Derivatives on the Chicago Board Options Exchange volatility index (VIX) have gained significant popularity over the last decade. The pricing of VIX derivatives involves evaluating the square root of the expected realised variance which cannot be computed by direct Monte Carlo methods. Least...

According to Basel III, financial institutions have to charge a Credit Valuation Adjustment (CVA) to account for a possible counterparty default. Calculating this measure and its sensitivities is one of the big challenges in risk management. Here we introduce an efficient method for the...

Certificates are structured financial instruments that aim to provide investors with investment solutions tailored to their needs. Certificates can be modeled using a bond component and a derivative component, typically an options strategy. The pricing of certificates is typically performed...

The recently proposed canonical least-squares Monte Carlo (CLM) method is extended by incorporating uniquely a variance constraint in the derivation of the equivalent martingale measure used by CLM. This derivation can be viewed as a change of measure numerically by modifying both the drift term...

The least squares Monte Carlo method of Longstaff and Schwartz (2001) has become a standard numerical method for option pricing with many potential risk factors. An important choice in the method is the number of regressors to use and using too few or too many regressors leads to biased results....

Pushing models to extremes can expose output biases that stem from underlying assumptions. In the case of industry standard option valuation models, long term, high volatility securities provide a stress test vehicle. For instance, in evaluating a stock with 60% volatility, industry standard...

This paper examines the efficiency of standard variance reduction techniques across option characteristics when pricing American-style call and put options with the Least-Squares Monte Carlo algorithm of Longstaff & Schwartz (2001). Our numerical experiments evaluate the efficiency of antithetic...

In this paper, we evaluate American-style, path-dependent derivatives with an artificial intelligence technique. Specifically, we use swarm intelligence to find the optimal exercise boundary for an American-style derivative. Swarm intelligence is particularly efficient (regarding computation and...

This paper demonstrates that it is possible to improve significantly on the estimated call prices obtained with the regression and simulation-based least-squares Monte Carlo method by using put-call symmetry. The results show that, for a large sample of options with characteristics of relevance...