A Generic Decomposition Formula for Pricing Vanilla Options Under Stochastic Volatility Models

Merino, Raúl; Vives, Josep

doi:10.1007/978-3-319-51753-7_20

Cited by 4 publications

(11 citation statements)

References 7 publications

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“…It is interesting to realize that the approximation found in this case has more terms than the one obtained for stochastic volatility models (see [4]). We have applied this technique to the CEV model, doing a comparison between exact prices, Black-Scholes using Hagan and Woodward implied volatility, and our price approximation.…”

Section: Resultsmentioning

confidence: 86%

“…The formula presented in [4] uses, as a base function, function BS( , , ), but this formula is numerically worse than the new formula presented here that uses as a base function BS( , , ( )). This happens because in the formula presented in [4] the volatility is put into the approximated term, instead of keeping it on the Black-Scholes term as we do here. It is precisely because volatility is a deterministic function of the underlying asset price that we can do that.…”

Section: Remarkmentioning

confidence: 83%

Section: Remarkmentioning

confidence: 99%

“…In [4], an alternative formula that can be used for local volatility models is proved. The formula presented in [4] uses, as a base function, function BS( , , ), but this formula is numerically worse than the new formula presented here that uses as a base function BS( , , ( )). This happens because in the formula presented in [4] the volatility is put into the approximated term, instead of keeping it on the Black-Scholes term as we do here.…”

Section: Remarkmentioning

confidence: 99%

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Option Price Decomposition in Spot-Dependent Volatility Models and Some Applications

Merino

Vives

2017

International Journal of Stochastic Analysis

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We obtain a Hull and White type option price decomposition for a general local volatility model. We apply the obtained formula to CEV model. As an application we give an approximated closed formula for the call option price under a CEV model and an approximated short term implied volatility surface. These approximated formulas are used to estimate model parameters. Numerical comparison is performed for our new method with exact and approximated formulas existing in the literature.

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Section: Resultsmentioning

confidence: 86%

Section: Remarkmentioning

confidence: 83%

Section: Remarkmentioning

confidence: 99%

Section: Remarkmentioning

confidence: 99%

See 2 more Smart Citations

Option Price Decomposition in Spot-Dependent Volatility Models and Some Applications

Merino

Vives

2017

International Journal of Stochastic Analysis

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“…The second goal is to discuss the properties of the model (in other words the stylized facts satsified by the model) that address these limitations of the Black-Scholes model stated above. To study the options valuation, we provide an estimate of the option price using a decomposition method as in Alòs (2012), Merino and Vives (2015), Merino and Vives (2017). In addition, a numerical solution of the option price using Monte Carlo techniques is obtained.…”

Section: Introductionmentioning

confidence: 99%

Approximate pricing formula to capture leverage effect and stochastic volatility of a financial asset

El-Khatib

Goutte

Makumbe

et al. 2022

Finance Research Letters

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In this paper a hybrid model is investigated to capture both financial behaviors of an asset: (i) the leverage effect and (ii) the stochastic volatility component. For this we consider a hybrid model that takes the strengths of the Heston and the CEV models. The pricing of European options is investigated both theoretically and empirically. A decomposition formula that allows to estimate the option price is obtained. Moreover, numerical simulations of the asset price are done to give a better and concrete vision of the adding of this approach. In addition, the price of a European call option under the hybrid model is computed using the Monte Carlo method and our formula. Illustrations and tables show the efficiency of the numerical method based on our approximate formula.

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Higher order approximation of call option prices under stochastic volatility models

Gulisashvili,

Merino,

Lagunas

et al. 2019

Preprint

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In the present paper, a decomposition formula for the call price due to Alòs is transformed into a Taylor type formula containing an infinite series with stochastic terms. The new decomposition may be considered as an alternative to the decomposition of the call price found in a recent paper of Alòs, Gatheral and Radoičić. We use the new decomposition to obtain various approximations to the call price in the Heston model with sharper estimates of the error term than in the previously known approximations. One of the formulas obtained in the present paper has five significant terms and an error estimate of the form O(ν 3 (|ρ| + ν)), where ν is the vol-vol parameter, and ρ is the correlation coefficient between the price and the volatility in the Heston model. Another approximation formula contains seven more terms and the error estimate is of the form O(ν 4 (1 + |ρ|). For the uncorrelated Hestom model (ρ = 0), we obtain a formula with four significant terms and an error estimate O(ν 6 ). Numerical experiments show that the new approximations to the call price perform especially well in the high volatility mode.

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A Generic Decomposition Formula for Pricing Vanilla Options Under Stochastic Volatility Models

Cited by 4 publications

References 7 publications

Option Price Decomposition in Spot-Dependent Volatility Models and Some Applications

Option Price Decomposition in Spot-Dependent Volatility Models and Some Applications

Approximate pricing formula to capture leverage effect and stochastic volatility of a financial asset

Higher order approximation of call option prices under stochastic volatility models

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