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<p>An Asian basket option is a path-dependent multi-asset option whose payoff depends on the weighted average prices of several underlying assets at expired time. It is one of the most popular options in the over-the-counter (OTC) market, and provides the advantage of representing various kinds and any number of assets as a single product to satisfy investor’s hedging requirements. However, investors who hold standard Asian basket options may face problems caused by the increasing apprehension of counterparty’s default risk in the OTC market during the global financial crisis or COVID-19 pandemic. To overcome such disadvantages, we propose an European-style geometric <i>n</i>-asset Asian basket options with counterparty risk (named vulnerable geometric Asian basket options, vulnerable-GABOs), which have generally the effect of decreasing the variance and exhibit the original features of standard Asian basket options. In this paper, we investigate the pricing of the vulnerable geometric basket options under multi-asset stochastic volatility jump diffusion (SVJD) model, in which the dynamics of both multi-asset underlying the option and the asset of option writers follows the normal jump-diffusion models with Heston’s stochastic volatility process. Based on the proposed model, we obtain closed-form analytical formulas of the option price and its delta value via means of the Fourier transform and the joint characteristic function obtained by the Esscher-Girsanov transform and Feynman-Kac theorem. Besides, the approximate solutions of the vulnerable geometric Asian basket option and its delta value can be quickly calculated by using the discrete fast Fourier transform (FFT) method. Furthermore, we numerically test the accuracy and efficiency of the price of a vulnerable geometric Asian basket options (as obtained using FFT in the SVJD model) by comparing that obtained by Monte Carlo simulations. The results indicate that FFT is accurate, fast and easy to implement. Finally, sensitivity analysis is presented to further explain the theoretical results.</p>

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Valuing Vulnerable Geometric Asian Basket Options Under Stochastic Volatility Jump Diffusion Model

  • 期刊论文

  • 发表日期：

    2025年4月30日

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  • Guohe Deng,
  • Zhiqin Hong

摘要

An Asian basket option is a path-dependent multi-asset option whose payoff depends on the weighted average prices of several underlying assets at expired time. It is one of the most popular options in the over-the-counter (OTC) market, and provides the advantage of representing various kinds and any number of assets as a single product to satisfy investor’s hedging requirements. However, investors who hold standard Asian basket options may face problems caused by the increasing apprehension of counterparty’s default risk in the OTC market during the global financial crisis or COVID-19 pandemic. To overcome such disadvantages, we propose an European-style geometric n-asset Asian basket options with counterparty risk (named vulnerable geometric Asian basket options, vulnerable-GABOs), which have generally the effect of decreasing the variance and exhibit the original features of standard Asian basket options. In this paper, we investigate the pricing of the vulnerable geometric basket options under multi-asset stochastic volatility jump diffusion (SVJD) model, in which the dynamics of both multi-asset underlying the option and the asset of option writers follows the normal jump-diffusion models with Heston’s stochastic volatility process. Based on the proposed model, we obtain closed-form analytical formulas of the option price and its delta value via means of the Fourier transform and the joint characteristic function obtained by the Esscher-Girsanov transform and Feynman-Kac theorem. Besides, the approximate solutions of the vulnerable geometric Asian basket option and its delta value can be quickly calculated by using the discrete fast Fourier transform (FFT) method. Furthermore, we numerically test the accuracy and efficiency of the price of a vulnerable geometric Asian basket options (as obtained using FFT in the SVJD model) by comparing that obtained by Monte Carlo simulations. The results indicate that FFT is accurate, fast and easy to implement. Finally, sensitivity analysis is presented to further explain the theoretical results.