On estimation of volatility surface and prediction of future spot volatility

Fima Klebaner, Truc Le, Robert Liptser

Research output: Contribution to journalArticlepeer-review

Abstract

A stochastic process v(t) is considered as a model for asset's spot volatility. A new approach is introduced for predicting future spot volatility and future volatility surface using a finite set of observed option prices. When the volatility parameter σ2 in the Black-Scholes formula L=SΦ(d1)-Ke-r(T-t)Φ(d2) is represented by the integrated volatility ∫tT v(s)ds/(T-t), then the local volatility surface can be estimated. The main idea is to linearize the expressions for implied volatility by using a result on Normal correlation. This linearization is obtained by introducing various ad hoc approximations.

Original languageEnglish
Pages (from-to)245-263
Number of pages19
JournalApplied Mathematical Finance
Volume13
Issue number3
DOIs
StatePublished - 1 Sep 2006

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