A variance/volatility swap is an instrument that allows explicit exposure to the realized variance/volatility of an index, stock, etc., without exposure to other risks commonly encountered with derivatives: delta, gamma, etc.

We review the equity forward and futures pricing models. Consider an index level, I, at a future time, T. With respect to I, we calculate 1) the forward price, 2) the futures price, and 3) delta.

A valuation model is presented to calculate price, hedge ratio, and implied volatility for forward starting European calls and puts. The model focuses on the numerical accuracy of the implementation.

The model calculates numbers that characterize the effect of adding an extra instrument to a portfolio of loan commitments. To be useful, these numbers should be additive with respect to the facilities making up the portfolio, so that their total would have the same meaning for the portfolio as each individual number has for the respective…[Read more]

La théorie du chaos n’est pas aussi complexe qu’on le prétend souvent Comme l’observe Robert Juliano, le principe sous-jacent est que “dans le caractère aléatoire apparent des systèmes complexes chaotiques, il existe des modèles sous-jacents, des interconnexions, des boucles de rétroaction constantes, la répétition, l’auto-similarité , fractales…[Read more]

Equity value at risk (VaR) model requires implied volatilities with respect to various indices and maturities, which range from three months to five years. A model is presented for generating a term-structure of implied equity index volatilities for use in calculating VaR.

Since 2016, the academic narrative emerging from the Zora Neale Hurston Festival of the Arts and Humanities in Eatonville, Florida, has increasingly relied on a public scholarship model to bridge the gap between institutional practice and community knowledge. Inspired by Zora Neale Hurston’s legacy as an interdisciplinary scholar, these a…[Read more]

A model is used to price a derivative whose payoff depends on returns over N periods on a shrinking basket of originally N assets. Each period, the worst return is added to the cumulative sum after being capped and floored, and the corresponding asset removed from the basket (hence a shrinking basket). The cap and floor rates are given for each…[Read more]

Credit value at risk (VaR) is used for measuring and analyzing credit risk of a portfolio. The basic methodology of the Credit VaR employs the credit migration approach spearheaded by RiskMetrics. It assumes that obligor’s credit quality is determined by the obligor’s asset value, which in turn is approximated by its standardized equity return.

Chaos theory is not as complex as it si often made out to be As Robert Juliano observes, the underlying principle is that “within the apparent randomness of chaotic complex systems, there are underlying patterns, interconnectedness, constant feedback loops, repetition, self-similarity, fractals, and self-organization.”

“Chaos has been for…[Read more]

This paper presented at the Fourth International Conference and Industrial Exhibitoion on Dairy Science Park IV, Nov 1-5, 2017, Konya, Turkey, has reviewed the philosophy of Mevlana Jalal ud Din Rumi regarding love, tolerance, respect and spiritualism; appreciating each others and knowing the value of each other. Rumi (1230) told Iqbal (1930)…[Read more]