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...

Nonzero-sum stochastic differential games with impulse controls offer a realistic and far-reaching modelling framework for applications within finance, energy markets, and other areas, but the difficulty in solving such problems has hindered their proliferation. Semi-analytical approaches make...

We consider a tractable affine stochastic volatility model that generalizes the seminal Heston (1993) model by augmenting it with jumps in the instantaneous variance process. In this framework, we consider options written on the realized variance, and we examine the impact of the distribution of...

In the seismological and geophysics literature, it is suggested by numerous authors that the elapsed time between two earthquakes at a given location should be represented by either an exponential or Weibull distribution. In addition, the seismic gap hypothesis states that large waiting times...

Markov chain Monte Carlo (MCMC) methods have an important role in solving high dimensionality stochastic problems characterized by computational complexity. Given their critical importance, there is need for network and security risk management research to relate the MCMC quantitative...

In this short note, we prove by an appropriate change of variables that the SVI implied volatility parameterization presented in Gatheral's book and the large-time asymptotic of the Heston implied volatility agree algebraically, thus confirming a conjecture from Gatheral as well as providing a...

A one-dimensional partial differential-difference equation (pdde) under forward measure is developed to value European option under jump-diffusion, stochastic interest rate and local volatility. The corresponding forward Kolmogorov partial differential-difference equation for transition...

We introduce a new approach to model the market smile for inflation-linked derivatives by defining the Quadratic Gaussian Year-on-Year inflation model -- the QGY model. We directly define the model in terms of a year-on-year ratio of the inflation index on a discrete tenor structure, which,...

Linear Methods are often used to compute approximate solutions to dynamic models, as these models often cannot be solved analytically. Linear methods are very popular, as they can easily be implemented. Also, they provide a useful starting point for understanding more elaborate numerical...

We model the dynamics of asset prices and associated derivatives by consideration of the dynamics of the conditional probability density process for the value of an asset at some specified time in the future. In the case where the asset is driven by Brownian motion, an associated "master...