VaR (Value at Risk) and CVaR (Conditional Value at Risk) are implied by option prices. Their relationships to option prices are derived initially under the pricing measure. It does not require assumptions about the distribution of portfolio returns. The effects of changes of measure are modest...

In the existing literature on barrier options, much effort has been exerted to ensure convergence through placing the barrier in close proximity to, or directly onto, the nodes of the tree lattice. In this paper we show that this may not be necessary to achieve accurate option price...

The ability of option-based measures to predict future stock returns is not a sufficient condition for the existence of incremental information in options. If options markets are informationally more efficient than the stock market, then option measures may be used to predict future actual stock...