# On decoupling of volatility smile and term structure in inverse option pricing

@article{Egger2006OnDO, title={On decoupling of volatility smile and term structure in inverse option pricing}, author={Herbert Egger and Torsten Hein and Bernd Hofmann}, journal={Inverse Problems}, year={2006}, volume={22}, pages={1247-1259} }

Correct pricing of options and other financial derivatives is of great importance to financial markets and one of the key subjects of mathematical finance. Usually, parameters specifying the underlying stochastic model are not directly observable, but have to be determined indirectly from observable quantities. The identification of local volatility surfaces from market data of European vanilla options is one very important example of this type. As with many other parameter identification…

## 45 Citations

Convergence rates results for recovering the volatility term structure including at-the-money options

- Mathematics
- 2009

Abstract Determining the term structure of local volatilities with at-the-money options represents a singular situation. On the one hand, prices of options with strikes close to the current asset…

Convex Regularization of Local Volatility Models from Option Prices : Convergence Analysis and Rates

- 2012

We study a convex regularization of the local volatility surface identification problem for the Black-Scholes partial differential equation from prices of European call options. This is a highly…

Convex regularization of local volatility models from option prices: Convergence analysis and rates

- Mathematics
- 2012

Abstract We study a convex regularization of the local volatility surface identification problem for the Black–Scholes partial differential equation from prices of European call options. This is a…

Simultaneous identification of volatility and interest rate functions-a two-parameter regularization approach

- MathematicsETNA - Electronic Transactions on Numerical Analysis
- 2019

This paper investigates a specific ill-posed nonlinear inverse problem that arises in financial markets. Precisely, as a benchmark problem in the context of volatility surface calibration, we…

Stable Parameter Identification Evaluation of Volatility

- Mathematics
- 2012

Using the dual Black-Scholes partial differential equation, Dupire [6] derived an explicit formula, involving the ratio of partial derivatives of the evolving fair value of a European call option…

Calibrating local volatility in inverse option pricing using the Levenberg–Marquardt method

- Mathematics
- 2010

Abstract We derive an iterative algorithm for an Inverse Problem of Option Pricing. The aim is to determine the local volatility such that the corresponding solutions of the Black–Scholes equation…

A direct formulation of implied volatility in the Black- Scholes model

- Economics
- 2010

The inverse problem of option pricing, also known as market calibration, attracted the attention of a large number of practitioners and academics, from the moment that Black-Scholes formulated their…

Recovery of time-dependent volatility in option pricing model*

- Mathematics
- 2016

In this paper we investigate an inverse problem of determining the time-dependent volatility from observed market prices of options with different strikes. Due to the non linearity and sparsity of…

Some aspects of parameter identification in a mean reverting financial asset model with time-dependent volatility

- Mathematics, Computer ScienceInt. J. Comput. Math.
- 2009

The present paper deals with several aspects and procedures of identification in a financial market model with time-dependent volatility function and mean reverting stochastic drift term and suggests an estimator that is based on a projection on an orthonormal wavelet basis.

On implied volatility recovery of a time-fractional Black-Scholes equation for double barrier options

- MathematicsApplicable Analysis
- 2020

ABSTRACT This paper investigates a time-fractional Black-Scholes equation with an implied volatility which is assumed to be associated with underlying price. Two aspects are considered. One is for…

## References

SHOWING 1-10 OF 35 REFERENCES

Tikhonov regularization applied to the inverse problem of option pricing: convergence analysis and rates

- Mathematics
- 2005

This paper investigates the stable identification of local volatility surfaces σ(S, t) in the Black–Scholes/Dupire equation from market prices of European Vanilla options. Based on the properties of…

Computation of Deterministic Volatility Surfaces

- Economics
- 1998

The 'volatility smile' is one of the well-known biases of Black-Scholes models for pricing options. In this paper, we introduce a robust method of reducing this bias by pricing subject to a…

A technique for calibrating derivative security pricing models: numerical solution of an inverse problem

- Economics
- 1997

A technique is presented for calibrating derivative security pricing models with respect to observed market prices. This technique can be applied in a very general multifactor setting where model…

Calibration of the Local Volatility in a Generalized Black-Scholes Model Using Tikhonov Regularization

- Mathematics, Computer ScienceSIAM J. Math. Anal.
- 2003

Applying general results available in the theory of Tikhonov regularization for ill-posed nonlinear inverse problems, the stability of this approach, its convergence towards a minimum norm solution of the calibration problem, and convergence rates issues are proved.

On the nature of ill-posedness of an inverse problem arising in option pricing

- Mathematics
- 2003

Inverse problems in option pricing are frequently regarded as simple and resolved if a formula of Black–Scholes type defines the forward operator. However, precisely because the structure of such…

The inverse problem of option pricing

- Mathematics
- 1997

Valuation of options and other financial derivatives critically depends on the underlying stochastic process specified for a particular market. An inverse problem of option pricing is to determine…

Pricing with a Smile

- Economics
- 1994

prices as a function of volatility. If an option price is given by the market we can invert this relationship to get the implied volatility. If the model were perfect, this implied value would be the…

Identifying the volatility of underlying assets from option prices

- Mathematics
- 2001

In this paper, we use an optimal control framework to determine implied volatility and make a rigorous mathematical analysis of this inverse problem. We also prove the approximate optimal solutions…

Some Analysis of Tikhonov Regularization for the Inverse Problem of Option Pricing in the Price-Dependent Case

- Mathematics
- 2005

This paper deals with analytic studies for solving the inverse problem of identifying purely price-dependent volatilities from given option price data. Using the classical theory of parabolic di…

TOPICAL REVIEW: Uniqueness, stability and numerical methods for the inverse problem that arises in financial markets

- Mathematics
- 1999

Market prices of financial derivatives such as options are directly observable. This information can be used to recover an unobservable local volatility function for the underlying stochastic…