Rho of Put options

Quantitative Finance Level 1

What happens to the rho of a put option as the underlying moves up?

Rho increases and is more positive Rho stays constant Rho decreases and is less positive Rho increases and is less negative Rho decreases and is more negative

1 solution

Chew-Seong Cheong
Mar 19, 2015

The rho of a call is zero or positive $\ge 0$ and the rho of a put is zero or negative $\le 0$ . When the price of the underlying stock increase rho increases. For a put, its rho is getting less negative. The following graph (credit to: www.OptionTradingTips.com shows the rhos of a call and put of $100 strikes against stock price.

Why is rho of the put option always negative?

Why is it more significant when the stock is trading lower than the strike?

Calvin Lin Staff - 6 years, 2 months ago

Call price increases while put price decreases as interest increases. Therefore, call rho is positive and put rho is negative.
When an option is in the money it has a larger premium $V$ and hence a larger $\partial V$ and a larger rho $\rho = \dfrac {\partial V}{\partial r}$ .

Chew-Seong Cheong - 6 years, 2 months ago

Suppose we exercise the put option early. In that case, our rho position should change inverse to the rho of the option (if the rho of the put option is negative, then exercising the put should cause us to gain rho, and vice versa).

Exercising the put option means we sell stock and gain money. When we have more money, higher interest rate is good, so that means exercising the put option caused us to gain rho. This means the put option itself had negative rho.

It is more significant when the stock is trading lower than the strike (put option In The Money) because the amount of money that you gain relative to the price of the stock increases as the price of the stock decreases. Therefore, exercising the put option early would gain even more $, which would make increasing interest rates subsequently more appealing. This means that the rho must be more significant!

Ellis Soodak - 1 year, 7 months ago

Rho of Put options

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