In a tractable stochastic volatility model, we identify the price of the smile as the price of the unspanned risks traded in SPX option markets. The price of the smile reflects two persistent volatility and skewness risks, which imply a downward sloping term structure of low-frequency variance...

A P-sigma-martingale density for a given stochastic process S is a local P-martingale Z0 starting at 1 such that the product ZS is a P-sigma-martingale. Existence of a P-sigma-martingale density is equivalent to a classic absence-of-arbitrage property of S, and it is invariant if we replace the...

We investigate a deterministic criterion to determine whether a diffusive local martingale with a single jump and state-dependent characteristics is a uniformly integrable martingale. We allow the diffusion coefficient, the jump hazard rate and the relative jump size to depend on the state and...

A new class of risk measures called cash sub-additive risk measures is introduced to assess the risk of future financial, nonfinancial and insurance positions. The debated cash additive axiom is relaxed into the cash sub-additive axiom to preserve the original difference between the numeraire of...

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...

We analyze American put options in a hyper-exponential jump-diffusion model. Our contribution is threefold. Firstly, by following a maturity randomization approach, we solve the partial integro-differential equation and obtain a tight lower bound for the American option price. Secondly, our...

Classical option pricing theories are usually built on the law of one price, neglecting the impact of market liquidity that may contribute to significant bid-ask spreads. Within the framework of conic finance, we develop a stochastic liquidity model, extending the discrete-time constant...

The main result of the paper is a formula for zero time-to-maturity limit of implied volatilities of European options under a broad class of stochastic volatility models. Based on this formula, we propose a closed-form approximation of the implied volatility smile. Numerical examples suggest...

Return anomalies are most pronounced among distressed stocks. We attribute this finding to the role of misvaluation and investors' inability to value distressed stocks correctly. We treat distressed stocks as options and construct a valuation model that explicitly takes into account the value of...

We analyze the impact of funding costs and margin requirements on prices of index options traded on the CBOE. We propose a model that gives upper and lower bounds for option prices in the absence of arbitrage in an incomplete market with differential borrowing and lending rates. We show that...