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Archive for the ‘Hedging’ Category

Risk and Volatility: Econometric Models and Financial Practice

14 Oct

Article by: Robert F. Engle III
Nobel lecture
Date: 8 Dec 2003

“The advantage of knowing about risks is that we can change our behavior to
avoid them. Of course, it is easily observed that to avoid all risks would be impossible;
it might entail no flying, no driving, no walking, eating and drinking
only healthy foods and never being touched by sunshine. Even a bath could
be dangerous. I could not receive this prize if I sought to avoid all risks. There
are some risks we choose to take because the benefits from taking them exceed
the possible costs. Optimal behavior takes risks that are worthwhile. This
is the central paradigm of finance; we must take risks to achieve rewards but
not all risks are equally rewarded. Both the risks and the rewards are in the future,
so it is the expectation of loss that is balanced against the expectation of
reward. Thus we optimize our behavior, and in particular our portfolio, to
maximize rewards and minimize risks.

“This simple concept has a long history in economics and in Nobel citations.
Markowitz (1952) and Tobin (1958) associated risk with the variance in
the value of a portfolio. From the avoidance of risk they derived optimizing
portfolio and banking behavior. Sharpe (1964) developed the implications
when all investors follow the same objectives with the same information. This
theory is called the Capital Asset Pricing Model or CAPM, and shows that
there is a natural relation between expected returns and variance.”

Full article (PDF): Link

 

Understanding VIX futures and options

30 Sep

Article by: Dennis Dzekounoff
Published by: FuturesMag.com
Date: 18 Aug 2010

“Since the Chicago Board Options Exchange (CBOE) introduced futures and, subsequently, options on its Volatility Index, or VIX, traders have asked why the contracts don’t necessarily track the underlying in the same way other equity futures track their indexes. Others may wonder why the put-call parity is violated for VIX options. Then, there are the options that trade underwater, the vastly different implied volatilities for each expiration cycle and the question of arbitrage between S&P 500 derivatives and VIX contracts.

“Thankfully, all of these questions can be answered with theoretical research on VIX futures and options pricing and, along the way, can offer guidance to some practical applications of these products. Our findings also apply to recently launched VSTOXX index futures and options listed on Eurex.”

Full article: Link

 
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