Numerical analysis for Spread option pricing model of markets with finite liquidity: first-order feedback model

Shidfar, A.; Paryab, Kh.; Yazdanian, A. R.; Pirvu, Traian A.

doi:10.1080/00207160.2014.887274

Cited by 3 publications

(4 citation statements)

References 32 publications

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“…For example, Liu and Yong (2005) [18] studied a price impact model for single asset options. Pirvu et al (2014) [25] also studied a price impact model for spread option. In this paper, we adopt the following price impact function:…”

Section: Analysis Of Replication Of Exchange Option By Delta Hedging Asmentioning

confidence: 99%

“…In fact, this ensures the λ(t, s 1 )Γ 11 (t) term stays small, which ultimately guarantees the existence of δ 0 . There is a more detailed explanation in Pirvu et al (2014) [25].…”

Section: • Condition (3)mentioning

confidence: 99%

“…The aforementioned studies predominately involve stochastic volatility models. Similar to Exchange Options, studies on Spread Option pricing have been conducted in the presence of full or partial price impact [25,22].…”

mentioning

confidence: 99%

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Numerical Simulation of Exchange Option with Finite Liquidity: Controlled Variate Model

Zhang¹,

Pirvu²

2020

Preprint

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In this paper we develop numerical pricing methodologies for European style Exchange Options written on a pair of correlated assets, in a market with finite liquidity. In contrast to the standard multi-asset Black-Scholes framework, trading in our market model has a direct impact on the asset's price. The price impact is incorporated into the dynamics of the first asset through a specific trading strategy, as in large trader liquidity model. Two-dimensional Milstein scheme is implemented to simulate the pair of assets prices. The option value is numerically estimated by Monte Carlo with the Margrabe option as controlled variate. Time complexity of these numerical schemes are included. Finally, we provide a deep learning framework to implement this model effectively in a production environment.

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Section: Analysis Of Replication Of Exchange Option By Delta Hedging Asmentioning

confidence: 99%

“…In fact, this ensures the λ(t, s 1 )Γ 11 (t) term stays small, which ultimately guarantees the existence of δ 0 . There is a more detailed explanation in Pirvu et al (2014) [25].…”

Section: • Condition (3)mentioning

confidence: 99%

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Numerical Simulation of Exchange Option with Finite Liquidity: Controlled Variate Model

Zhang¹,

Pirvu²

2020

Preprint

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“…In this scenario, the portfolio used for replication have two assets and one cash account. The full argument can be found in Pirvu and Yazdanian (2016) [1]. The resulting PDE will be linear and parabolic.…”

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confidence: 99%

Pricing spread option with liquidity adjustments

Zhang¹,

Pirvu²

2021

Preprint

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We study the pricing and hedging of European spread options on correlated assets when, in contrast to the standard framework and consistent with imperfect liquidity markets, the trading in the stock market has a direct impact on stocks prices. We consider a partial-impact and a full-impact model in which the price impact is caused by every trading strategy in the market. The generalized Black-Scholes pricing partial differential equations (PDEs) are obtained and analysed. We perform a numerical analysis to exhibit the illiquidity effect on the replication strategy of the European spread option. Compared to the Black-Scholes model or a partial impact model, the trader in the full impact model buys more stock to replicate the option, and this leads to a higher option price.

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Spread Option Pricing Under Finite Liquidity Framework

Pirvu,

Zhang

2024

Risks

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This work explores a finite liquidity model to price spread options and assess the liquidity impact. We employ Kirk approximation for computing the spread option price and its delta. The latter is needed since the liquidity impact is caused by the delta hedging of a large investor. Our main contribution is a novel methodology to price spread options in this paradigm. Kirk approximation in conjunction with Monte Carlo simulations yields the spread option prices. Moreover, the antithetic and control variates variance reduction techniques improve the performance of our method. Numerical experiments reveal that the finite liquidity causes a liquidity value adjustment in option prices ranging from 0.53% to 2.81%. The effect of correlation on prices is also explored, and as expected the option price increases due to the diversification effect, but the liquidity impact decreases slightly.

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Numerical analysis for Spread option pricing model of markets with finite liquidity: first-order feedback model

Cited by 3 publications

References 32 publications

Numerical Simulation of Exchange Option with Finite Liquidity: Controlled Variate Model

Numerical Simulation of Exchange Option with Finite Liquidity: Controlled Variate Model

Pricing spread option with liquidity adjustments

Spread Option Pricing Under Finite Liquidity Framework

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