As negative interest rates started popping up around the world, quantitative analysts and traders have been asking a mundane but fundamental question: How to price trillions of dollars of financial instruments when their complex pricing models don’t work with negative numbers? Intuitively, we would say that negative interest rates will affect the prices of interest-rate sensitive instruments such as interest rate swaps and swaptions the most. Indeed, Bloomberg recently elaborated:
As far as equity derivatives are concerned, the impact will not be as dramatic as with interest-rate sensitive instruments. However, some subtleties in the mathematical approaches can still have an impact on the accuracy of equity-derivative valuation models.
Specifically, when we price an American call option, we often argue that if the underlying stock pays no dividend, then it’s never optimal to exercise earlier, i.e. the price of an American call option is equal to its European counterpart. To see this, recall that there exists a lower bound for an American call option on a non-dividend paying stock [1]: where
From this equation, it follows that when However, when
[1] J.C. Hull, Article Source Here: How Negative Interest Rates Affect Derivative Pricing Models
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