Journal Article10.1007/S102030050004
Volatility estimation from observed option prices
Phelim P. Boyle,Draviam Thangaraj +1 more
- 01 May 2000
- Vol. 23, Iss: 1, pp 31-52
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TL;DR: In this paper, the authors modify the implementation of Andersen and Brotherton-Ratcliffe to provide another way of dealing with this issue, which is reasonably successful in reproducing the input prices.
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Abstract: It is well established that the standard Black-Scholes model does a very poor job in matching the prices of vanilla European options. The implied volatility varies by both time to maturity and by the moneyness of the option. One approach to this problem is to use the market option prices to back out a local volatility function that reproduces the market prices. Since option price observations are only available for a limited set of maturities and strike prices, most algorithms require a smoothing technique to implement this approach. In this paper we modify the implementation of Andersen and Brotherton–Ratcliffe to provide another way of dealing with this issue. Numerical examples indicate that our approach is reasonably successful in reproducing the input prices.
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Citations
Volatility smile by multilevel least square
Yves Achdou,Olivier Pironneau +1 more
TL;DR: In this article, the authors proposed several algorithms for finding the local volatility from partial observations of the price of an European vanilla option using the Dupire's equation, and the inverse problem is formulated as a least square problem and minimization is done by an interior point method.
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Numerical Procedure for Calibration of Volatility with American Options
Yves Achdou,Olivier Pironneau +1 more
TL;DR: In this article, the discretization of the variational inequality by finite elements is studied in detail, and a calibration procedure, where the volatility belongs to a finite-dimensional space (finite element or bicubic splines) is described.
21
Data driven recovery of local volatility surfaces
TL;DR: The authors examines issues of data completion and location uncertainty, popular in many practical PDE-based inverse problems, in the context of option calibration via recovery of local volatility surfaces, and shows how a model-based adjustment of the asset price may prove advantageous in such situations.
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Recovery of Time-Dependent Parameters of a Black-Scholes-Type Equation: An Inverse Stieltjes Moment Approach
TL;DR: It is shown that the problem of recovering the time-dependent parameters of an equation of Black-Scholes type can be formulated as an inverse Stieltjes moment problem.
A new representation of the local volatility surface
TL;DR: In this article, the authors address the problem of recovering the local volatility surface from option prices consistent with observed market data and derive an explicit formula for the implied volatility together with bounds for the call price and its derivative with respect to the strike price.
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References
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TL;DR: In this article, an option pricing formula was derived for the more general case when the underlying stock returns are generated by a mixture of both continuous and jump processes, and the derived formula has most of the attractive features of the original Black-Scholes formula.
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The Pricing of Options on Assets with Stochastic Volatilities
John Hull,Alan White +1 more
TL;DR: In this article, the option price is determined in series form for the case in which the stochastic volatility is independent of the stock price, and the solution of this differential equation is independent if (a) the volatility is a traded asset or (b) volatility is uncorrelated with aggregate consumption, if either of these conditions holds, the risk-neutral valuation arguments of Cox and Ross [4] can be used in a straightfoward way.
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Dynamic Asset Pricing Theory
Darrell Duffie
- 01 Jan 1992
TL;DR: The "Dynamic Asset Pricing Theory" (DAT) as discussed by the authors is a textbook for doctoral students and researchers on the theory of asset pricing and portfolio selection in multi-period settings under uncertainty.
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Empirical Performance of Alternative Option Pricing Models
TL;DR: In this article, an option pricing model that allows volatility, interest rates and jumps to be stochastic is presented. But it is not known whether and by how much each generalization improves option pricing and hedging.
Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options
TL;DR: In this paper, an efficient method was developed for pricing American options on stochastic volatility/jump-diffusion processes under systematic jump and volatility risk, and the parameters implicit in deutsche mark (DM) options of the model and various submodels were estimated over the period 1984 to 1991 via nonlinear generalized least squares, and tested for consistency with $/DM futures prices and the implicit volatility sample path.