Calibration and simulation of Heston model

Mrázek, Milan; Pospı́šil, J.

doi:10.1515/math-2017-0058

Cited by 22 publications

(8 citation statements)

References 41 publications

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“…Existen diversas mejoras a la fórmula propuesta por Heston, como puede ser the little Heston trap o la fórmula de Lewis. Se puede ver un resumen en [32].…”

Section: El Modelo De Hestonunclassified

La fórmula de descomposición para la valoración de opciones de compra bajo el modelo de Heston

Merino¹,

Barcelona²

2021

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Resumen. En este artículo se presenta una breve introducción a los derivados financieros. Por una parte, recorremos parte de la historia y características de los derivados financieros. Por otra, se introduce el modelo de Black-Scholes-Merton, pilar básico de la valoración de opciones, y el modelo de Heston, uno de los modelos de volatilidad estocástica más populares. Además, se explica la teoría de la fórmula de descomposición que nos permite aproximar el precio de una opción en el modelo de Heston mediante el uso de la fórmula de Itô.

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“…Existen diversas mejoras a la fórmula propuesta por Heston, como puede ser the little Heston trap o la fórmula de Lewis. Se puede ver un resumen en [32].…”

Section: El Modelo De Hestonunclassified

La fórmula de descomposición para la valoración de opciones de compra bajo el modelo de Heston

Merino¹,

Barcelona²

2021

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“…Accordingly, in order to calculate under this Inverse Generalized Gamma RND the price of a call option at a strike K when the current price of the spot is S, we will utilize (23) with µ ≡ S e rt , k ≡ K and with λ * ≡ 1/ h1 (ξ * ) and ξ * ≡ ξ(ν) as is determined by equation ( 20) above with ν ≡ σ √ t to obtain, C S (K) = e −rt c µ (K) as,…”

Section: The Igg Distributionmentioning

confidence: 99%

The Generalized Gamma distribution as a useful RND under Heston's stochastic volatility model

Boukai¹

2021

Preprint

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Following Boukai (2021) we present the Generalized Gamma (GG) distribution as a possible RND for modeling European options prices under Heston's (1993) stochastic volatility (SV) model. This distribution is seen as especially useful in situations in which the spot's price follows a negatively skewed distribution and hence, Black-Scholes based (i.e. the log-normal distribution) modeling is largely inapt. We apply the GG distribution as RND to modeling current market option data on three large market-index ETFs, namely the SPY, IWM and QQQ as well as on the TLT (an ETF that tracks an index of long term US Treasury bonds). The current option chain of each of the three market-index ETFs shows of a pronounced skew of their volatility 'smile' which indicates a likely distortion in the Black-Scholes modeling of such option data. Reflective of entirely different market expectations, this distortion appears not to exist in the TLT option data. We provide a thorough modeling of the available option data we have on each ETF (with the October 15, 2021 expiration) based on the GG distribution and compared it to the option pricing and RND modeling obtained directly from a well-calibrated Heston's (1993) SV model (both theoretically and empirically, using Monte-Carlo simulations of the spot's price). All three market-index ETFs exhibit negatively skewed distributions which are well-matched with those derived under the GG distribution as RND. The inadequacy of the Black-Scholes modeling in such instances which involve negatively skewed distribution is further illustrated by its impact on the hedging factor, delta, and the immediate implications to the retail trader. In contrast, for the TLT ETF, which exhibits no such distortion to the volatility 'smile', the three pricing models (i.e. Heston's, Black-Scholes and Generalized Gamma) appear to yield similar results.

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“…We consider the well-known two-dimensional Heston model, which contains at least four parameters implicit in the market data. In contrast to recent research in this area, we focus on optimizing the parameters within a PDE approach instead of a stochastic differential equation (SDE) approach [7,9]. The parameter calibration results in a constrained optimization problem to minimize a cost functional.…”

Section: Introductionmentioning

confidence: 99%

A Gradient Descent Algorithm for the Heston model

Clevenhaus¹,

Totzeck²,

Ehrhardt³

2021

Preprint

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The Heston model is a well-known two-dimensional financial model. Since the Heston model contains implicit parameters that cannot be determined directly from real market data, calibrating the parameters to real market data is challenging. Moreover, some of the parameters within the model are nonlinear, which makes it difficult to find the global minimum of the optimization problem. In our paper, we present a gradient descent algorithm for parameter calibration of the Heston model. Numerical results show that our calibration of the Heston partial differential equation (PDE) works well for the various challenges in the calibration process. Since the model and algorithm are well known, this work is formulated as a proof of concept. This proof of concept will be incorporated into the space mapping approach in the future.

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Calibration and simulation of Heston model

Cited by 22 publications

References 41 publications

La fórmula de descomposición para la valoración de opciones de compra bajo el modelo de Heston

La fórmula de descomposición para la valoración de opciones de compra bajo el modelo de Heston

The Generalized Gamma distribution as a useful RND under Heston's stochastic volatility model

A Gradient Descent Algorithm for the Heston model

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