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...

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...

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...

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 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...

Distributed ledger technologies rely on consensus protocols confronting traders with random waiting times until the transfer of ownership is accomplished. This time consuming settlement process exposes arbitrageurs to price risk and imposes limits to arbitrage. We derive theoretical arbitrage...

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 propose two structural models for stochastic losses given default which allow to model the credit losses of a portfolio of defaultable financial instruments. The credit losses are integrated into a structural model of default events accounting for correlations between the default events and...