Volatility

s&p500 index skew forward pde option pricing numerical methods jumps volatility calibration delta-hedging vix options local stochastic volatility hedging strategies jump risk implied volatility volatility trading merton structural default model credit value adjustment cva fft and pde methods for credit derivatives counterparty default risk credit risk sharpe ratio volatility trading strategies profit-and-loss of delta-hedging strategies optimal hedging beta stochastic volatility implied volatility dynamics log-normal stochastic volatility karasinski-sepp volatility model volatility dynamics volatility beta volatility skew-beta two-factor stochastic volatility model vix futures realized variance transaction costs variance swap volatility jump-to-default affine models credit