This paper studies contingent claim valuation in a Lucas-type exchange economy. The derived fundamental valuation equation differs from its Cox-Ingersoll-Ross production-economy counterpart in that it is expressed in terms of the direct utility function and an exogenous output process, thus offering superior tractability. We apply our approach to derive closed-form solutions for bond, bond option, individual stock, and stock option prices, under a more general setting than allowable in the Cox-Ingersoll-Ross framework. The resulting interest rate and stock price dynamics are empirically plausible. Moreover, our stock option pricing formula with stochastic volatility and interest rates can reconcile certain puzzling empirical regularities, including the volatility smile.

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 nonmonetary 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.

This article empirically analyzes some properties shared by all one-dimensional diffusion option models. Using S&P 500 options, we find that sampled intraday (or interday) call (put) prices often go down (up) even as the underlying price goes up, and 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.

In existing theory, wealth is no more valuable than its implied consumption rewards. In reality investors acquire wealth not just for its implied consumption, but for the resulting social status. Max M. Weber refers to this desire for wealth as the spirit of capitalism. We examine, both analytically and empirically, implications of Weber's hypothesis for consumption, savings, and stock prices. When investors care about relative social status, propensity to consume and risk-taking behavior will depend on social standards, and stock prices will be volatile. The spirit of capitalism seems to be a driving force behind stock-market volatility and economic growth.

We study the effects of Confucian social norms on savings rates in China. In our simple two-period model, parents have the option to invest in either a risk-free asset or their children’s human capital. We assume that the filial piety norms and thus the enforcement mechanisms for supporting old-age parents differ across regions. Consequently, the probability of children’s non-performance of their repayment obligations to parents and the returns parents can expect from investing in their children vary. We test the model predictions using data from the China Household Finance Survey. We find that stronger Confucian social norms reduce the gap in the savings rate between families with sons and with daughters. Modeling default by children as a function of the prevailing social norms gives us the flexibility to study the impacts of declining Confucian influence on consumption–savings trends in China.

This article studies the equilibrium valuation of foreign exchange contingent claims. Within a continuous‐time Lucas (1982) two‐country model, exchange rates, interest rates and, in particular, factor risk prices are all endogenously and jointly determined. This guarantees the internal consistency of these price processes with a general equilibrium. In the same model, closed‐form valuation formulas are presented for currency options and currency futures options. Common to these formulas is that stochastic volatility and stochastic interest rates are admitted. Hedge ratios and other comparative statics are also provided analytically. It is shown that most existing currency option models are included as special cases.

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.

Substantial progress has been made in developing more realistic option pricing models. Empirically, however, it is not known whether and by how much each generalization improves option pricing and hedging. We fill this gap by first deriving an option model that allows volatility, interest rates and jumps to be stochastic. Using S&P 500 options, we examine several 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. Overall, incorporating stochastic volatility and jumps is important for pricing and internal consistency. But for hedging, modeling stochastic volatility alone yields the best performance.

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.