Maximum Entropy Evaluation of Asymptotic Hedging Error under a Generalised Jump-Diffusion Model

In this paper we propose a maximum entropy estimator for the asymptotic distribution of the hedging error for options. Perfect replication of financial derivatives is not possible, due to market incompleteness and discrete-time hedging. We derive the asymptotic hedging error for options under a generalised jump-diffusion model with kernel bias, which nests a number of very important processes in finance. We then obtain an estimation for the distribution of hedging error by maximising Shannon’s entropy subject to a set of moment constraints, which in turn yields the value-at-risk and expected shortfall of the hedging error. The significance of this approach lies in the fact that the maximum entropy estimator allows us to obtain a consistent estimate of the asymptotic distribution of hedging error, despite the non-normality of the underlying distribution of returns.

On statistical indistinguishability of complete and incomplete market models

Purpose This paper aims to investigate possibility of statistical detection of market completeness for continuous time diffusion stock market models. Design/methodology/approach The paper uses theory of forecasting to find criteria of predictability of market parameters such as volatilities and the appreciation rates. Findings It is known that the market completeness is not a robust property: small random deviations of the coefficients convert a complete market model into an incomplete one. The paper shows that market incompleteness is also non-robust: for any incomplete market from a wide class of models, there exists a complete market model with arbitrarily close paths of the stock prices and the market parameters. Originality/value The paper results lead to a counterintuitive conclusion that the incomplete markets are indistinguishable in the terms of the market statistics.

Incomplete Financial Markets and the Booming Housing Sector in China

Housing is by far the most important asset in Chinese households’ balance sheets. However, despite forceful and frequent government interventions, the rise in Chinese housing prices has not been contained as much as intended, a trend that has not been reversed by the COVID-19 shock. In this paper, we first provide some stylized facts and then a DSGE model (encompassing both demand and supply channels) to highlight the impact of a “slow-moving” structural vulnerability—financial market incompleteness—on China’s housing prices. The model implies that to eradicate the root causes of the rising housing price, policymakers need to go beyond the housing market itself; instead, it would be desirable to deepen financial markets because these markets would help channel financial resources to productive sectors rather than to housing speculation. This is particularly important in the COVID era because without addressing this structural vulnerability, the higher household savings and the government stimulus may fuel the housing bubble and sow seeds for a future crisis. The paper can also shed light on the housing markets in other economies that face similar vulnerabilities.