New PDF release: Semiparametric Modeling of Implied Volatility

By Matthias R. Fengler

ISBN-10: 3540262342

ISBN-13: 9783540262343

This booklet bargains contemporary advances within the concept of implied volatility and subtle semiparametric estimation recommendations and measurement relief equipment for useful surfaces. the 1st half is dedicated to smile-consistent pricing methods. the second one half covers estimation options which are traditional applicants to satisfy the demanding situations in implied volatility surfaces. Empirical investigations, simulations, and photographs illustrate the concepts.

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7. As has been stated earlier, the assumption of no-arbitrage is equivalent to the existence of an equivalent martingale measure. Unlike to Sect. 1, the market is not complete due to the additional source of risk. In general, there exists an entire set of equivalent martingale measures Q. A martingale measure Q ∈ Q can be characterized by the Radon-Nikod´ ym derivative using Girsanov’s Theorem, Chap. 85) 0 are (Ft )0≤t≤T ∗ -adapted processes. 86) 0 are Brownian motions on the space (Ω, F, Q) for all t ∈ [0, T ∗ ].

OTM put regions display higher levels of IV than OTM call regions, lower panel of Fig. 8 and Fig. 9. However, this has not always been the case: a more or less symmetric smile became strongly asymmetric (a ‘sneer’, or ‘smirk’) and considerably more pronounced after the 1987 crash. It is widely argued that this is due to the investors’ increased awareness of market down-swings since this period, Rubinstein (1994). 4. The volatility of IV is biggest for short maturity options and monotonically declining with time to maturity, Fig.

Das and Sundaram (1999) investigate more deeply the implications of the models concerning the shape of the smile and the term structure of the IVS. According to them, stochastic volatility smiles are too shallow, while jump diffusions imply the smile only for short maturity options. Moreover, they prove that jump diffusions always imply an increasing term structure of IV. However, empirically, also a decreasing or at least humped term structure is observed, compare Fig. 11 for the years 1997 and 2000.

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Semiparametric Modeling of Implied Volatility by Matthias R. Fengler

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