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I'm reading in Radu Tunaru's book "Model Risk in Financial Markets" and he argues that two parties in the financial contract do not have the same magnitude of exposure to model risk. The reason for that is the following:

"call option contracts have no downside and variation comes from the upside and also because the process used for modelling the underlying index cannot become non-positive"

Can someone clarify what he means by "call option contracts have no downside" and "variation comes from the upside"? What variation is he talking about?

And why is the fact that the underlying can't be negative an influence for the risk?

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Below is my understanding, although I find the statement inaccurate on some points and borderline wrong on others.

If you have bought an option contract, your payoff is $(S-K)^+\geq0$ where $S$ is your underlying and $K$ the strike. Therefore you can only receive a positive cash flow: there is "no downside". I guess he means that, because you can only get a positive payoff, it matters less whether you got it right when modelling the option price: anyway, you can't lose money once you've paid the premium.

By "variation comes from the upside", I guess he means that, the more in-the-money an option is (so for a call option, the more $S$ is above $K$), the more your delta is closer to 1. So the variation in (absolute) value from your option is greater the greater you are in-the-money. On the other hand, depending on how out-the-money your option is, then a change in the underlying won't really have much impact on the option value. So: when you're losing, modelling risk accurately is not necessary because anyway the variation in the option value is low; and when the variation is large, it doesn't matter that much either because anyway you're in a winning situation.

"The process used for modelling the underlying index cannot become non-positive": I don't know what that means. That's only true for options on positive processes obviously, such as a stock or an equity index, but not true for a caplet on a LIBOR rate for example, which can be modeled with stochastic processes that might take negative values. I have no clue as to why he thinks that generates asymmetric model risk.

That statement ignores a few facts:

  • It does not account for counterparty risk. It is correct that, once you've paid the option premium to your counterparty (e.g. an investment bank), then you can only receive a positive cash flow, but the party that sold the option to you might default and not be able to pay you back the option payoff: that is what CVA prices, and it is important to model it right, otherwise if your counterparties do default you're in for nasty surprises.
  • It also seems to ignore mark-to-market accounting rules: even if you hold a call option which can only pay a positive cash flow at maturity, in the meantime you hold that option in your balance sheet. The underlying value $S$ can vary; this will make the value of your option vary; and this will be reflected in your balance sheet and income statement. I think it's pretty important to have an accurate model to represent those values.
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