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 Vega Hedging Principles
Issued on March 10 2010 par Strategies-options.com
Implied volatility tends to vary.
Black & Scholes Model assumes that volatility is quite constant. This is far from reality and it's a risk that needs to be hedged.
Market prices are built by demand and supply much more than by a model. Of course there are some relations that prevent from basic arbitrage such as call-put parity, but even those relations could sometime be misleading. - In real world it's possible for a call to be worth less after an up move on the underlying, because the implied volatility decreased. - In real world it's possible for a put to be worth much more after an up move on the underlying, because the implied volatility soared. That way, there is a natural need for a serious protection against implied volatility moves. I - Principle If we want to have an impact on the way implied volatility varies, we have to deal with options. Vega exists only for options. As far as we we to hedge a vega, we would have to trade another option. II - Example Options V1 et V2 are quoted with vegas υ1=0.015 and υ2=0.005. The portfolio is long 50 shares and long 10 V1 options. A Problem : If volatility moves up, it's good, and we gonna have an additional profit made by that move. If it drops, we would lose money. That's a risk we would rather not incur. A solution : υ1=0.015 υ2=0.005 If one just trades 100*0.015/0.005=30 options V2, it would be enough to neutralize the whole vega. The portfolio would be then : - long 50 shares - long 10 V1 options - short 30 V2 options In fact, it's enough to trade υ1 / υ2 options to be vega hedged. Sell short (Buy) υ1/υ2 V2 options for each V1 option bought (sold) Where υ1 is V1 option vega υ2 is V2 option vega III - A local Hedge As far as markets move on, vega ratio moves too. Hence there is no such a thing as a steady vega stability in an options book. By vega hedging long Atm/Itm options with short deep out of the money options, there is a need to trade a large quantity of that short position. Big short selling of out the money options positions can be revealed dangerous for a portfolio management. Next : Volatility Arbitrage Previous : Gamma Hedging Hedging : Principles Delta Hedging Principles Gamma Hedging Principles Vega Hedging Principles Hedging : A First Attempt Delta Hedging : A First Attempt Gamma Hedging : A First Attempt Hedging Delta Hedging Related Pdf : - Delta-hedging Vega Risk ? - Implied Volatility Term Structure and Vega Hedging in the Q-Alpha-Sigma Model - The Sensitivity of Vega - Foreign Exchange Options Strategies-options.com |
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