Looking at Options Greeks: Rho

January 29, 2014
By Vlad Karpel

Over the last few weeks we have been looking at options Greeks, invaluable tools for serious options traders. Greeks measure the sensitivity of the price of an option to a change in a specific variable. We already explored delta, gamma, and vega. Today we focus on rho.

Rho is a measure of the change in an option’s price due to a change in the interest rate. The number usually tells us the amount of change we should expect if interest rates change by 1% (100 basis points). For example, let’s consider an option that is currently trading at $2.50 and has a rho of 0.12. If interest rates rise from 2% to 3%, the option should rise from $2.50 to $2.62.

Traders don’t often pay attention to rho because interest rates tend to remain fairly steady over short time intervals. In the preceding example, the rise in the interest rate would most likely be 25 basis points, or 50 basis points max, because central banks usually don’t change interest rates abruptly. Therefore, the effect on the price of the option would be very small.

But if you trade long-term options and if central banks are more interventional, the effect of interest rates on options shouldn’t be disregarded. Interest rates may move quickly under certain conditions. The year 2008 is a good case in point. The Fed funds rate started the year at 4.25% but changed seven times to end at 0.25%. Using our example, the expected change in the option would have been $0.48 (4 x 0.12) because interest rates dropped 4%.

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Call options have positive rho values while put options have negative values. The impact of interest rates on options relates to the cost of carry. When you buy a call option on a stock, you are effectively avoiding part of the cost it takes to buy the stock because the option trades at a fraction of this cost. You are then borrowing funds, and the cost is included in the option price. If the interest rate rises, the cost rises accordingly, thus the price of a call option is positively correlated with interest rates. A similar concept applies to put options, which are negatively correlated with interest rates.

In general, the longer the time to maturity, the higher the impact of interest rates (which means rho is higher, in absolute terms). Deeper out-of-the-money options have low rho values. At-the-money and in-the-money options have higher rho values. Again, the cost of carry explains this. As the money and time to maturity of an option increase, option premiums also increase. Because it requires more cash to hold them, the sensitivity to interest rates increases as well.


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