Download Semiparametric Modeling of Implied Volatility by Matthias R. Fengler PDF

By Matthias R. Fengler

This booklet bargains fresh advances within the concept of implied volatility and sophisticated semiparametric estimation ideas and measurement aid tools for sensible surfaces. the 1st half is dedicated to smile-consistent pricing ways. the second one half covers estimation recommendations which are traditional applicants to satisfy the demanding situations in implied volatility surfaces. Empirical investigations, simulations, and images illustrate the concepts.

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Extra resources for Semiparametric Modeling of Implied Volatility

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67), Wilmott (2001a, Chap. 70) where f is some smooth function. 70), yields 2 ∂H ∂t 1 2∂ H = σ 2 (t)S 2 . 73) which is independent from time in its coefficients. Also, the boundary condition for a (European) call H(S T , T ) = H(ST , T ) = (ST − K)+ (or a European put) stays the same after these manipulations. 73), we can rewrite this in the original variables as H(S, t) = e−r(T −t) H{Se(r−δ)(T −t) , f (t)} . 74) Now denote by H BS the BS solution with constant volatility σ. 75) BS for some function H .

G. Jorion (1995), and Amin and Ng (1997), respectively. Most recent research focusses on long memory and fits fractionally integrated autoregressive models for the volatility forecast, Andersen et al. (2003) and Pong et al. (2003). This appears to be a promising line of research. The overall consensus of the literature regardless of the market and the forecasting horizon under scrutiny appears to be – for an exception see Canina and Figlewski (1993) – that IV based predictors do contain a substantial amount of information on future volatility and are better than (only) time series based methods.

Volatility risk is unpriced. This is sensible if volatility risk can diversified away, or preferences are logarithmic, Pham and Touzi (1996). The measure Q0 can also be interpreted as the closest measure to P in an relative entropy sense, F¨ollmer and Schweizer (1990). e. a self-financing strategy with minimum initial costs is seeked such that any future obligation from selling the contingent claim is covered, while in quantile-hedging one tries to cover this obligation only with a sufficiently high probability.

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