or hedging any further while adding random jumps to the modeling framework only helps the pricing of extremely short-term options but not the hedging performance. Given that only options of relatively short terms are used in existing studies, this paper addresses two related questions: Do long-term options contain different information than short-term options? If so, can long-term options better differentiate among alternative models? Our inquiry starts by first demonstrating analytically that differences among alternative models usually do not surface when applied to short term options, but do so when applied to long-term contracts. For instance, within a wide parameter range, the Arrow-Debreu state price densities implicit in different stochastic-volatility models coincide almost everywhere at the short horizon, but diverge at the long horizon. Using regular options (of less than a year to expiration) and LEAPS, both written on the S&P 500 index, we find that short- and long-term contracts indeed contain different information and impose distinct hurdles on any candidate option pricing model. While the data suggest that it is not as important to model stochastic interest rates or random jumps (beyond stochastic volatility) for pricing LEAPS, incorporating stochastic interest rates can nonetheless enhance hedging performance in certain cases involving long-term contracts.

Abstract:
Substantial progress has been made in extending the Black-Scholes model to incorporate such features as stochastic volatility, stochastic interest rates and jumps.On the empirical front, however, it is not yet known whether and by how much each generalized feature will improve option pricing and hedging performance. This paper fills this gap by first developing an implementable option model in closed form that allows volatility, interest rates and jumps to bestochastic and that is parsimonious in the number of parameters. The model includes many known ones as special cases. Delta-neutral and single-instrument minimum-variance hedging strategies are derived analytically. Using S&P 500 options, we examine a set of alternative models from three perspectives: (1) internal consistency of implied parameters/volatility with relevant time-series data, (2)out-of-sample pricing and (3) hedging performance. The models of focus include the benchmark Black-Scholes formula and the ones that respectively allow for (i) stochastic volatility, (ii) both stochastic volatility and stochastic interest rates, and (iii) stochastic volatility and jumps.Overall, incorporating both stochastic volatility and random jumps produces the best pricing performance and the most internally-consistent implied-volatility process. Its implied volatility does not "smile" across moneyness. But, for hedging, adding either jumps or stochastic interest rates does not seem to improve performance any further once stochastic volatility is taken into account.

Abstract:
Substantial progress has been made in extending the Black- Scholes model to incorporate such features as stochastic volatility, stochastic interest rates and jumps. On the empirical front, however, it is not yet known whether and by how much each generalized feature will improve option pricing and hedging performance. This paper fills this gap by first developing an implementable option model in closed form that allows volatility, interest rates and jumps to be stochastic and that is parsimonious in the number of parameters. The model includes many known ones as special cases. Delta- neutral and single-instrument minimum-variance hedging strategies are derived analytically. Using S&P 500 options, we examine a set of alternative models from three perspectives: (1) internal consistency of implied parameters/ volatility with relevant time-series data, (2) out-of-sample pricing and (3) hedging performance. The models of focus include the benchmark Black-Scholes formula and the ones that respectively allow for (i) stochastic volatility, (ii) both stochastic volatility and stochastic interest rates, and (iii) stochastic volatility and jumps. Overall, incorporating both stochastic volatility and random jumps produces the best pricing performance and the most internally-consistent implied-volatility process. Its implied volatility does not "smile" across moneyness. But, for hedging, adding either jumps or stochastic interest rates does not seem to improve performance any further once stochastic volatility is taken into account.