A General Closed Form Option Pricing Formula

Necula, Ciprian; Drimus, Gabriel G.; Farkas, Walter

doi:10.2139/ssrn.2210359

Cited by 7 publications

(12 citation statements)

References 31 publications

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“…For pricing options in this model we employed the methodology based on Gauss-Hermite series expansion developed in Necula, Drimus and Farkas (2013). The option pricing performance of the new nonaffine one-factor model was tested in comparison to the classical one-factor model proposed by Heston and the affine two-factor double Heston model.…”

Section: Discussionmentioning

confidence: 99%

“…Finally, we employ the general closed form option pricing formula obtained in Necula, Drimus and Farkas (2013). This method for option pricing is based on the fact that a probability density can be represented as a Gauss-Hermite series expansion (GHSE).…”

Section: Option Pricingmentioning

confidence: 99%

“…The Gauss-Hermite series expansion is an attractive alternative for approximating the risk-neutral density due to its improved convergence for heavy tailed distributions and because it allows for a closed form formula for pricing European options as shown in Necula, Drimus and Farkas (2013). More specifically, the price of at time t of a European call option with strike price K and maturity t + τ is given by:…”

Section: Option Pricingmentioning

confidence: 99%

“…where I n (τ, S t , X t ) and J n (τ, S t , X t ) satisfy simple recursion equations that are described in Necula, Drimus and Farkas (2013).…”

Section: Option Pricingmentioning

confidence: 99%

“…The purpose of the paper is to develop an endogenous and non-affine stochastic volatility model where the volatility induced by fundamentals is amplified due to the interaction and herding of the agents involved in trading a financial asset. At the same time, we show how one can price European options in the context of the model using the closed form formula based on the Gauss-Hermite series expansion methodology (Necula, Drimus and Farkas, 2013). We estimate the parameters of the model by a combination of non-linear optimization techniques using S&P 500 index options, and conduct a study about the performance of the new option pricing model.…”

Section: Introductionmentioning

confidence: 99%

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Herding and Stochastic Volatility

2015

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In this paper we develop a one-factor non-affine stochastic volatility option pricing model where the dynamics of the underlying is endogenously determined from micro-foundations. The interaction and herding of the agents trading the underlying asset induce an amplification of the volatility of the asset over the volatility of the fundamentals. Although the model is non-affine, a closed form option pricing formula can still be derived by using a Gauss-Hermite series expansion methodology. The model is calibrated using S&P 500 index options for the period 1996-2013. When its results are compared to some benchmark models we find that the new non-affine one-factor model outperforms the affine one-factor Heston model and it is competitive, especially out-of-sample, with the affine two-factor double Heston model.

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Section: Discussionmentioning

confidence: 99%

Section: Option Pricingmentioning

confidence: 99%

Section: Option Pricingmentioning

confidence: 99%

“…where I n (τ, S t , X t ) and J n (τ, S t , X t ) satisfy simple recursion equations that are described in Necula, Drimus and Farkas (2013).…”

Section: Option Pricingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Herding and Stochastic Volatility

2015

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Option pricing with Legendre polynomials

Hok¹,

Chan

2017

Journal of Computational and Applied Mathematics

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Here we develop an option pricing method based on Legendre series expansion of the density function.The key insight, relying on the close relation of the characteristic function with the series coefficients, allows to recover the density function rapidly and accurately. Based on this representation for the density function, approximations formulas for pricing European type options are derived. To obtain highly accurate result for European call option, the implementation involves integrating high degree Legendre polynomials against exponential function. Some numerical instabilities arise because of serious subtractive cancellations in its formulation (96) in proposition 7.1. To overcome this difficulty, we rewrite this quantity as solution of a second-order linear difference equation and solve it using a robust and stable algorithm from Olver. Derivation of the pricing method has been accompanied by an error analysis. Errors bounds have been derived and the study relies more on smoothness properties which are not provided by the payoff functions, but rather by the density function of the underlying stochastic models. This is particularly relevant for options pricing where the payoffs of the contract are generally not smooth functions. The numerical experiments on a class of models widely used in quantitative finance show exponential convergence.

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Pricing and hedging basket options with exact moment matching

Leccadito

Paletta

Tunaru

2016

Insurance: Mathematics and Economics

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Theoretical models applied to option pricing should take into account the empirical characteristics of financial time series. In this paper, we show how to price basket options when the underlying asset prices follow a displaced log-normal process with jumps, capable of accommodating negative skewness and excess kurtosis. Our technique involves Hermite polynomial expansion that can match exactly the first m moments of the model-implied basket return. This method is shown to provide superior results for basket options not only with respect to pricing but also for hedging.

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A General Closed Form Option Pricing Formula

Cited by 7 publications

References 31 publications

Herding and Stochastic Volatility

Herding and Stochastic Volatility

Option pricing with Legendre polynomials

Pricing and hedging basket options with exact moment matching

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