English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We present a new Monte Carlo methodology for the accurate estimation of thedistribution of the sum of dependent log-normal random variables. Themethodology delivers statistically unbiased estimators for three distributionalquantities of significant interest in finance and risk management: the lefttail, or cumulative distribution function, the probability density function,and the right tail, or complementary distribution function of the sum ofdependent log-normal factors. In all of these three cases our methodologydelivers fast and highly accurate estimators in settings for which existingmethodology delivers estimators with large variance that tend to underestimatethe true quantity of interest. We provide insight into the computationalchallenges using theory and numerical experiments, and explain their much widerimplications for Monte Carlo statistical estimators of rare-eventprobabilities. In particular, we find that theoretically strongly-efficientestimators should be used with great caution in practice, because they mayyield inaccurate results in the pre-limit. Further, this inaccuracy may not bedetectable from the output of the Monte Carlo simulation, because thesimulation output may severely underestimate the true variance of theestimator.

Accurate Computation of the Distribution of Sums of Dependent Log-Normals with Applications to the Black-Scholes Model