Do S&P 500 index options violate the martingale restriction?

Article Abstract:

A lognormal distribution analysis of the Standard and Poor's 500-Stock Price Index (S&P 500 index) from 1990 to 1994 reveals a systematic violation of Longstaff's martingale restriction. The restriction states that the implied value of the options must never go beyond the value of the market. A generalized distribution, which includes solving for the initial four implied moments, was determined to be a better model for analyzing the performance of the S&P 500.

All Other Publishers, Miscellaneous publishing, Business Service Index Pubs, Analysis, Usage, Stock price indexes, Indexes (Information retrieval), Business literature, Standard and Poor's 500-Stock Price Index, Martingales (Mathematics)

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Pricing VIX futures: evidence from integrated physical and risk-neutral probbaility measures

Article Abstract:

Volatility index (VIX) futures models allowing for stochastic and state-dependent volatility are derived. The stochastic volatility model with price jumps (SVJ model) works best for short-dated VIX futures, while the stochastic volatility model with state-dependent and correlated jumps (SVSCJ model) works best for medium and long-dated VIX futures.

Taiwan, Science & research, Models, Financial futures, Report, Volatility (Finance)

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Pricing FTSE 100 index options under stochastic volatility

Article Abstract:

Research into the improvement in the pricing of FTSE 100 index options when taking stochastic volatility into consideration indicates that there is strong evidence of stochastic volatility implicit in option prices. There is significant mispricing for short-term options.

Prices and rates, Options (Finance), Stochastic systems

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