Semi-nonparametric estimation of the call-option price surface under strike and time-to-expiry no-arbitrage constraints

Fengler, Matthias R.; Hin, Lin-Yee

doi:10.1016/j.jeconom.2014.09.003

Cited by 58 publications

(40 citation statements)

References 97 publications

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“…Moreover, similar conditions can be derived for a continuous call price surface to be free of static arbitrage (see for example Fengler and Hin (2013) and Roper (2010)). However, these results make certain assumptions about the underlying process, and are not applicable to the case when there is a positive probability of default.…”

Section: Introductionmentioning

confidence: 82%

Novel no-arbitrage conditions for options written on defaultable assets

Orosi

2014

J Deriv Hedge Funds

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is currently an assistant professor in the Department of Mathematics and Statistics at American University of Sharjah. He holds a PhD in Applied Mathematics with a specialization in mathematical finance from the University of Calgary. His research areas include computational finance and applications, numerical methods applied to derivative pricing, empirical performance of option pricing models, and non-parametric modeling.Correspondence: Greg Orosi, Department of Mathematics and Statistics, American University of Sharjah, Office: Nab 254, PO Box 26666, Sharjah, UAE E-mail: gorosi@ucalgary.ca ABSTRACT In this work, we derive an improved lower bound for European-style put options written on defaultable assets. Furthermore, we establish two additional no-arbitrage conditions, one for European-style puts and one for calls, which are tighter than the ones commonly reported in current literature. All of our results are based on static arbitrage arguments and have important implications for constructing arbitrage-free call or put option surfaces. In particular, we point out that the commonly stated conditions required for a call option surface are not always sufficient to generate an arbitrage-free call option surface.

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Section: Introductionmentioning

confidence: 82%

Novel no-arbitrage conditions for options written on defaultable assets

Orosi

2014

J Deriv Hedge Funds

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“…Our framework corresponds to the regularization with respect to the uniform kernel. Examples of applications of non-uniform kernels such as Nadaraya-Watson kernel, local polynomial kernel and spline kernel for non-parametric modelling of the implied volatility surface can be found in Ben Hamida and Cont (2005), Coleman et al (2013) and Fengler and Hin (2015), among many others. Their implementation relies on modelling the implied volatility as a tensor-product of kernel basis with respect to times to maturity and strike prices of the options contract assuming that the risk-free rate is known.…”

Section: Joint Inference Of Implied Parameters Using Longitudinal Optmentioning

confidence: 99%

Computation of the implied discount rate and volatility for an overdefined system using stochastic optimization

Hin

Dokuchaev

2015

IMA J Management Math

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This paper studies estimation of the implied volatility and the impact of the choice of the corresponding risk-free rate proxy. We suggest to analyze the implied volatility and the riskfree rate proxy inferred in conjunction with the observed option prices. We formulate and solve an overdefined system of nonlinear equations for the Black-Scholes model using options data. More precisely, we seek an optimal approximate solution via differential evolution, a stochastic optimization technique. Some experiments with historical prices reveal a higher inferred risk-free rate than commonly used proxies. This leads to narrower volatility spread, or smaller difference between implied and realized volatilities.

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“…Fingler-Hin (2013) [8] use semi-nonparametric estimator for the entire call price surface based on a tensor-product B-spline.…”

Section: Introductionmentioning

confidence: 99%

Robust Calibration For SVI Model Arbitrage Free

Ferhati¹

2020

SSRN Journal

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The purpose of this paper is to study the Stochastic Volatility Inspired model (SVI) as implied volatility model: we study the analytic part of the SVI with the arbitrage conditions, we establish the initial guess and the parameter's boundaries. Until recently it was not possible to find sufficient conditions that would guarantee an SVI model calibration arbitrage-free. The main contribution in this paper is that we provide two methods to resolve the arbitrage problem (butterfly and calendar spread): the first one is numerical using the Sequential Least-Squares Quadratic Programming (SLSQP) algorithm, and the second one is analytical by using sufficient conditions that guarantee an SVI arbitrage-free.Our method guarantee to get SVI calibration with butterfly and calendar spread arbitrage-free, We provide many numerical examples with arbitrage such as Vogt Axel example and we show how to fix them. The calibration method is tested on 23 equity indexes with 14 maturities each and we get 322 slices fits using the same initial guess and the SVI parameters boundaries for all indexes.This new calibration method is very important and it meets practical need: resolving this arbitrage problem will pave the way to the surface calibration and the transition from implied volatility to local volatility using Dupire's formula, therefore, it allows price different kind of pathdependent options such as barrier options, and American options. The SVI model could also be applied to price interest rate derivatives such as swaptions, interest rate caps, and floors.

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Semi-nonparametric estimation of the call-option price surface under strike and time-to-expiry no-arbitrage constraints

Cited by 58 publications

References 97 publications

Novel no-arbitrage conditions for options written on defaultable assets

Novel no-arbitrage conditions for options written on defaultable assets

Computation of the implied discount rate and volatility for an overdefined system using stochastic optimization

Robust Calibration For SVI Model Arbitrage Free

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