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Thread: Put call parity risk free rate

  1. #1
    Actuary.com - Newbie Poster
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    Jun 2012
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    Put call parity risk free rate

    Hi,

    I've come across this past paper question and I'm having some doubts about this question:

    An European call and put option on a dividend paying stock both have a strike price of Rs. 50 and expire in 3 months. Both of them are available for Rs 10 each. The stock is currently trading at Rs 50 and is expected to pay a dividend of Rs 5 in three month’s time just before the expiration of the options. Is there an arbitrage opportunity available? If yes, what trades should the trader execute to benefit from the opportunity?

    In the solutions they find the risk free rate to be r=0.1. I take it they get it from 5/50.

    i.e. In the term e^(-rT) they use r=0.1 and T=0.25.

    Shouldn't r be converted to a yearly effective rate before using it like that, or shouldn't it be 0.1 * 3, instead of 0.1 * 0.25?

    If not, why is that?

    Thanks heaps

  2. #2
    Actuary.com - Posting Master
    Join Date
    Oct 2007
    Posts
    3,110
    Quote Originally Posted by actuarium View Post
    Hi,

    I've come across this past paper question and I'm having some doubts about this question:

    An European call and put option on a dividend paying stock both have a strike price of Rs. 50 and expire in 3 months. Both of them are available for Rs 10 each. The stock is currently trading at Rs 50 and is expected to pay a dividend of Rs 5 in three month’s time just before the expiration of the options. Is there an arbitrage opportunity available? If yes, what trades should the trader execute to benefit from the opportunity?

    In the solutions they find the risk free rate to be r=0.1. I take it they get it from 5/50.

    i.e. In the term e^(-rT) they use r=0.1 and T=0.25.

    Shouldn't r be converted to a yearly effective rate before using it like that, or shouldn't it be 0.1 * 3, instead of 0.1 * 0.25?

    If not, why is that?

    Thanks heaps
    Well for one thing 3 months = 3/12 = 1/4 of a year hence an annual rate is multiplied by 1/4. If you still don't get it, write down the P-C Parity formula for me.

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