The State Price Density Implied by Crude Oil Futures and Option Prices

Both large oil price increases and decreases are associated with deteriorating economic conditions. The projection of the state price density (SPD) onto oil returns estimated from oil futures and option prices displays a U-shaped pattern. Because investors assign high state prices to large negative and large positive oil returns, the U-shaped SPD may steepen in either tail when economic conditions deteriorate. The positive return region of the SPD is more closely related to economic conditions. The oil SPD contains information about economic conditions and future security returns that is distinct from the information in the stock index SPD.

Nonparametric Estimation of Fractional Option Pricing Model

The establishment of the fractional Black–Scholes option pricing model is under a major condition with the normal distribution for the state price density (SPD) function. However, the fractional Brownian motion is deemed to not be martingale with a long memory effect of the underlying asset, so that the estimation of the state price density (SPD) function is far from simple. This paper proposes a convenient approach to get the fractional option pricing model by changing variables. Further, the option price is transformed as the integral function of the cumulative density function (CDF), so it is not necessary to estimate the distribution function individually by complex approaches. Finally, it encourages to estimate the fractional option pricing model by the way of nonparametric regression and makes empirical analysis with the traded 50 ETF option data in Shanghai Stock Exchange (SSE).

A Theory of Equivalent Expectation Measures for Expected Prices of Contingent Claims

This paper introduces a theory of equivalent expectation measures, such as the R measure and the RT1 measure, generalizing the martingale pricing theory of Harrison and Kreps (1979) for deriving analytical solutions of expected prices - both the expected current price and the expected future price - of contingent claims. We also present new R-transforms which extend the Q-transforms of Bakshi and Madan (2000) and Duffie et al. (2000), for computing the expected prices of a variety of standard and exotic claims under a broad range of stochastic processes. Finally, as a generalization of Breeden and Litzenberger (1978), we propose a new concept of the expected future state price density which allows the estimation of the expected future prices of complex European contingent claims as well as the physical density of the underlying asset's future price, using the current prices and only the first return moment of standard European OTM call and put options.

Two Trees with Heterogeneous Beliefs: Spillover Effect of Disagreement

In a model where investors disagree about the fundamentals of two stocks, the state-price density depends on investor disagreements for both stocks, especially the larger stock. This implies that disagreement among investors in a large firm has a spillover effect on the pricing of other stocks owned by these investors. The pricing effects of investor disagreements crucially depend on the average belief biases. Empirical findings support the novel model prediction of a disagreement spillover effect and help reconcile some mixed evidence in the literature.