Moment Explosions in Stochastic Volatility Models

Andersen, Leif; Piterbarg, Vladimir

doi:10.2139/ssrn.559481

Cited by 163 publications

(278 citation statements)

References 37 publications

Supporting

Mentioning

271

Contrasting

Order By: Relevance

“…Since the discretization scheme is supposed to stick rather closely to the SDE, this roughly amounts to assuming that the SDE has uniformly bounded moments, which holds when the drift b(x) and the volatility function σ(x) have a sublinear growth. In the Heston model the diffusion coefficient σ(x) does not have a sublinear growth, and it is proved indeed that the moments explode in a finite time (see Andersen and Piterbarg [3] for details). Therefore, the framework developed in this paper is not well suited to getting a rigorous estimate of the weak error within the Heston model.…”

Section: 2mentioning

confidence: 99%

See 1 more Smart Citation

High order discretization schemes for the CIR process: Application to affine term structure and Heston models

2010

View full text Add to dashboard Cite

Abstract. This paper presents weak second and third order schemes for the Cox-Ingersoll-Ross (CIR) process, without any restriction on its parameters. At the same time, it gives a general recursive construction method for getting weak second order schemes that extend the one introduced by Ninomiya and Victoir. Combine both these results, this allows us to propose a second order scheme for more general affine diffusions. Simulation examples are given to illustrate the convergence of these schemes on CIR and Heston models.

show abstract

Section: 2mentioning

confidence: 99%

“…The schemeX x t = 1 {U≤π(t,x)} x + (t, x) + 1 {U>π(t,x)} x − (t, x) is a potential third order scheme on x ∈ [0, K 3 (t)]: for any f ∈ C ∞ pol (R + ), there are positive constants C and η that depend on a good sequence of f s.t. for t ∈ (0, η) and x ∈ [0, K 3 …”

mentioning

confidence: 99%

High order discretization schemes for the CIR process: Application to affine term structure and Heston models

2010

View full text Add to dashboard Cite

show abstract

“…A precise mathematical formulation and a complete characterization of regular affine processes are due to Duffie et al [12]. Later several authors have contributed to the theory of general affine processes: to name a few, Andersen and Piterbarg [1], Dawson and Li [11], Filipović and Mayerhofer [13], Glasserman and Kim [16], Jena et al [22] and Keller-Ressel et al [26].…”

Section: Introductionmentioning

confidence: 99%

Stationarity and Ergodicity for an Affine Two-Factor Model

Barczy

Doering

et al. 2014

Adv. Appl. Probab.

View full text Add to dashboard Cite

show abstract

“…In this section, we study the implications of Andersen and Piterbarg (2007) to the extreme strike behavior of option prices on leveraged and inverse ETFs. 13 Our results build heavily upon the work by Lee (2004) wherein the author showed that the extreme strike behavior is related to the number of finite moments of the return distribution.…”

Section: Symmetry In Implied Variances For Letf Optionsmentioning

confidence: 99%

“…13 Andersen and Piterbarg (2007) have studied the time of moment explosion within the Heston model. 14 See Leung and Sircar (2012) for a recent study of implied volatility surfaces implied by the market prices of options on LETFs.…”

mentioning

confidence: 99%

Crooked Volatility Smiles: Evidence from Leveraged and Inverse ETF Options

et al. 2012

View full text Add to dashboard Cite

We find that leverage in exchange traded funds (ETFs) can affect the "crookedness" of volatility smiles. This observation is consistent with the intuition that return shocks are inversely correlated with volatility shocks -resulting in more expensive out-of-the-money put options and less expensive out-of-the-money call options. We show that the prices of options on leveraged and inverse ETFs can be used to better calibrate models of stochastic volatility. In particular, we study a sextet of leveraged and inverse ETFs based on the S&P 500 index. We show that the Heston model (Heston , 1993) can reproduce the crooked smiles observed in the market price of options on leveraged and inverse leveraged ETFs. We show further that the model predicts a leverage dependent moneyness, consistent with empirical data, at which options on positively and negatively leveraged ETFs have the same price. Finally, by analyzing the asymptotic behavior for the implied variances at extreme strikes, we observe an approximate symmetry between pairs of LETF smiles empirically consistent with the predictions of the Heston model.

show abstract

Moment Explosions in Stochastic Volatility Models

Cited by 163 publications

References 37 publications

High order discretization schemes for the CIR process: Application to affine term structure and Heston models

High order discretization schemes for the CIR process: Application to affine term structure and Heston models

Stationarity and Ergodicity for an Affine Two-Factor Model

Crooked Volatility Smiles: Evidence from Leveraged and Inverse ETF Options

Contact Info

Product

Resources

About