Uniform Bounds for Black--Scholes Implied Volatility
نویسندگان
چکیده
منابع مشابه
Uniform Bounds for Black-Scholes Implied Volatility
The Black–Scholes implied total variance function is defined by VBS(k, c) = v ⇔ Φ ( − k/ √ v + √ v/2 ) − eΦ ( − k/ √ v − √ v/2 ) = c. The new formula VBS(k, c) = inf x∈R [ Φ−1 ( c + eΦ(x) ) − x ]2 is proven. Uniform bounds on the function VBS are deduced and illustrated numerically. As a by-product of this analysis, it is proven that F is the distribution function of a logconcave probability me...
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ژورنال
عنوان ژورنال: SIAM Journal on Financial Mathematics
سال: 2016
ISSN: 1945-497X
DOI: 10.1137/14095248x