Derivatives Pricing and Hedging

Derivatives HedgingThe financial crisis has placed a magnifying glass over the world of derivatives.  Though they have been characterized as “financial weapons of mass destruction”, financial derivatives have been around for centuries and serve as a way for individuals and institutions that are risk averse to transfer risk to someone whom is willing to take it.

Typical users include investment banks and hedge funds.

Problem: The Black-Scholes-Merton (BSM) options pricing model was first published in 1973.  In it, Black and Scholes showed provided a closed-form solution to the value of options prices.  This model has been the subject of controversy.  Many people dispute point to the limitations of the BSM mode in pointing out the model under-estimates the probability of extreme moves, and assumes cost-free, riskless trading to properly hedge.  How should options be priced and hedged if various assumptions of the BSM model are relaxed?

Solution: With optimized derivatives pricing and hedging, traders can make their own assumptions regarding the distribution of returns as well as the costs of properly hedging the option given available prices and volumes of hedges in the market.  The trader can determine how much of the option is not hedged, what is the optimum hedge given a budget, and what are the remaining risks after hedging?

Resources on Options Pricing and Hedging:
Minimizing CVaR and VaR for a Portfolio of Derivatives