We consider calibration of log-normal stochastic volatility model and computation of option delta consistently with statistical dynamics of the asset price and its implied volatility surface. We introduce the concept of volatility skew-beta which serves as an empirical adjustment for empirical...

We consider the delta-hedging strategy for a vanilla option under the discrete hedging and transaction costs, assuming that an option is delta-hedged using the Black-Scholes-Merton model with the log-normal volatility implied by the market price of the option. We analyze the expected...

We provide a practical and technical overview of volatility trading strategies:1) The insight for the design and back-testing of systematic volatility strategies2) Understanding of risk-reward trade-off and potential pitfalls of volatility strategies We focus on systematic and rule-based trading...

Academics and practitioners have developed many models for volatility measurement and forecast – I estimate that the total number of available models to be about 200-300 if we count all modifications of intraday estimators, GARCH-type and continuous-time models.In practice, the estimate and...

We analyse the profit-and-loss (P&L) of delta-hedging strategies for vanilla options in the presence of the implied volatility skew and derive an approximation for the P&L under the quadratic parametrization of the implied volatility. We apply this approximation to study the P&L of a straddle, a...

The calibration of local volatility models to market data is one of the most fundamental problems of financial engineering. Under the restrictive assumption that the entire implied volatility surface is known, this problem can be solved by virtue of the so-called Dupire equation. In reality,...

We use stochastic volatility models to describe the evolution of the asset price, its instantaneous volatility, and its realized volatility. In particular, we concentrate on the Stein-Stein model (SSM) (1991) for the stochastic asset volatility and the Heston model (HM) (1993) for the stochastic...

We introduce the beta stochastic volatility model and discuss empirical features of this model and its calibration. This model is appealing because, first, its parameters can be easily understood and calibrated and, second, it produces steeper forward skews, compared to traditional stochastic...

We develop analytical methodology for pricing and hedging options on the realized variance under the Heston stochastic variance model (1993) augmented with jumps in asset returns and variance. By employing generalized Fourier transform we obtain analytical solutions (up to numerical inversion of...

We propose a structural default model to evaluate the counterparty risk by trading in credit default swap (CDS) contracts. We model the joint evolution of the firm value of the entity underlying the CDS contract and the counterparty using a correlated jump-diffusion process. Unlike the...