Central limit theorem and moderate deviation principle for CKLS model with small random perturbation

Cai, Yujie; Wang, Shaochen

doi:10.1016/j.spl.2014.11.017

Cited by 4 publications

(3 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In particular, their results are not directly applicable to the Heston model. The paper by Cai and Wang (2015) is also worth mentioning here: It presents moderate deviations for the CIR process (the Heston variance process) and a generalization, where the exponent in the dynamics is not necessarily 1∕2. The paper uses estimates tied to the (generalized) CIR stochastic differential equation.…”

Section: Other Approaches At Motm Asymptoticsmentioning

confidence: 99%

Option pricing in the moderate deviations regime

Friz

Gerhold

Pinter

2017

Mathematical Finance

View full text Add to dashboard Cite

We consider call option prices close to expiry in diffusion models, in an asymptotic regime (“moderately out of the money”) that interpolates between the well‐studied cases of at‐the‐money and out‐of‐the‐money regimes. First and higher order small‐time moderate deviation estimates of call prices and implied volatilities are obtained. The expansions involve only simple expressions of the model parameters, and we show how to calculate them for generic local and stochastic volatility models. Some numerical computations for the Heston model illustrate the accuracy of our results.

show abstract

Section: Other Approaches At Motm Asymptoticsmentioning

confidence: 99%

Option pricing in the moderate deviations regime

Friz

Gerhold

Pinter

2017

Mathematical Finance

View full text Add to dashboard Cite

show abstract

“…For any x > 0, y ≥ 0 and 1 2 ≤ β < 1, we have |x β − y β | ≤ |x − y|x β−1 , see e.g. Lemma 2.2. in Cai and Wang [10]. Hence,…”

Section: I(x)mentioning

confidence: 90%

“…We assume in this Section that the asset value S t follows a Square-root process: (10) dS t = (r − q)S t dt + σ S t dW t , with S 0 > 0 and W t is a standard Brownian motion starting at zero at time zero W 0 = 0. We have the following result.…”

Section: Short Maturity Asian Options In the Square-root Modelmentioning

confidence: 99%

Short Maturity Asian Options for the Cev Model

Pirjol¹,

Zhu²

2018

Prob. Eng. Inf. Sci.

View full text Add to dashboard Cite

We present a rigorous study of the short maturity asymptotics for Asian options with continuous-time averaging, under the assumption that the underlying asset follows the Constant Elasticity of Variance (CEV) model. We present an analytical approximation for the Asian options prices which has the appropriate short maturity asymptotics, and demonstrate good numerical agreement of the asymptotic results with the results of Monte Carlo simulations and benchmark test cases for option parameters relevant in practical applications.T T 0 S t dt, and short maturity asymptotics for outof-money (OTM) Asian options. Using call-put parity, the corresponding short maturity asymptotics for in-the-money (ITM) Asian options can be obtained as well. Finally, the short maturity asymptotics for at-the-money (ATM) Asian options has been derived too. The result in [47] covers in particular the Black-Scholes case, and the explicit formulas are derived for the short maturity asymptotics for the Black-Scholes case in [47].

show abstract

A moderate deviation principle for stochastic Volterra equation

Wang

Yao

et al. 2017

Statistics & Probability Letters

View full text Add to dashboard Cite

Central limit theorem and moderate deviation principle for CKLS model with small random perturbation

Cited by 4 publications

References 7 publications

Option pricing in the moderate deviations regime

Option pricing in the moderate deviations regime

Short Maturity Asian Options for the Cev Model

A moderate deviation principle for stochastic Volterra equation

Contact Info

Product

Resources

About