We extend the valuation of contingent claims in presence of default, collateral and funding to a random functional setting and characterise pre-default value processes by martingales. Pre-default value semimartingales can also be described by BSDEs with random path-dependent coefficients and...

We consider the problem of using risk-return analysis tools in investment decisions. According to cumulative prospect theory, people make decisions based on an S-shaped value function. This means that the risk-return analysis tools that are derived from expected utility theory, may inconsistent...

The main assumption of the vanna-volga method is the existence of a flat but stochastic implied volatility for the pricing of vanilla options. Even though `flat but stochastic' appears to be self-contradictory, it is to an extent justified on empirical grounds. In this short note we argue that...

This supplementary material for "Asymptotics for the Survival Probability of Time-Inhomogeneous Diffusion Processes" contains (i) some facts related to the normal density and distribution functions (Section 1), which are used in the calculation of explicit formulas in Equation (19) (Section 2);...

We consider the joint SPX-VIX calibration within a general class of Gaussian polynomial volatility models in which the volatility of the SPX is assumed to be a polynomial function of a Gaussian Volterra process defined as a stochastic convolution between a kernel and a Brownian motion. By...

This study provides a sufficient and necessary condition in which the risk-neutral measure is first-order stochastically dominated by the physical measure. Various sufficient conditions are also developed under the consumption-based equilibrium model. We also show that, if stochastic dominance...

Deribit exchange offers about 90\% open interest in the recent cryptocurrency options market. The dominating type of options listed in Deribit is the inverse BTC option, which is settled in BTC and thus allows professional traders to avoid frequent convert between cryptocurrency and fiat...

We apply a two-step strategy to forecast the dynamics of the volatility surface implicit in option prices to all American-style options written on the stocks that have entered the Dow Jones Industrial Average Index between 2004 and 2016. We explore whether the implied volatilities extracted...