Portfolio risk estimation in volatile markets requires employing fat-tailed models for financial returns combined with … copula functions to capture asymmetries in dependence and an appropriate downside risk measure. In this survey, we discuss … how these three essential components can be combined together in a Monte Carlo based framework for risk estimation and …

incomplete market with stochastic volatility that is not perfectly hedgeable. By combining standard asymptotic expansion … technique for the underlying volatility process, we derive explicit expression for the solution of the FBSDE up to the third … order of volatility-of-volatility, which can be directly translated into the optimal investment strategy. We compare our …

We derive robust good-deal hedges and valuations under combined model ambiguity about the drift and volatility of asset … for overly attractive reward-to-risk ratios are excluded, by restricting instantaneous Sharpe ratios for any market …-arbitrage bounds. In mathematical terms, it demands however that not just ambiguities about the volatility but also about the drift …

volatility and its curve resembles a smile, meaning that the introduction of jumps is quantified via a smile according to implied … volatility. In order to derive such an implied volatility smile, an iterative search procedure referred to as the Newton …-Raphson algorithm is proposed. Numerical experiments of both the in-house pricing formula and its implied volatility recursive algorithm …

patterns of implied volatility can actually be reproduced as a consequence of dynamical hedging. The simulations are performed …We consider an option pricing model proposed by, where the implementation of dynamic hedging strategies has a feedback … maturity classes. Overall, nonlinear feedback due to hedging strategies can, at least in part, contribute to explain from a …

minimizes the cost of hedging a path dependent contingent claim with given expected success ratio, in a discrete-time, semi …-static market of stocks and options. Based on duality results which link quantile hedging to a randomized composite hypothesis test … measure, which guarantees the existence of the optimal hedging strategy and enables numerical calculation of the quantile …

We introduce the beta stochastic volatility model and discuss empirical features of this model and its calibration … steeper forward skews, compared to traditional stochastic volatility models …