Pricing Barrier and Average Options Under Stochastic Volatility Environment

Shiraya, Kenichiro; Takahashi, Akihiko; Toda, Masashi

doi:10.2139/ssrn.1491937

Cited by 26 publications

(26 citation statements)

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“…The paper [26] used heat kernel expansion methods and developed approximate formulae expressed in terms of elementary functions for the density, the price and the Greeks of path dependent options of Asian style. Asymptotic expansion leading to analytical approximations with error bounds for Asian options have been obtained also using Malliavin calculus in [45,32].…”

Section: Introductionmentioning

confidence: 99%

Short Maturity Asian Options in Local Volatility Models

Pirjol¹,

Zhu²

2016

SIAM J. Finan. Math.

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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 a local volatility model. The asymptotics for out-of-the-money, in-the-money, and at-the-money cases are derived, considering both fixed strike and floating strike Asian options. The asymptotics for the out-of-the-money case involves a non-trivial variational problem which is solved completely. We present an analytical approximation for Asian options prices, and demonstrate good numerical agreement of the asymptotic results with the results of Monte Carlo simulations and benchmark test cases in the Black-Scholes model for option parameters relevant in practical applications.

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Section: Introductionmentioning

confidence: 99%

Short Maturity Asian Options in Local Volatility Models

Pirjol¹,

Zhu²

2016

SIAM J. Finan. Math.

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“…We also note that the higher order expansions can be derived in the similar manner, which is expected to provide more precise approximations as in the diffusion cases in [28,29].…”

Section: Resultsmentioning

confidence: 96%

An approximation formula for basket option prices under local stochastic volatility with jumps: An application to commodity markets

Shiraya

Takahashi

2016

Journal of Computational and Applied Mathematics

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a b s t r a c tThis paper develops a new approximation formula for pricing basket options in a localstochastic volatility model with jumps. In particular, the model admits local volatility functions and jump components in not only the underlying asset price processes, but also the volatility processes. To the best of our knowledge, the proposed formula is the first one which achieves an analytical approximation for the basket option prices under this type of the models.Moreover, in numerical experiments, we provide approximate prices for basket options on the WTI futures and Brent futures based on the parameters through calibration to the plain-vanilla option prices, and confirm the validity of our approximation formula.

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“…The paper [32] used heat kernel expansion methods and developed approximate formulae expressed in terms of elementary functions for the density, the price and the Greeks of path dependent options of Asian style. Asymptotic expansion leading to analytical approximations with error bounds for Asian options have been obtained also using Malliavin calculus in [49,39].…”

Section: Introductionmentioning

confidence: 99%

Short Maturity Asian Options for the Cev Model

Pirjol¹,

Zhu²

2018

Prob. Eng. Inf. Sci.

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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].

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Pricing Barrier and Average Options Under Stochastic Volatility Environment

Cited by 26 publications

References 27 publications

Short Maturity Asian Options in Local Volatility Models

Short Maturity Asian Options in Local Volatility Models

An approximation formula for basket option prices under local stochastic volatility with jumps: An application to commodity markets

Short Maturity Asian Options for the Cev Model

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