The exact Taylor formula of the implied volatility
نویسندگان
چکیده
منابع مشابه
The Moment Formula for Implied Volatility at Extreme Strikes
Consider options on a nonnegative underlying random variable with arbitrary distribution. In the absence of arbitrage, we show that at any maturity T , the large-strike tail of the Black-Scholes implied volatility skew is bounded by the square root of 2|x|/T , where x is log-moneyness. The smallest coefficient that can replace the 2 depends only on the number of finite moments in the underlying...
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It is “well known” that there is no explicit expression for the Black-Scholes implied volatility. We prove that, as a function of underlying, strike, and call price, implied volatility does not belong to the class of Dfinite functions. This does not rule out all explicit expressions, but shows that implied volatility does not belong to a certain large class, which contains many elementary funct...
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By a deformation of the integers we mean a sequence x = {xn, n ∈ N} of polynomials in one or more variables and with integral coefficients, having the property that there exists some value q0 of the variables such that ∀n ∈ N, xn(q0) = n. The quantum integers xn = ∑n−1 l=0 q l are a typical example of a deformation of the integers. Another example is given by the version of the Chebyshev polyno...
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The author considers SABR (stochastic-αβρ) model which is a two factor stochastic volatility model and give an asymptotic expansion formula of implied volatilities for this model. His approach is based on infinite dimensional analysis on the Malliavin calculus and large deviation. Furthermore, he applies the approach to a foreign exchange model where interest rates and the FX volatilities are s...
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ژورنال
عنوان ژورنال: Finance and Stochastics
سال: 2017
ISSN: 0949-2984,1432-1122
DOI: 10.1007/s00780-017-0330-x