Detecting Jump Risk and Jump-Diffusion Model for Bitcoin Options Pricing and Hedging

In this paper, we conduct a fast calibration in the jump-diffusion model to capture the Bitcoin price dynamics, as well as the behavior of some components affecting the price itself, such as the risk of pitfalls and its ambiguous effect on the evolution of Bitcoin’s price. In addition, in our study of the Bitcoin option pricing, we find that the inclusion of jumps in returns and volatilities are significant in the historical time series of Bitcoin prices. The benefits of incorporating these jumps flow over into option pricing, as well as adequately capture the volatility smile in option prices. To the best of our knowledge, this is the first work to analyze the phenomenon of price jump risk and to interpret Bitcoin option valuation as “exceptionally ambiguous”. Crucially, using hedging options for the Bitcoin market, we also prove some important properties: Bitcoin options follow a convex, but not strictly convex function. This property provides adequate risk assessment for convex risk measure.

Anomalies in Commodity Futures Markets

In recent years, commodity markets have become increasingly popular among financial investors. While previous studies document a factor structure, not much is known about how prominent anomalies are priced in commodity futures markets. We examine a large set of such anomaly variables. We identify sizable premia for jump risk, momentum, skewness, and volatility-of-volatility. Other prominent variables, such as downside beta, idiosyncratic volatility, and MAX, are not priced in commodity futures markets. Commodity investors should rebalance their portfolios regularly. Returns for annual holding periods are substantially weaker than for monthly rebalancing.

LOCALLY RISK-MINIMIZING HEDGING FOR EUROPEAN CONTINGENT CLAIMS WRITTEN ON NON-TRADABLE ASSETS WITH COMMON JUMP RISK

This article investigates the optimal hedging problem of the European contingent claims written on non-tradable assets. We assume that the risky assets satisfy jump diffusion models with a common jump process which reflects the correlated jump risk. The non-tradable asset and jump risk lead to an incomplete financial market. Hence, the cross-hedging method will be used to reduce the potential risk of the contingent claims seller. First, we obtain an explicit closed-form solution for the locally risk-minimizing hedging strategies of the European contingent claims by using the Föllmer–Schweizer decomposition. Then, we consider the hedging for a European call option as a special case. The value of the European call option under the minimal martingale measure is derived by the Fourier transform method. Next, some semi-closed solution formulae of the locally risk-minimizing hedging strategies for the European call option are obtained. Finally, some numerical examples are provided to illustrate the sensitivities of the optimal hedging strategies. By comparing the optimal hedging strategies when the underlying asset is a non-tradable asset or a tradable asset, we find that the liquidity risk has a significant impact on the optimal hedging strategies.

Seasoned Equity Offerings and Stock Price Crash Risk

Using a large sample of U.S. firms during 1987–2011, we find robust evidence that the issuance of seasoned equity is associated with abnormally high future stock price crash risk. The association between seasoned equity offerings and crash risk is stronger among offerings that involve the sale of secondary shares (existing shares sold by insiders or large blockholders). We also find that recent seasoned equity issuers are far less likely to experience sudden positive price jumps relative to firms that have not recently issued equity. Our findings of elevated crash risk and diminished jump risk, when taken together, are consistent with a heightened propensity for firms to hoard bad news but not good news when issuing equity.