Skip to content

IAI Actuarial Core Principles · Economic Modelling · Black-Scholes derivative-pricing model

An analyst prices a European call and a European put on a dividend-paying share with the same strike and expiry, with continuous dividend yield q. Which put-call parity relation holds?

Put-call parity with a continuous dividend yield is C minus P equals S0 times e^(-qT) minus K times e^(-rT). The option holder misses dividends, so the share is valued net of their present value, while the strike is discounted at the risk-free rate.

  1. AC - P = S0 - K·e^(-rT)
  2. BC - P = S0·e^(-qT) - K·e^(-rT)Correct
  3. CC - P = S0·e^(qT) - K·e^(-rT)
  4. DC - P = S0·e^(-qT) - K·e^(rT)
  5. C - P = S0 - K·e^(-(r-q)T)

Explanation

A portfolio of long call and short put replicates a forward: payoff S_T-K. The share bought without dividends costs S0·e^(-qT), and K is discounted at r. Hence C-P = S0·e^(-qT) - K·e^(-rT). The first option ignores dividends.

Did you get it right without looking?

One question tells you little. A timed set on Black-Scholes derivative-pricing model shows your real accuracy, how long you take and where you lose marks.

Practise Black-Scholes derivative-pricing modelFree diagnostic mock

More Black-Scholes derivative-pricing model questions