First- and second-order Greeks in the Heston model

Chan, Jiun Hong; Joshi, Mark S.; Zhu, Dan

doi:10.21314/jor.2015.300

Cited by 6 publications

(3 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This also holds for @V t =@V 0 , because when the discretized SDE of the variance process is differentiated with respect to V 0 , the square root will appear in the denominator, which makes the derivative intractable. Further, in Chan and Joshi (2010) it is noted that the sensitivities of the variance process with respect to initial inputs can grow very quickly and potentially blow up. We therefore approximate these partial derivatives by a local bump-and-revalue approach, as follows:…”

Section: Sensitivity With Respect To Initial Variancementioning

confidence: 99%

Efficient Estimation of Sensitivities for Counterparty Credit Risk with the Finite Difference Monte-Carlo Method

2014

View full text Add to dashboard Cite

According to Basel III, financial institutions have to charge a credit valuation adjustment (CVA) to account for a possible counterparty default. Calculating this measure and its sensitivities is one of the biggest challenges in risk management. Here, we introduce an efficient method for the estimation of CVA and its sensitivities for a portfolio of financial derivatives. We use the finite difference Monte Carlo (FDMC) method to measure exposure profiles and consider the computationally challenging case of foreign exchange barrier options in the context of the Black-Scholes as well as the Heston stochastic volatility model, with and without stochastic domestic interest rate, for a wide range of parameters. In the case of a fixed domestic interest rate, our results show that FDMC is an accurate method compared with the semi-analytic COS method and, advantageously, can compute multiple options on one grid. In the more general case of a stochastic domestic interest rate, we show that we can accurately compute exposures of discontinuous one-touch options by using a linear interpolation

show abstract

Section: Sensitivity With Respect To Initial Variancementioning

confidence: 99%

Efficient Estimation of Sensitivities for Counterparty Credit Risk with the Finite Difference Monte-Carlo Method

2014

View full text Add to dashboard Cite

show abstract

“…These option price sensitivities are hence functions of (x, y, t, p, τ, K). The numerical computation of option price sensitivities has been explored in Broadie and Kaya (2004), Chan and Joshi (2010) and we propose here an alternate approach.…”

Section: Option Price Sensitivity : Definitionmentioning

confidence: 99%

Option Pricing Accuracy for Estimated Heston Models

Azencott¹,

Gadhyan²,

Glowinski³

2014

Preprint

View full text Add to dashboard Cite

We consider assets for which price Xt and squared volatility Yt are jointly driven by Heston joint stochastic differential equations (SDEs). When the parameters of these SDEs are estimated from N sub-sampled data (XnT , YnT ), estimation errors do impact the classical option pricing PDEs. We estimate these option pricing errors by combining numerical evaluation of estimation errors for Heston SDEs parameters with the computation of option price partial derivatives with respect to these SDEs parameters. This is achieved by solving six parabolic PDEs with adequate boundary conditions. To implement this approach, we also develop an estimator λ for the market price of volatility risk, and we study the sensitivity of option pricing to estimation errors affecting λ. We illustrate this approach by fitting Heston SDEs to 252 daily joint observations of the S&P 500 index and of its approximate volatility VIX, and by numerical applications to European options written on the S&P 500 index.

show abstract

“…In the context of affine and polynomial models, this approach has been shown to perform well when combined with Fourier transform techniques as in Callegaro et al (2017b), or polynomial expansion techniques as in Callegaro et al (2017), whose results could be further improved with the new expansions presented in our paper. The calculation of Greeks for stochastic volatility models is a difficulty task often adressed by Monte Carlo simulations, see for examples Broadie and Kaya (2004) for a discussion of different simulation based estimators in the Heston model, and Chan et al (2015) for more recent advances using algorithmic differentiation.…”

Section: Introductionmentioning

confidence: 99%

Option Pricing with Orthogonal Polynomial Expansions

Ackerer

Filipović

2017

SSRN Journal

View full text Add to dashboard Cite

We derive analytic series representations for European option prices in polynomial stochastic volatility models. This includes the Jacobi, Heston, Stein-Stein, and Hull-White models, for which we provide numerical case studies. We find that our polynomial option price series expansion performs as efficiently and accurately as the Fourier transform based method in the nested affine cases. We also derive and numerically validate series representations for option Greeks. We depict an extension of our approach to exotic options whose payoffs depend on a finite number of prices.

show abstract

First- and second-order Greeks in the Heston model

Cited by 6 publications

References 11 publications

Efficient Estimation of Sensitivities for Counterparty Credit Risk with the Finite Difference Monte-Carlo Method

Efficient Estimation of Sensitivities for Counterparty Credit Risk with the Finite Difference Monte-Carlo Method

Option Pricing Accuracy for Estimated Heston Models

Option Pricing with Orthogonal Polynomial Expansions

Contact Info

Product

Resources

About