Actuarial Outpost Actex Study Manual Exercise 5.2 #6
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#1
12-20-2018, 02:58 AM
 lilj0825 CAS SOA Join Date: Apr 2017 College: college graduate Posts: 2
Actex Study Manual Exercise 5.2 #6

Can anyone help me with this one?

The Question is:

Consider a stock that follows the Black-Scholes framework. You are given:

i) The current stock price is 50.

ii) The stock pays dividend continuously at a rate proportional to its price. The dividend yield is 0.02.

iii) The continuously compounded rate of appreciation on the stock is 0.05.

iv) The median of the stock price at time 2 is 50.

v) The continuously compounded risk-free interest rate is 0.02.

Calculate the price of a 1-year 50-strike Euro put option.

The solution does not use the dividend yield for getting the volatility of the stock from the median, yet use the dividend yield for getting d_1.

Last edited by lilj0825; 12-20-2018 at 03:02 AM..
#2
12-20-2018, 08:09 PM
 Abraham Weishaus Member SOA AAA Join Date: Oct 2001 Posts: 7,227

Statement iii) refers to the rate at which the stock's price increases. This already takes dividends into account - it is after dividends. The rate of return on the stock is 0.07.

On the other hand, the risk-free interest rate is the total risk-free rate of return (so it corresponds to the true rate of return of 0.07).

#3
12-21-2018, 01:04 AM
 lilj0825 CAS SOA Join Date: Apr 2017 College: college graduate Posts: 2

Yes, I think it does answer my question. Thank you very much!