Explaining asset pricing puzzles associated with the 1987 market crash

The 1987 market crash was associated with a dramatic and permanent steepening of the implied volatility curve for equity index options, despite minimal changes in aggregate consumption. We explain these events within a general equilibrium framework in which expected endowment growth and economic uncertainty are subject to rare jumps. The arrival of a jump triggers the updating of agents' beliefs about the likelihood of future jumps, which produces a market crash and a permanent shift in option prices. Consumption and dividends remain smooth, and the model is consistent with salient features of individual stock options, equity returns, and interest rates.     

What is the impact of wealth shocks on asset allocation?

I test the assumption of constant relative risk aversion using U.S. macroeconomic data and analyse the role of wealth shocks in generating transitory changes in asset portfolio composition. I show that the risky asset share exhibits cyclical behavior and it is significantly (and positively) affected by unexpected variation in wealth. Therefore, the empirical evidence suggests that risk aversion is counter-cyclical. I also find that the portfolio share of housing wealth falls when the agent is faced with a positive wealth shock, i.e. housing is a hedge against unfavorable wealth fluctuations. Finally, considering a variety of wealth definitions, the results show that: (i) wealth effects are stronger for direct holdings of risky assets than for indirect holdings, which highlights that investors do not typically trade some assets such as pension or mutual funds; (ii) although significant, wealth effects on asset allocation are mainly temporary as agents quickly rebalance the asset portfolio composition (i.e. there is weak evidence of inertia or slow adjustment in asset allocation); and (iii) changes in expected returns partially explain the variation in risky asset allocation.     

Two-dimensional risk-neutral valuation relationships for the pricing of options

The Black–Scholes model is based on a one-parameter pricing kernel with constant elasticity. Theoretical and empirical results suggest declining elasticity and, hence, a pricing kernel with at least two parameters. We price European-style options on assets whose probability distributions have two unknown parameters. We assume a pricing kernel which also has two unknown parameters. When certain conditions are met, a two-dimensional risk-neutral valuation relationship exists for the pricing of these options: i.e. the relationship between the price of the option and the prices of the underlying asset and one other option on the asset is the same as it would be under risk neutrality. In this class of models, the price of the underlying asset and that of one other option take the place of the unknown parameters.      

A new approach for option pricing under stochastic volatility

We develop a new approach for pricing European-style contingent claims written on the time T spot price of an underlying asset whose volatility is stochastic. Like most of the stochastic volatility literature, we assume continuous dynamics for the price of the underlying asset. In contrast to most of the stochastic volatility literature, we do not directly model the dynamics of the instantaneous volatility. Instead, taking advantage of the recent rise of the variance swap market, we directly assume continuous dynamics for the time T variance swap rate. The initial value of this variance swap rate can either be directly observed, or inferred from option prices. We make no assumption concerning the real world drift of this process. We assume that the ratio of the volatility of the variance swap rate to the instantaneous volatility of the underlying asset just depends on the variance swap rate and on the variance swap maturity. Since this ratio is assumed to be independent of calendar time, we term this key assumption the stationary volatility ratio hypothesis (SVRH). The instantaneous volatility of the futures follows an unspecified stochastic process, so both the underlying futures price and the variance swap rate have unspecified stochastic volatility. Despite this, we show that the payoff to a path-independent contingent claim can be perfectly replicated by dynamic trading in futures contracts and variance swaps of the same maturity. As a result, the contingent claim is uniquely valued relative to its underlying’s futures price and the assumed observable variance swap rate. In contrast to standard models of stochastic volatility, our approach does not require specifying the market price of volatility risk or observing the initial level of instantaneous volatility. As a consequence of our SVRH, the partial differential equation (PDE) governing the arbitrage-free value of the contingent claim just depends on two state variables rather than the usual three. We then focus on the consistency of our SVRH with the standard assumption that the risk-neutral process for the instantaneous variance is a diffusion whose coefficients are independent of the variance swap maturity. We show that the combination of this maturity independent diffusion hypothesis (MIDH) and our SVRH implies a very special form of the risk-neutral diffusion process for the instantaneous variance. Fortunately, this process is tractable, well-behaved, and enjoys empirical support. Finally, we show that our model can also be used to robustly price and hedge volatility derivatives.     

Tax liens: a novel application of asset pricing theory

Although relatively obscure, the market for distressed real estate tax liens exists in over 30 U.S. states, with a market size estimated to be around 20 billion dollars. While this niche asset class is relatively unknown to academics, internet advertising hypes tax liens to the populace as providing extraordinary returns. Not yet scientifically studied, this market provides a fertile and untouched arena for the application of asset pricing theory. Using insights from several areas of asset pricing, we formulate and test a pricing model for tax liens. The empirical evidence supports the pricing model, the (increasing) competitiveness of the tax lien market, and an unfair tax auction bidding mechanism for property owners that may provide extraordinary returns to investors, lending some credibility to the industry claims. We suggest avenues for extensions and further research.     

Cross-sectional tests of deterministic volatility functions

We study the cross-sectional performance of option pricing models in which the volatility of the underlying stock is a deterministic function of the stock price and time. For each date in our sample of FTSE 100 index option prices, we fit an implied binomial tree to the panel of all European style options with different strike prices and maturities and then examine how well this model prices a corresponding panel of American style options. We find that the implied binomial tree model performs no better than an ad-hoc procedure of smoothing Black–Scholes implied volatilities across strike prices and maturities. Our cross-sectional results complement the time-series findings of Dumas et al. [J. Finance 53 (1998) 2059].     

What determines early exercise of employee stock options in Australia?

Employee stock options (ESOs) are a popular way of remunerating employees. We analyse factors at the firm and option level affecting the employee's decision to exercise ESOs before they mature. Exercises over the period 1998–2004 are analysed and the key factor influencing early exercise is found to be dividends. Exercises frequently occur well before maturity, but in most cases little time value is sacrificed. Our findings have implications for the ‘fair’ valuation of ESOs in companies’ financial statements, as required by the relevant Australian accounting standard, AASB 2.     

Pricing commercial mortgages and their mortgage-backed securities

This article has taken considerable effort to accurately model the complexity of a commercial mortgage and its mortgage-backed security. In fact, it is the first example in the general literature on mortgage pricing to present a comprehensive set of numerical results in which the valuation of a mortgage-backed security is explicitly tied to that of the underlying mortgage. The conclusion we reach is that option pricing provides an accurate and flexible approach to valuing the complex mortgage instruments now being developed in the financial community.     

Realizing smiles: Options pricing with realized volatility

We develop a discrete-time stochastic volatility option pricing model exploiting the information contained in the Realized Volatility (RV), which is used as a proxy of the unobservable log-return volatility. We model the RV dynamics by a simple and effective long-memory process, whose parameters can be easily estimated using historical data. Assuming an exponentially affine stochastic discount factor, we obtain a fully analytic change of measure. An empirical analysis of Standard and Poor's 500 index options illustrates that our model outperforms competing time-varying and stochastic volatility option pricing models.