Option pricing by transform methods: extensions, unification and error control

Lee, Roger W.

doi:10.21314/jcf.2004.121

Cited by 286 publications

(210 citation statements)

References 40 publications

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“…It is, however, possible to calculate the moment generating function without this assumption (see Huang and Wu, 2004;Carr and Wu, 2004). Lee (2004) treats error bounds for a fast Fourier transform (FFT) implementation of the Fourier transform method and list the generalized Fourier transforms for some common pay-off functions such as e.g. the European call option.…”

Section: The Nig-cir Modelmentioning

confidence: 99%

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Sequential calibration of options

Lindström

Ströjby

Brodén

et al. 2008

Computational Statistics & Data Analysis

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Robust calibration of option valuation models to quoted option prices is non-trivial but crucial for good performance. A framework based on the state-space formulation of the option valuation model is introduced. Non-linear (Kalman) filters are needed to do inference since the models have latent variables (e.g. volatility). The statistical framework is made adaptive by introducing stochastic dynamics for the parameters. This allows the parameters to change over time, while treating the measurement noise in a statistically consistent way and using all data efficiently. The performance and computational efficiency of standard and iterated extended Kalman filters (EKF and IEKF) are investigated. These methods are compared to common calibration such as weighted least squares (WLS) and penalized weighted least squares (PWLS). A simulation study, using the Bates model, shows that the adaptive framework is capable of tracking time varying parameters and latent processes such as stochastic volatility processes. It is found that the filter estimates are the most accurate, followed by the PWLS estimates. The estimates from all of the advanced methods are significantly closer to the true parameters than the WLS estimates which overfits data. The filters are also faster than least squares methods. All calibration methods are also applied to daily European option data on the S&P 500 index, where the Heston, Bates and NIG-CIR models are considered. The results are similar to the simulation study and it can be seen that the overfitting is a real problem for the WLS estimator when applied complex models.

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Section: The Nig-cir Modelmentioning

confidence: 99%

“…In order to price a European call option we need to calculate the inverse Fourier transform (Lee, 2004):…”

Section: Implementation and Numerical Aspects Of The Inverse Fourier mentioning

confidence: 99%

Sequential calibration of options

Lindström

Ströjby

Brodén

et al. 2008

Computational Statistics & Data Analysis

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“…Bounds for sampling and truncation errors of this approximation have been developed in [19]. Approximation (8) suggests to apply the Fast Fourier algorithm which is an efficient algorithm to compute sums of the form…”

Section: Fast Fourier Transform Methods To Calculate Call Option Pricesmentioning

confidence: 99%

Parametric Estimation of Risk Neutral Density Functions

Grith

Krätschmer

2011

Handbook of Computational Finance

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Summary. This chapter deals with the estimation of risk neutral distributions for pricing index options resulting from the hypothesis of the risk neutral valuation principle. After justifying this hypothesis, we shall focus on parametric estimation methods for the risk neutral density functions determining the risk neutral distributions. We we shall differentiate between the direct and the indirect way. Following the direct way, parameter vectors are estimated which characterize the distributions from selected statistical families to model the risk neutral distributions. The idea of the indirect approach is to calibrate characteristic parameter vectors for stochastic models of the asset price processes, and then to extract the risk neutral density function via Fourier methods. For every of the reviewed methods the calculation of option prices under hypothetically true risk neutral distributions is a building block. We shall give explicit formula for call and put prices w.r.t. reviewed parametric statistical families used for direct estimation. Additionally, we shall introduce the Fast Fourier Transform method of call option pricing developed in [6]. It is intended to compare the reviewed estimation methods empirically.

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“…The attractiveness of the Heston model is its analytical tractability and the consideration of the correlation between the underlying asset price process and volatility process. Subsequently, a couple of papers on the numerically stable and efficient computation of European-style option prices were published, e.g., (Andersen 2008;Carr and Madan 1999;Kahl and Jäckel 2005;Lee 2004;Lewis 2001;Lipton 2002).…”

Section: Introductionmentioning

confidence: 99%

Numerical Simulation of the Heston Model under Stochastic Correlation

Teng¹,

Ehrhardt²,

Günther³

2017

IJFS

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Stochastic correlation models have become increasingly important in financial markets. In order to be able to price vanilla options in stochastic volatility and correlation models, in this work, we study the extension of the Heston model by imposing stochastic correlations driven by a stochastic differential equation. We discuss the efficient algorithms for the extended Heston model by incorporating stochastic correlations. Our numerical experiments show that the proposed algorithms can efficiently provide highly accurate results for the extended Heston by including stochastic correlations. By investigating the effect of stochastic correlations on the implied volatility, we find that the performance of the Heston model can be proved by including stochastic correlations.

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Option pricing by transform methods: extensions, unification and error control

Cited by 286 publications

References 40 publications

Sequential calibration of options

Sequential calibration of options

Parametric Estimation of Risk Neutral Density Functions

Numerical Simulation of the Heston Model under Stochastic Correlation

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