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Homework answers / question archive / A trader buys a European call option and sells a European put option
A trader buys a European call option and sells a European put option. The options have the same underlying asset, strike price and maturity. Describe the trader’s position
Your answer cannot exceed 350 words.
For options on the same underlying asset, strike price and maturity: Using put call parity
C-P=S-X/(1+r)^t
where C is price of call option
P is price of put option
S is price of underlying stock
X is strike price of the options
r is the risk free rate
t is the time to expiry
As options are on the same underlying asset, strike price and maturity, we can use put call parity to simplify the trader's position. From above, we see that buying a call option and selling a put option is C-P. Using law of one price the price of C-P should be the same as S-X/(1+r)^t. This is replicated using S-X/(1+r)^t, which means buying or long a stock and borrowing (for time equal to the expiry of the options) at risk free rate or selling a risk free bond with face value equal to the strike price of the option. Hence, trader's position is that he has borrowed money and purchased stock.