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Pricing path-dependent options under the Hawkes jump diffusion process

This study was supported by the National Natural Science Foundation of China (No. 11701084)

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  • 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.

    Mathematics Subject Classification: Primary: 60G51, 91B70; Secondary: 65K10.

    Citation:

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  • Figure 1.  Fader option prices against strike prices. The dotted, solid, dashed and dot-dashed lines correspond to fader option prices with default risk and $ \alpha = 0.40 $, fader option prices with default risk and $ \alpha = 0.50 $, fader option prices with default risk and $ \alpha = 0.60 $, and fader option prices without default risk, respectively

    Figure 2.  Fader option prices against initial levels of the intensity. The dotted, solid, dashed and dot-dashed lines correspond to fader option prices with default risk and $ \alpha = 0.40 $, fader option prices with default risk and $ \alpha = 0.50 $, fader option prices with default risk and $ \alpha = 0.60 $, and fader option prices without default risk, respectively

    Figure 3.  Fader option prices against the values of $ \theta $. The dotted, solid, dashed and dot-dashed lines correspond to fader option prices with default risk and $ \alpha = 0.40 $, fader option prices with default risk and $ \alpha = 0.50 $, fader option prices with default risk and $ \alpha = 0.60 $, and fader option prices without default risk, respectively

    Figure 4.  Fader option prices against the values of $ \delta $. The dotted, solid, dashed and dot-dashed lines correspond to fader option prices with default risk and $ \alpha = 0.40 $, fader option prices with default risk and $ \alpha = 0.50 $, fader option prices with default risk and $ \alpha = 0.60 $, and fader option prices without default risk, respectively

    Figure 5.  Fader option prices against initial values of issuer's assets. The dotted, solid, dashed and dot-dashed lines correspond to fader option prices with default risk and $ \alpha = 0.40 $, fader option prices with default risk and $ \alpha = 0.50 $, fader option prices with default risk and $ \alpha = 0.60 $, and fader option prices without default risk, respectively

    Figure 6.  Fader option prices against the levels of issuer's debt. The dotted, solid, dashed and dot-dashed lines correspond to fader option prices with default risk and $ \alpha = 0.40 $, fader option prices with default risk and $ \alpha = 0.50 $, fader option prices with default risk and $ \alpha = 0.60 $, and fader option prices without default risk, respectively

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