Advanced Option Pricing Models by Jeffrey Owen Katz

By Jeffrey Owen Katz

Complicated choice Pricing types info particular stipulations less than which present choice pricing types fail to supply exact fee estimates after which indicates choice investors tips to build better types for greater pricing in a much broader diversity of marketplace stipulations. Model-building steps conceal techniques pricing below conditional or marginal distributions, utilizing polynomial approximations and curve becoming, and compensating for suggest reversion. The authors additionally advance powerful prototype versions that may be positioned to rapid use, with real-time examples of the types in motion.

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Delta can be understood and roughly approximated as the ratio of such a rectangle’s height, measured in option price units, to its width, measured in stock price units. The approximation becomes precise to the extent that the rectangle is small in relationship to the curvature of the price response. Delta is positive when the slope of the response curve is upward, normal for call options, and negative when it is downward, normal for put options. As evident in Figure 1–1, Delta changes with both stock price and time remaining before expiration.

Finally, synthetics and equivalent positions were discussed. , a stock). Equivalent positions were defined as distinct positions that, nevertheless, have the same profit and loss behavior and, consequently, the same profit graphs. The goal of this chapter has been to provide the reader with a working knowledge of the fundamentals and jargon of options. Much of what follows in this book assumes knowledge of such option basics. One fundamental concept of great importance to options traders, arbitrageurs, and investors, is the notion of fair value.

Option premium was found to be influenced by well-known factors such as stock price and strike price, time, volatility, interest and dividends, and by lesser-known factors such as skew, kurtosis, trend, and cycles. Estimating a fair premium, based on such factors, was recognized as a problem for which an option pricing model was the solution. An option pricing model was characterized as a mathematical formula or algorithm that enables its user to calculate a theoretical fair price. An option pricing model, it was noted, not only provides fair value estimates, but also makes it possible to calculate the so-called Greeks.

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