Developing a closed-form integral Vasicek representation of loss distribution for non-uniform credit portfolio (i.e. with varying PDs and structured correlations), which i) is non-iterative and computationally fast as opposed to standard Monte-Carlo, and ii) enables efficient analytic estimators...

Procedures for constructing the characteristic functions of risk neutral densities, from option prices at a fixed maturity, are developed. The logarithm of these characteristic functions are shown to synthesize the Fourier transform of formal Lévy tails. The formal Lévy tails are actual Lévy...

Abrupt changes are a prevalent feature of financial data sets, such as prices of financial assets, returns of stocks, exchange rates, etc. An early warning system (EWS) can detect existing changes and predict possible future changes before they occur. Two important statistical models for change...

In this paper, we derive a probabilistic approximation for three different versions of the SABR model: Normal, Log-Normal and a displaced diffusion version for the general constant elastic of variance case. Specifically, we focus on capturing the terminal distribution of the underlying process...

Structural models have been developed and used in financial literature to assess the probability of default of corporations. This article aims at reversing this approach, using this probability as an input and investigating if the default barrier can be considered flat, as done in similar...

We present a portable model of distorted learning which embodies Tversky and Kahneman's (1971) “belief in the law of small numbers.” When adjusting beliefs in response to new information the decision maker overweights the sample, updating as if the sample size were inflated. The degree of...

We derive a simple integral equation for the default probability over a finite time horizon of a company that makes coupon payments on its debt and infrequently returns to its leverage target by increasing its debt unless it defaults on its debt. Compared to the conventional (constant default...

For most events, risk-neutral outcome probabilities are identical across numeraire currencies. Some events, however, such as elections or referendums, may have an impact on exchange rates. This implies numeraire dependence in risk-neutral outcome probabilities, which leads to different state...

We present a general purpose technique for the efficient and accurate valuation of options in the shifted Stochastic Alpha Beta Rho (shifted-SABR) model which includes SABR as a special case. The method is based on a novel double-layer continuous-time Markov chain (CTMC) from which closed-form...