SABR stochastic volatility model is appealing for modeling smile and skew of option prices. Hagan, who first proposed this model, derived a closed form approximation for european options and showed that it provides consistent and stable hedges. Here I prove a new exact closed formula for the...

We employ a refined tree method to value employee stock options (ESOs) in the stochastic volatility model of Heston. Our setting covers risk-averse employees maximizing expected utility where we in particular focus on subjective option valuation, personal market beliefs and stochastic...

We introduce an asymptotic expansion for forward start options in a multi-factor local-stochastic volatility model. We derive explicit approximation formulas for the so-called forward implied volatility which can be useful to price complex path-dependent options, as cliquets. The expansion...

Stocks with high idiosyncratic volatility perform poorly relative to low idiosyncratic volatility stocks. We offer a novel explanation of this anomaly based on real options, which is consistent with earlier findings on idiosyncratic volatility (the positive contemporaneous relation between...

The Gaussian affine interest rate models are widely used in the financial industry for pricing, hedging and also risk management purposes. We consider the multifactor models with time dependent parameters. Usually the models are simulated using some appropriate discretization schema because the...

We propose a novel method for the analytical approximation in local volatility models with Lévy jumps. The main result is an expansion of the characteristic function in a local Lévy model, which is worked out in the Fourier space by considering the adjoint formulation of the pricing problem....

We present a simplified approach to the analytical approximation of the transition density related to a general local volatility model. The methodology is sufficiently flexible to be extended to time-dependent coefficients, multi-dimensional stochastic volatility models, degenerate parabolic...

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...

The interaction between the volatility and price dynamics is explored. We model stochastic asset prices using the asset flow model with randomness arising directly from supply and demand. We show that the volatility is smallest at the extrema of the price. Linearizing the stochastic differential...

An enhanced option pricing framework that makes use of both continuous and discontinuous time paths based on a geometric Brownian motion and Poisson-driven jump processes respectively is performed in order to better fit with real-observed stock price paths while maintaining the analytical...