Workshop 11 solutions

BUS333 Derivative Securities

Workshop 11

Problem 15.11.

An index currently stands at 696 and has a volatility of 30% per annum. The risk-free rate of interest
is 7% per annum and the index provides a dividend yield of 4% per annum. Calculate the value of a
three-month European put with an exercise price of 700.


In this case S0  696 , K  700 , r  007 ,   03 , T  025 and q  004 .

The option can be valued using equation (15.5).
 rf T
c  S0e N (d1 )  Xe  rT N (d 2 )
rf T
p  Xe rT N (d 2 )  S 0 e N (  d1 )
ln( S 0 / X )  (r  q   )T
where d1 
 T
ln( S 0 / X )  (r  q   )T
d2 
 T

That is:
ln(696  700)  (007  004  009  2)  025
d1   00868
03 025
d 2  d1  03 025  00632
and

N (d1 )  04654 N (d2 )  05252


The value of the put, p , is given by:

p  700e007025  05252  696e004025  04654  406


i.e., it is 40.6 (index points)



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, Problem 15.13.

Show that a European call option on a currency has the same price as the corresponding European
put option on the currency when the forward price equals the strike price.


This follows from put–call parity and the relationship between the
forward price, F0 , and the spot price, S 0 .
 rf T
c  Ke rT  p  S0e
and
( r  r f )T
F0  S0e




The result that c  p when K  F0 is true for options on all
underlying assets, not just options on currencies.




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