Default Intensity and Equity Option Pricing in Jump Diffusion Models

Summary

The document raises a modeling question about how default intensity affects equity option values in a jump-diffusion framework. The author observes that a formula from a referenced model appears to make an option more valuable as jump or default intensity rises, potentially approaching the stock price, and asks how this squares with the intuition that default risk should depress equity value.

The discussion also distinguishes compensated from non-compensated jump processes, asking whether a process without a jump-intensity drift adjustment would better represent the situation. No answer or resolution is included, so the document does not establish a credit adjustment method or explain the assumptions behind the cited formula. Its value is as a prompt to examine jump compensation, the meaning of intensity, and how default losses enter the underlying stock process and option valuation.

Key ideas

• The author questions how rising default intensity affects equity option values in a jump-diffusion model.
• The concern is that the cited formula seems inconsistent with the intuition that default risk reduces equity value.
• The document asks whether a non-compensated jump process better represents the stock dynamics.
• It provides no resolution or specific method for incorporating credit adjustment.

Tags

# How option value default adjusted in jump diffusion model


# How option value default adjusted in jump diffusion model












According to the doc here: http://faculty.baruch.cuny.edu/jgatheral/JumpDiffusionModels.pdf.

Formula 7 specifies that the option value under jump diffusion model becomes:

So when the default intensity lambda is high, the equity option seems to become ITM and you will soon have option value equal to the stock price. This seems to be contradicted to my understand that if default intensity goes high, you expect a default event which would likely drag the company price to go lower.

So my question is when you price an option with these kind of model, how do you do credit adjustment? It seems that the stock process, if follow non-compensated jump diffusion process, which means there is no lambda drift term, makes more sense.

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