1
$\begingroup$

I try to solve this exercise:

a) Calclculate the price of a 3-month European put option on a non-dividend-paying stock with a strike price of 45 when the current stock price is 40, the risk-free interest rate is 5% per annum, and the volatility is 40% per annum.

b) What dierence does it make to the option price if a dividend of 1.50 is expected in 2 months?

While I can solve a) im not able to solve b). My solution for a) is: $T=\frac{1}{4}, K=45, S_0=40,r=0.05,\sigma=0.4$ leads to $$d_{+}=\frac{\ln\left( \frac{S_0}{K}\right)-(r+\frac{\sigma^2}{2})T}{\sigma \sqrt T}=-0.7514$$ and $$d_{-}=-0.9514.$$ Hence the put option price is given by $$P_0=-S_0N(-d_{+})+Ke^{-rT}N(-d_{-})=5.9042.$$

Can anybody explain how b) works?

Greetings

Improve this question
$\endgroup$

1 Answer 1

Reset to default
1
$\begingroup$

One solution is to calculate the annual dividend yield implied by that. $Div_{yield}=\delta=1.5/40$ and then replace the $r$ on $d_+$ by $r-\delta$.

A cleaner way would be to compute it using a binomial tree.

Improve this answer
$\endgroup$
4
  • 1
    $\begingroup$ And I use the exact same formula for $P_0$? I don't use $-S_0 e^{-\delta T}$ instead of $-S_0$? $\endgroup$
    – user154085
    Commented Jul 10, 2015 at 14:27
  • $\begingroup$ Yes, you are right. $\endgroup$
    – phdstudent
    Commented Jul 10, 2015 at 14:41
  • $\begingroup$ Sorry for asking, but with "Yes, you are right." you mean that I have to use $-S_0e^{-\delta T}$? $\endgroup$
    – user154085
    Commented Jul 10, 2015 at 17:14
  • $\begingroup$ Yes you have to use $-S_0e^{-\delta T}$ $\endgroup$
    – phdstudent
    Commented Jul 10, 2015 at 17:29

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.