Asymptotics of Implied Volatility far from Maturity

By Michael Tehranchi. Journal of Applied Probability, 2009

59 citations recorded by the source corpus.

Subfields: Finance

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Asymptotics for Exponential Levy Processes and Their Volatility Smile: Survey and New Results (2012, result): “Under mild regularity conditions, [117], [103] use large deviation principles to demonstrate that the implied volatility surface will always flatten out for large enough maturities and finite strikes, irrespective of the underlying process assumptions, which agrees with earlier observations by [11].”
Asymptotic formulae for implied volatility in the Heston model (2009, unknown): “Recently Tehranchi [33] studied the large-time behaviour of the implied volatility when the stock price is a non-negative local martingale and obtained an analogue of formula (2) in that setting.”
A NEW LOOK AT SHORT‐TERM IMPLIED VOLATILITY IN ASSET PRICE MODELS WITH JUMPS (2012, unknown): “fixed t and k → ±∞ [15, 9, 12]; t → ∞ with k constant [25] or proportional [14] to t; t→ 0 and k constant [20, 24, 8] etc.”
Pricing and Hedging in Exponential Lévy Models: Review of Recent Results (2011, methodology): “However, the results of Rogers and Tehranchi [45] suggest otherwise: they give the following upper bound, valid in exponential Lévy models as soon as E[|Xt| ∞], for the rate of convergence of the implied volatility skew to zero: lim sup τ→∞ sup k1,k2∈[−M,M ] τ ∣ ∣ ∣ ∣ I(τ, k2) 2 − I(τ, k1)2 k2 − ”