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...

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 introduce a multivariate Hawkes process with constraints on its conditional density. It is a multivariate point process with conditional intensity similar to that of a multivariate Hawkes process but certain events are forbidden with respect to boundary conditions on a multidimensional...

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 consider the problem of superhedging under volatility uncertainty for an investor allowed to dynamically trade the underlying asset, and statically trade European call options for all possible strikes with some given maturity. This problem is classically approached by means of the Skorohod...

The model derives risky corporate bond prices (or equivalently credit spreads) subject to credit default and migration risk, based on an extended version of the Jarrow, Lando and Turnbull model, under a risk-neutral framework, as a result of the simulation of a continuous time, time-homogeneous...

We present two robust extensions of the CreditGrades model: the first one assumes that the variance of returns on the firm's assets is stochastic, and the second one assumes that the firm's asset value process follows a double-exponential jump-diffusion. We derive closed-form formulas for...

Since Bachelier's thesis in 1900 (laying the foundation of the stochastic process, or Brownian motion, as a model of stock price changes), attempts at understanding the nature of prices and at predicting them have failed. Statistical methods have only found minor regularities/anomalies, and...

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 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...