In this paper, we investigate the behavior of the bitcoin (BTC) price through the vanilla options available on the market. We calibrate a series of Markov models on the option surface. In particular, we consider the Black-Scholes model, Laplace model, five Variance Gamma related models and the...

We document widespread violations of stochastic dominance in the one-month S&P 500 index options market over the period 1986-2002. These violations imply that a trader can improve her expected utility by engaging in a zero-net-cost trade. We allow the market to be incomplete and also imperfect...

Widespread violations of stochastic dominance by one-month Samp;P 500 index call options over 1986-2006 imply that a trader can improve expected utility by engaging in a zero-net-cost trade net of transaction costs and bid-ask spread. Although pre-crash option prices conform to the...

We document that the skew of S&P500 index puts is non-decreasing in the disaster index and risk-neutral variance, contrary to the implications of no-arbitrage models. Our model resolves the puzzle by recognizing that, as the disaster risk increases, customers demand more puts as insurance while...

We document that the implied volatility skew of S&P 500 index puts is non-decreasing in the disaster index and risk-neutral variance, contrary to the implications of a broad class of no-arbitrage models. The key to the puzzle lies in recognizing that, as the disaster risk increases, customers...

It is generally said that out-of-the-money call options are expensive and one can ask the question from which moneyness level this is the case. Expensive actually means that the price one pays for the option is more than the discounted average payoff one receives. If so, the option bears a...

The optimal portfolio of a utility-maximizing investor trading in the S&P 500 index and cash, subject to proportional transaction costs, becomes stochastically dominated when overlaid with a zero-net-cost portfolio of S&P 500 options bought at their ask and written at their bid price in most...