We consider a stochastic local volatility model with domestic and foreign stochastic interest rates and identify a bias with respect to the deterministic local volatility with deterministic rates. Relating the local volatility of our model to that of the forward price, we quantify that bias by...

Financial time series exhibit multifractal scaling behaviour indicating a complex behaviour with long-range time correlations manifested on different intrinsic time scales. Such a behaviour typically points to the presence of recurrent economic cycles, crises, large fluctuations, and other...

Parametric volatility models can be seen as the result of some form of dimensionality reduction obtained by projecting the volatility surface into a basis of risk factors. Examples include polynomial models and stochastic volatility models having an explicit expression for the smile, such as the...

To capture the extra returns embedded in the tails of the market distributions, the literature focused on adding stochastic processes to the diffusion coefficient of the asset prices or even jumps to the asset prices as the drift was forced to match the risk-free rate. However, if we assume that...

The only thing one can say about financial markets is that parsimonious information on option prices is available in time and space, and that we can only use the No-Dominance law (or stronger version of No-Arbitrage) to account for it. Thus, one requires a consistent model to assess relative...

We describe a single parametric model for the entire volatility surface with interpolation and extrapolation technique generating a smooth and robust implied volatility surface without arbitrage in space and time. It is used for marking option prices on indices and single stocks as well as for...

We consider a stochastic local volatility model with domestic and foreign stochastic interest rates such that the volatility decomposes into a deterministic local volatility plus some bias terms. Assuming a collapse process for the variance with the same random variable for all time and...

The implied volatility surface being a mapping from Black-Scholes prices, necessary and sufficient conditions for the surface to be free from static arbitrage must be defined in terms of the properties and limits of the Black-Scholes formula. Acknowledging this argument, we develop a parametric...

We seek to estimate a portfolio of option prices in an entirely data driven way, at any future time, for trading and risk management purposes in a model independent way. We do not know the model driving the dynamics of the actual stock prices, but only observe discretely their evolution in the...

In the second part of a series of articles on the pricing of interest rate contingent claims in the multifactor Quadratic Gaussian model, we concentrate on the pricing of swaptions. Assuming the zero-coupon bond volatility to be a deterministic function of some Markov processes, we derive the...