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 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...

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...

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 propose an estimator for the stochastic discount factor (SDF) that does not require macroeconomic proxies or preference assumptions. It depends only on observed asset returns, yet is immune to the form of the multivariate return distribution, including the distribution's factor structure....

By assuming that stochastic discount factor (SDF) M be a proper but unspecified function of state variables X, we show that this function M(X) must solve a simple second-order linear differential equation specified by state variables' risk-neutral dynamics. Therefore, this assumption determines...

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...