Short Maturity Asian Options for the Cev Model

Pirjol, Dan; Zhu, Lingjiong

doi:10.1017/s0269964818000165

Cited by 9 publications

(9 citation statements)

References 79 publications

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“…For a general local volatility model the short maturity asymptotics is expressed in terms of a rate function which is given in terms of quadratures. The result can be put in explicit form for the CEV model [42]. The at-the-money (ATM) asymptotics has been obtained as well, which is dominated by the fluctuations of the asset price around the spot price.…”

Section: Introductionmentioning

confidence: 80%

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: 80%

Short Maturity Asian Options in Local Volatility Models

Pirjol¹,

Zhu²

2016

SIAM J. Finan. Math.

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“…We consider here the pricing of floating strike forward start Asian options. Following the same approach as in [36], we consider them as call/put options on the underlying B Requiring agreement with the short maturity option pricing asymptotics gives the following short maturity asymptotics for the normal equivalent volatility Σ N (K, T ). Proposition 4.9.…”

Section: Numerical Tests For Forward Start Floating Strike Asian Optionsmentioning

confidence: 99%

“…Recently the pricing of Asian options with continuous time averaging has been studied in the short maturity asymptotic regime [1,35,36] in the local volatility model. This approach uses large deviations theory, and relates the short maturity asymptotics to a rate function for the time average of the asset price.…”

Section: Introductionmentioning

confidence: 99%

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Short Maturity Forward Start Asian Options in Local Volatility Models

Pirjol

Wang

Zhu

2019

Applied Mathematical Finance

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We study the short maturity asymptotics for prices of forward start Asian options under the assumption that the underlying asset follows a local volatility model. We obtain asymptotics for the cases of out-of-the-money, in-the-money, and at-the-money, considering both fixed strike and floating Asian options. The exponential decay of the price of an out-of-the-money forward start Asian option is handled using large deviations theory, and is controlled by a rate function which is given by a double-layer optimization problem. In the Black-Scholes model, the calculation of the rate function is simplified further to the solution of a non-linear equation. We obtain closed form for the rate function, as well as its asymptotic behaviors when the strike is extremely large, small, or close to the initial price of the underlying asset.A Notations 39 1−τ 1 τ S T t dt > K , which is a rare event when K > S 0 and T → 0. A natural approach is to use large deviation theory and the contraction principle [13]. For instance, we can obtain that the price of an forward

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“…Furthermore, it is shown to yield stable option Greeks. This method is not based on asymptotic expansions (see Foschi, Pagliarani, & Pascucci, ; Pirjol & Zhu, ; Pirjol & Zhu, , for related discussions), which often perform poorly for medium dated options. Our proposed method is valid for any fixed maturity.…”

Section: Introductionmentioning

confidence: 99%

An efficient and stable method for short maturity Asian options

Chatterjee

Cui

Fan

et al. 2018

Journal of Futures Markets

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In this paper, we develop a Markov chain‐based approximation method to price arithmetic Asian options for short maturities under the case of geometric Brownian motion. It has the advantage of being a closed‐form approximation involving only matrices. It is an accurate, efficient, and stable method for the pricing and hedging of short maturity arithmetic Asian options for which previous methods in the literature have shown either slower convergence or instabilities in hedging parameters. We demonstrate that this method is as good as and sometimes better than existing approximation methods in the literature.

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Short Maturity Asian Options for the Cev Model

Cited by 9 publications

References 79 publications

Short Maturity Asian Options in Local Volatility Models

Short Maturity Asian Options in Local Volatility Models

Short Maturity Forward Start Asian Options in Local Volatility Models

An efficient and stable method for short maturity Asian options

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