5.14.2005

Q&A: Which Rho is greater for...

...the following options on a stock selling for $65, with 5% risk-free rate?
  • Call option A: Exercise price X = $70, Days to option expiration = 15.
  • Call option B: Exercise price X = $70, Days to option expiration = 120.

CppQuant Answer

Option B. Rhoc (for call options) and Rhop (for put options) change as time passes, with both tending toward zero as expiration approaches.

Bonus Points

  • The sensitivity of the option price to the risk-free rate is called the Rho.
  • For a call option, Rho is always positive.
  • For a put option, Rho is always negative.

  • Large changes in the interest rate have relatively little impact on the option prices. (ie, the price of a European option on an asset is not very sensitive to the risk-free rate.)

Category: C++ Quant > Derivatives > Options

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  • Put option A: Exercise price X = $70, Days to option expiration = 15.
  • Put option B: Exercise price X = $70, Days to option expiration = 120.

Option B > A ??

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