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In Black-Scholes model $r$ is defined as risk-free interest rate. What I have understood is that risk-free comes from the yields on sale of government bonds. What does that mean if the interest rate(fed fund rate) are negative? Does the yield on government bonds then also go negative? I understand the price of the bond will go up, but is that yield correlated with the fed fund rate?

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The yield on government bonds is not necessarily equal to fed fund rate. Fed fund rate is a rate at which other banks can borrow from Fed.

This being said the funds rate affects interest rates on all debts since if the banks can borrow more cheaply from Fed they can also offer better terms to their own creditors. Bonds compete on markets for loanable funds so if the interest rate on loans go down the bond yield will also be lower.

If we are talking about risk free bond then it’s yield will be quite close to the funds rate but not necessarily equal. Also, yes the bond yield can be negative.

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Usually, no one uses government bond yields in Black Scholes, at least not professionals. You can have a look at this answer for some details.

In terms of the model, there is no difference if rates are positive or negative. You simply plug in the value (and all other parameters in the model) and get the option price. In fact, rates have been negative in many countries (e.g. EUR) for a very long time until recently.

Below is a screenshot from Bloomberg's OVME: enter image description here

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