Valuation of options on the maximum of two prices with default risk under GARCH models

Wang, Xingchun

doi:10.1016/j.najef.2021.101422

Cited by 10 publications

(5 citation statements)

References 36 publications

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“…Similarly, we can deal with the term ζ 1 (j, z). Using the measure change technique (see, e.g., Ma et al [20] and Wang [36]), we can obtain the following result easily,…”

Section: Fader Options Without Default Riskmentioning

confidence: 99%

“…It should be remarked that when the Hawkes process reduces to a Poisson process, the proposed pricing framework is essentially Merton's jump diffusion process and the derived pricing formula is the prices of fader options with/without default risk in closed form. Lastly, we can extend the proposed pricing framework to value options with default risk written on two underlying assets, such as power exchange options with default risk (see, e.g., Wang et al [37], and Pasricha and Goel [24]) and options on the maximum of two prices with default risk (see, e.g., Wang [36]).…”

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confidence: 99%

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Pricing path-dependent options under the Hawkes jump diffusion process

Wang¹

2023

JIMO

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<p style='text-indent:20px;'>In this paper, we investigate the pricing of a path-dependent option with default risk under the Hawkes jump diffusion process. For each asset, its dynamics are driven by a Hawkes jump diffusion process, and their diffusive components, Hawkes jumps as well as jump amplitudes are all correlated. In the proposed pricing framework, we obtain the prices of fader options with/without default risk in closed form. Finally, we present numerical examples to illustrate the prices of fader options with default risk.</p>

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“…Similarly, we can deal with the term ζ 1 (j, z). Using the measure change technique (see, e.g., Ma et al [20] and Wang [36]), we can obtain the following result easily,…”

Section: Fader Options Without Default Riskmentioning

confidence: 99%

mentioning

confidence: 99%

Pricing path-dependent options under the Hawkes jump diffusion process

Wang¹

2023

JIMO

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“…Deng and Huang [12] and Wang [13] investigated the pricing issue of options on the maximum or the minimum of multiassets by incorporating correlated jump risk (i.e., JD model). Wang [14,15] considered the extremum options pricing of two assets under Heston SV model (see Heston [16]) and GARCH model (see Wang [14]).…”

Section: Introductionmentioning

confidence: 99%

Extremum Options Pricing of Two Assets under a Double Nonaffine Stochastic Volatility Model

Deng

2023

Mathematical Problems in Engineering

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In this paper, we consider the pricing problem for the extremum options by constructing a double nonaffine stochastic volatility model. The joint characteristic function of the logarithm of two asset prices is derived by using the Feynman–Kac theorem and one-order Taylor approximation expansion. The semiclosed analytical pricing formulas of the European extremum options including option on maximum and option on minimum of two underlying assets are derived by using measure change technique and Fourier transform approach. Some numerical examples are provided to analyze the pricing results of extremum options under affine model, nonaffine model, Black–Scholes model, and the influences of some model parameters on the option. Numerical results show that the analytical pricing formulas have higher computational efficiency and accuracy than those of Monte Carlo simulation method. Also, results of sensitivity analysis report that the nonaffine models are more effective than other existing models in capturing the effect of volatility on option pricing.

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“…As options markets o¤er vital services and signals to hedgers, investors, and …nancial decision makers, American/European-type option pricing remains an extremely active research area in the …nancial economics literature (e.g. Almeida and Freire (2021), Amaya, Bégin, and Gauthier (2021), Aramonte, Jahan-Parvar, Rosen, and Schindler (2021), Bakshi, Cao, and Zhong (2021), Barro and Liao (2021), Battauz and Rotondi (2022), De Donno, Palmowski and Tumilewicz (2020), Figlewski (2021), Golez and Goyenko (2021), Jeon and Kim (2021), Jing, Li, and Ma (2021), Lee, Han and Lee (2021), Yu (2021), Wang (2021a), Wang (2021b), Wang, Wang and Shao (2022), and Wang and Zhang (2022)). Amid the impressive growth of the FX options markets (see for example James, Fullwood, and Billington (2015)), the appeal of quanto options comes from their ability of opening up hedging/investment opportunities in international markets as they are derivative contracts written on an underlying foreign security.…”

Section: Introductionmentioning

confidence: 99%