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...

Using the properties of the Affine and Quadratic models, we derive the price of a forward starting call option in a jump-diffusion model. Conditioning that price at the determination time of the strike we use a general pricing approximation technique for call options in a jump-diffusion model to...

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...

We discuss risk, preference and valuation in classical economics, which led academics to develop a theory of market prices, resulting in the general equilibrium theories. However, in practice, the decision process does not follow that theory since the qualitative aspect coming from human...

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...

The causal relationship between atmospheric CO2 concentrations and global temperature is well established, but the degree of sensitivity of future temperature rise to both existing levels of CO2 and continued carbon emissions is still subject to a high degree of uncertainty. Governments have...

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...

According to the World Economic and Social Survey 2009, the review of available estimates of mitigation and adaptation costs suggests that additional annual total investments in developing countries could be upwards of $1 trillion per year. Given the limited ability of developing countries to...

Natural hazard events in 2010 and 2011 such as the eruption of the volcano Eyjafjallajokull on Iceland, the heatwave in Russia, the extreme floods in northeastern Australia, and more recently the earthquake followed by a tsunami at Fukushima in Japan demonstrated the vulnerability of the...

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...