Option with largest Rho

Quantitative Finance Level 3

Which of the following options have the largest rho value when the stock is trading at 100?

Call on the 80 strike with 1 month to expiry Call on the 80 strike with 3 months to expiry Call on the 120 strike with 1 month to expiry Call on the 120 strike with 3 months to expiry

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 $\le 0$ . Rho (absolute) value is largest when the option is furthest ITM and decreases steady to ATM and OTM. Rho value also decreases as time to expiry decreases. The following graph by www.OptionTradingTips.com illustrates this point.

Is there a intuitive reason for why
1. ITM calls have a greater Rho
2. Longer term to expiry have a greater Rho?

Calvin Lin Staff - 6 years, 2 months ago

Because ITM calls have more premium and the incremental change in premium with regard to change is spot rates is more for ITM calls as compared to OTM call. Longer term to expiry has a greater rho attributing to the fact that interest rate stabilizes in the long term.

Shyam Kumar - 5 years, 9 months ago

Not quite. There are actually 2 types of rho, the discount rho (which is interest on premium) and the discount rho (forward price change * delta). For calls, both of these effects are positive, while for puts the latter is negative.

I disagree with "attributing to the fact that interest rate stabilizes in the long term". The extent of stability of the interest rate does not affect the value of rho. Longer term expiry rho (for calls) is greater simply because there is more time for these effects.

Calvin Lin Staff - 5 years, 9 months ago

Option with largest Rho

1 solution

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