منابع مشابه
Maturity cycles in implied volatility
The skew effect in market implied volatility can be reproduced by option pricing theory based on stochastic volatility models for the price of the underlying asset. Here we study the performance of the calibration of the S&P 500 implied volatility surface using the asymptotic pricing theory under fast mean-reverting stochastic volatility described in [7]. The time-variation of the fitted skew-s...
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This note explores the behaviour of the implied volatility of a European call option far frommaturity. Asymptotic formulae are derived with precise control over the error terms. The connection between the asymptotic implied volatility and the cumulant generating function of the logarithm of the underlying stock price is discussed in detail and illustrated by examples.
متن کاملThe Small-maturity Implied Volatility Slope for Lévy Models
We consider the at-the-money strike derivative of implied volatility as the maturity tends to zero. Our main results quantify the growth of the slope for infinite activity exponential Lévy models. As auxiliary results, we obtain the limiting values of short maturity digital call options, using Mellin transform asymptotics. Finally, we discuss when the at-the-money slope is consistent with the s...
متن کاملImplied Volatility Smirk
This paper studies implied volatility smirk quantitatively. We first propose a new concept of smirkness, which is defined as a triplet of at-the-money implied volatility, skewness (slope at the money) and smileness (curvature at the money) of implied volatility – moneyness curve. The moneyness is the logarithm of the strike price over the forward price, normalized by the standard deviation of e...
متن کاملDeterministic implied volatility models
Abstract In this paper, we characterize two deterministic implied volatility models, defined by assuming that either the per-delta or the per-strike implied volatility surface has a deterministic evolution. Practitioners have recently proposed these two models to describe two regimes of implied volatility (see Derman (1999 Risk 4 55–9)). In an arbitrage-free sticky-delta model, we show that the...
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ژورنال
عنوان ژورنال: Finance and Stochastics
سال: 2004
ISSN: 0949-2984,1432-1122
DOI: 10.1007/s00780-004-0126-7