An Extension of the Chaos Expansion Approximation for the Pricing of Exotic Basket Options

Funahashi, Hideharu; Kijima, Masaaki

doi:10.1080/1350486x.2013.812855

Cited by 9 publications

(4 citation statements)

References 21 publications

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“…where ( ) is defined as in (7). The intrinsic value function ( ) will include the same four terms as ( ) in 7, and these four terms will be further denoted as 1 , 2 , 3 , and 4 .…”

Section: The Value Function For Proactive Hedging Europeanmentioning

confidence: 99%

“…This section discusses the pricing formula for the proactive hedging option when using the dynamic discrete position strategy that was introduced in Section 2.2. The pricing formula is obtained by solving the integral expression after combining the intrinsic value function in (7) and the pricing formula of the fractional European option in 3.9). The intrinsic value function in 7is a stepwise function, thus the pricing formula consists of four parts:…”

Section: Pricing Formula Of Proactive Hedging Option With Discretementioning

confidence: 99%

“…Exotic options, such as Asian, lookback, barrier, and passport options, have been a key focus of mathematical finance research since the late 1980s and early 1990s [1][2][3][4][5][6][7][8][9]. In this paper, we focus on an exotic option that is a proactive hedging strategy bundled into the classical European option, called proactive hedging European option.…”

Section: Introductionmentioning

confidence: 99%

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Pricing of Proactive Hedging European Option with Dynamic Discrete Position Strategy

Wang

Sun

2019

Discrete Dynamics in Nature and Society

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Proactive hedging European option is an exotic option for hedgers in the options market proposed recently by Wang et al. It extends the classical European option by requiring option holders to continuously trade in underlying assets according to a predesigned trading strategy, to proactively hedge part of the potential risk from underlying asset price changes. To generalize this option design for practical application, in this study, a proactive hedging option with discrete trading strategy is developed and its pricing formula is deducted assuming the underlying asset price follows Geometric Fractional Brownian Motion. Simulation studies show that proactive hedging option with discrete trading strategy still enjoys strong price advantage compared to the classical European option for majority of parameter space. The observed price advantage is stronger when the underlying asset has more volatility or when the asset price follows closer to Geometric Brownian Motion. Additionally, we found that a higher frequency trading strategy has stronger price advantage if there is no trading cost. The findings in this research strongly facilitate the practical application of the proactive hedging option, making this lower-cost trading tool more feasible.

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“…where ( ) is defined as in (7). The intrinsic value function ( ) will include the same four terms as ( ) in 7, and these four terms will be further denoted as 1 , 2 , 3 , and 4 .…”

Section: The Value Function For Proactive Hedging Europeanmentioning

confidence: 99%

Section: Pricing Formula Of Proactive Hedging Option With Discretementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Pricing of Proactive Hedging European Option with Dynamic Discrete Position Strategy

Wang

Sun

2019

Discrete Dynamics in Nature and Society

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“…• Laplace transform and series expansion by Geman and Yor [17], Dufresne [11], Dassios and Nagaradjasarma [10], Cai and Kou [6]; • partial differential equation (PDE) and partial integro-differential equation (PIDE) by Rogers and Shi [28], Alziary et al [2], Večeř [31], Fouque and Han [14], Foufas and Larson [13]; • Monte Carlo method by Boyle [4], Kemna and Vorst [18], Boyle and Potapchik [5]; • chaos expansion by Funahashi and Kijima [15];…”

Section: Introductionmentioning

confidence: 99%

Bounds on Prices for Asian Options via Fourier Methods

2016

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The problem of pricing arithmetic Asian options is nontrivial, and has attracted much interest over the last two decades. This paper provides a method for calculating bounds on option prices and approximations to option deltas in a market where the underlying asset follows a geometric Lévy process. The core idea is to find a highly correlated, yet more tractable proxy to the event that the option finishes in-the-money. The paper provides a means for calculating the joint characteristic function of the underlying asset and proxy processes, and relies on Fourier methods to compute prices and deltas. Numerical studies show that the lower bound provides accurate approximations to prices and deltas, while the upper bound provides good though less accurate results.

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Deep learning for derivatives pricing: a comparative study of asymptotic and quasi-process corrections

Funahashi

2024

Ann Oper Res

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In this study, we compare two methods for using neural networks to efficiently learn the price of derivatives. The first method, proposed by Funahashi (Quant Financ 21(4):575–592, 2021a), involves training the neural networks to learn the difference between the derivative price and its asymptotic expansion, rather than learning the derivative price directly. The target derivative price is then obtained by adding the approximate solution with the predicted value of neural networks. This method reduces the required amount of learning data, often by a factor of one hundred to one thousand, compared to the case where the derivative price is directly learned through neural networks. In the second method, established in this paper, the neural networks learn the difference between the derivative price written on the underlying asset price that follows the target complex stochastic process and the derivative price written on the underlying asset price that has a relatively simple stochastic process that has a closed-form solution for the target derivative prices. This method provides an alternative valuation method when no efficient approximate solution for the derivative value is observed and if one can arbitrarily determine the model parameters of the quasi-process that approximates the original process. We also propose a unified method to determine the model parameters of quasi-processes from underlying asset processes. These methods prove valuable in cases where general analytic solutions are absent, as seen in widely used financial models such as the stochastic volatility models. These cases involve time-consuming numerical calculations to generate learning data, highlighting the value of the two methods, which significantly compress calculation times.

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An Extension of the Chaos Expansion Approximation for the Pricing of Exotic Basket Options

Cited by 9 publications

References 21 publications

Pricing of Proactive Hedging European Option with Dynamic Discrete Position Strategy

Pricing of Proactive Hedging European Option with Dynamic Discrete Position Strategy

Bounds on Prices for Asian Options via Fourier Methods

Deep learning for derivatives pricing: a comparative study of asymptotic and quasi-process corrections

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