We develop a novel class of time-changed Lévy models which are tractable and readily applicable, capture the leverage effect, and exhibit pure jump processes with finite or infinite activity. Our models feature four nested processes reflecting market, volatility and jump risks, and observation...

Perpetual futures are contracts without expiration date in which the anchoring of the futures price to the spot price is ensured by periodic funding payments from long to short. We derive explicit expressions for the no-arbitrage price of various perpetual contracts, including linear, inverse,...

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...

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...

The 1987 stock market crash occurred with minimal impact on observable economic variables (e.g., consumption), yet dramatically and permanently changed the shape of the implied volatility curve for equity index options. Here, we propose a general equilibrium model that captures many salient...