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FRM Part I · FRM Exam Part I · Option Sensitivity Measures: The "Greeks"

A European put and call have the same strike and expiry on a non-dividend-paying stock. Using put-call parity, which expression correctly links the theta of the put to the theta of the call (r is the continuously compounded risk-free rate, K the strike, T expiry)?

Theta of the put equals theta of the call plus r times K times e^(-rT). Differentiating put-call parity with respect to calendar time, the stock price is unaffected and the present value of the strike accretes at rate r, giving this positive adjustment.

  1. ATheta(put) = Theta(call) + r*K*e^(-rT)Correct
  2. BTheta(put) = Theta(call) - r*K*e^(-rT)
  3. CTheta(put) = Theta(call)
  4. DTheta(put) = -Theta(call)

Explanation

Parity: c + K e^(-rT) = p + S. Differentiating with respect to time (theta is derivative with respect to calendar time, T falls) gives theta_c + r K e^(-rT) = theta_p, since S is unaffected by time. So theta_p = theta_c + rKe^(-rT). The subtraction version has the wrong sign on the discount-accretion term.

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