Hedging of illiquid financial instruments is carried out with liquid instruments that, as a rule, have simpler payoff functions. For example, hedging of Asian or long-dated put options is carried out with vanilla puts, hedging of Bermuda swaptions is done with vanilla swaptions, etc. This kind...

There has been a recent explosion in the application of nonlinear stochastic differential equations in various applied fields. Often, proposed solutions rely on passage to the corresponding deterministic Fokker-Planck equations. However, substitution of nonlinear stochastic differential...

The first ever explicit formulation of the concept of the option's probability density functions has been introduced in our publications “Breakthrough in Understanding Derivatives and Option Based Hedging - Marginal and Joint Probability Density Functions of Vanilla Options - True...

• It is not widely emphasized in the literature that derivatives are complex random quantities which should, by custom, be characterized by their probability density functions. • It is understood that Black-Scholes style of derivatives pricing represents an expected value, i.e. the...

• Various statistics of future price level excursions are driving decision making of both sophisticated and amateur traders, although the latter are not necessarily aware of it. Such statistics are of paramount importance in intelligent placement of limit orders and monitoring their...

Demonstration that noise filtered correlation matrices can be used for early detection of a regime change in temporal behavior of securities. This demonstration was carried out for a portfolio of 40 S&P500 securities with just two, randomly chosen, securities undergoing a deliberately arranged...

Demonstration that in-sample Markowitz type mean-variance optimization, carried out with noise filtered covariance matrices, results in asset allocation that leads to 2-3 times increase of the Sharpe ratio compared to the same optimization carried out without noise filtering.Demonstration of 2-3...

Demonstration that our noise filtering procedure is extremely robust on the basis of the following experiment. The noise filtering procedure was applied first to an empirical correlation matrix and, second, to the matrix built from the same time series deliberately contaminated with noise. The...

Demonstration that our noise filtering procedure is extremely robust on the basis of the following experiment. The noise filtering procedure was applied first to an empirical correlation matrix and, second, to the same matrix deliberately contaminated with noise. The final, noise filtered...

Demonstration of the omnipresence of noise in volatilities of returns of financial instruments.Demonstration that more than 30% of SP500 securities can have percentage change in volatility of more than 10% as a result of noise filtering.In our white paper “Filtering Noise From Correlation...