We propose a way to compute the hedging Delta using the Malliavin weight method. Our approach, which we name the l-method, generally outperforms the standard Monte Carlo finite difference method, especially for discontinuous payoffs. Furthermore, our approach is nonparametric, as we only assume...

We propose novel nonparametric estimators for stochastic volatility and the volatility of volatility. In doing so, we relax the assumption of a constant volatility of volatility and therefore, we allow the volatility of volatility to vary over time. Our methods are exceedingly simple and far...

In a thorough study of binomial trees, Joshi introduced the split tree as a two-phase binomial tree designed to minimize oscillations, and demonstrated empirically its outstanding performance when applied to pricing American put options. Here we introduce a "flexible" version of Joshi's tree,...

I document a sizeable bias that might arise when valuing out of the money American options via the Least Square Method proposed by Longstaff and Schwartz (2001). The key point of this algorithm is the regression-based estimate of the continuation value of an American option. If this regression...

We propose an alternative approach to the modeling of the positive dependence between the probability of default and the loss given default in a portfolio of exposures, using a bivariate urn process. The model combines the power of Bayesian nonparametrics and statistical learning, allowing for...

Using telematics data, we study the relationship between claim frequency and distance driven through different models by observing smooth functions. We used Generalized Additive Models (GAM) for a Poisson distribution, and Generalized Additive Models for Location, Scale, and Shape (GAMLSS) that...

Extrapolative methods are one of the most commonly-adopted forecasting approaches in the literature on projecting future mortality rates. It can be argued that there are two types of mortality models using this approach. The first extracts patterns in age, time and cohort dimensions either in a...

This paper considers an alternative way of structuring stochastic variables in a dynamic programming framework where the model structure dictates that numerical methods of solution are necessary. Rather than estimating integrals within a Bellman equation using quadrature nodes, we use nodes...

A new method to estimate longevity risk based on the kernel estimation of the extreme quantiles of truncated age-at-death distributions is proposed. Its theoretical properties are presented and a simulation study is reported. The flexible yet accurate estimation of extreme quantiles of...

Dependent Tail Value-at-Risk, abbreviated as DTVaR, is a copula-based extension of Tail Value-at-Risk (TVaR). This risk measure is an expectation of a target loss once the loss and its associated loss are above their respective quantiles but bounded above by their respective larger quantiles. In...