TY - JOUR

T1 - On estimation of volatility surface and prediction of future spot volatility

AU - Klebaner, Fima

AU - Le, Truc

AU - Liptser, Robert

N1 - Funding Information:
We thank W. Shaw for helpful comments and for bringing the issues of small Vega and model instability to our attention. This research was supported by the Australian Research Council Grant DP0451657 and was a joint-work with R. Liptser while he was visiting Monash university during year 2005.

PY - 2006/9/1

Y1 - 2006/9/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=33751558422&partnerID=8YFLogxK

U2 - 10.1080/13504860600564661

DO - 10.1080/13504860600564661

M3 - מאמר

AN - SCOPUS:33751558422

VL - 13

SP - 245

EP - 263

JO - Applied Mathematical Finance

JF - Applied Mathematical Finance

SN - 1350-486X

IS - 3

ER -