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Motivated by discrete price quotes in continuous time, we seek a fundamental theorem based on no arbitrage rather than a condition on limiting trading opportunities. We consider a vector of discounted prices taking values in a locally finite subset of $R^d$ in continuous time. For a locally bounded c\`adl\`ag price, we...
We study the short-maturity implied volatility and the skew stickiness ratio for baskets of assets with continuous, possibly rough, stochastic volatility. The fluctuation of the instantaneous basket variance has two sources: fluctuations of the constituent variances and fluctuations of the basket weights. We derive a n...
We derive a short-maturity expansion for up-and-out put barrier option prices under continuous stochastic volatility when the strike and the barrier approach the spot at the diffusive scale. Assuming joint weak convergence of the normalized terminal return, the relative volatility fluctuation, and the running maximum,...
We prove a functional stable limit theorem for the discretization error process of a local linearization scheme for stochastic differential equations with additive Brownian noise. The scheme includes the conditional mean of the second-order term involving the Brownian increment in the Taylor expansion of the drift. The...
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