Workshop 8 solutions

BUS333 Derivative Securities

Workshop 8

Problem 10.8.

Explain why the arguments leading to put–call parity for European options cannot be used to
give a similar result for American options.


When early exercise is not possible, we can argue that two portfolios
that are worth the same at time T must be worth the same at earlier
times.
When early exercise is possible, the argument falls down.

Suppose that P  S  C  Ke rT .
This situation does not lead to an arbitrage opportunity. If we buy the
call, short the put, and short the stock, we cannot be sure of the result
because we do not know when the put will be exercised.




Problem 10.9.

What is a lower bound for the price of a six-month call option on a non-dividend-paying
stock when the stock price is $80, the strike price is $75, and the risk-free interest rate is 10%
per annum?




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, Problem 10.14.

The price of a European call that expires in six months and has a strike price of $30 is $2.
The underlying stock price is $29, and a dividend of $0.50 is expected in two months and
again in five months. The term structure is flat, with all risk-free interest rates being 10%.
What is the price of a European put option that expires in six months and has a strike price of
$30?


Using the notation in the chapter, put-call parity [equation (10.10)]
gives

c  Ke rT  D  p  S0
or

p  c  Ke rT  D  S0

In this case

p  2  30e01612  (05e01212  05e01512 )  29  251


In other words the put price is $2.51.




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