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Unformatted text preview: The portfolio payoﬀs and prices:
Payoﬀ portfolio 1
C0 + Ke −rt
call payoﬀ + K
max (ST − K , 0) + K
max (ST , K ) portfolio 2
S0 + P0
ST + put payoﬀ
ST + max (K − ST , 0)
max (ST , K ) Equal payoﬀs implies equal prices:
C0 + Ke −rt = S0 + P0 or
Derivatives III: R. J. Hawkins C − P = S − Ke −rt
Econ 136: Financial Economics 2/ 10 Put-Call Parity: Example 1
Suppose the stock price is $31, exercise price is $30, risk-free rate
is 10% per year, the price of a 3-month European call is $3.00 and
the price of a 3-month European put is $2.25.
Calculate prices of our two portfolios
1 portfolio 1: C + Ke −rt = 3.00 + 30e −0.1×0.25 = 32.26 2 portfolio 2: P + S = 2.25 + 31 = 33.25 Execution: Buy cheap portfolio and sell (short) expensive portfolio
1 Construct position today: Sell portfolio 2 and buy portfolio 1.
P + S > C + Ke −rt
P + S − C − Ke −rt > 0 2 Unwind position at option expiration
Derivatives III: R. J. Hawkins Econ 136: Financial Econo...
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This note was uploaded on 01/23/2014 for the course ECON 136 taught by Professor Szeidl during the Fall '08 term at University of California, Berkeley.
- Fall '08