Negative interest rates may already be built into options prices. You may have experienced them without knowing it.
You could say that short-term interest rates like federal funds or the discount rate are relatively stable in the United States. Their fluctuations are small and don’t have as much impact on options prices as changes in stock price, volatility, or time. And interest rates have been positive in the United States since we’ve had a Treasury. But negative interest rates exist in many parts of the world.
Positive interest rates mean that if you borrow $100 and have to pay it back in a month, you’ll need to pay something more than $100, say $101, when the loan comes due. Negative interest rates mean that if you borrow $100, you’d only pay $99 in a month.
Negative rates aren’t a response to a specific economic event; instead, central banks use negative rates to encourage those holding cash in short-term government notes to move the funds into other, presumably more productive, parts of the economy. There’s nothing stopping the U.S. Federal Reserve from setting negative fed funds rates. It’s not likely, but it’s possible.
When it comes to options, though, will a negative rate blow up Black-Scholes and rip a tear in the space-time continuum? Actually, you may have already experienced the impact of negative interest rates on options prices without seeing negative interest rates.
Part of the price of an option is based on the cost of carrying the underlying—the interest rate charged on either borrowing money or forgoing interest earned when you buy stock. For calls, you have the right to buy the stock, but you don’t own it. So the cost of carry on long stock increases a call’s value, because the call is more valuable when you don’t have to pay the interest on long stock. For puts, you have the right to short the stock but don’t have short stock. That cost of carry decreases a put’s value, because the put can’t earn interest on cash generated from shorting stock. Higher interest rates push the theoretical values of calls up and puts down. Lower interest rates do the opposite.
But there’s more to the cost of carry than interest rates. Some stocks pay dividends, which can offset the interest paid when you buy stock (or you pay the dividend if you’re short stock). But calls or puts neither earn, nor pay, dividends. Call values are reduced because they don’t convey the ability to earn dividends, like long stock. Put values are increased because they don’t have to pay the dividend, like short stock.
When the dividend yield on a stock is higher than interest rates, it makes the cost of carry negative. That has the same effect on options prices as negative interest rates until dividend adjustment. So, negative interest rates would decrease the theoretical value of calls and increase the theoretical value of puts. If you look at stocks that have high dividend yields, it’s possible the interest rate is lower. Options on those stocks exhibit the same behavior as if interest rates were negative. Black-Scholes and other theoretical pricing models take this into account. So if interest rates go negative, options should take it in stride.