question archive Using the Black-Scholes formula for the European Call Option, and the Put- Call Parity deduce the Black-Scholes formula for the European Put Option

Using the Black-Scholes formula for the European Call Option, and the Put- Call Parity deduce the Black-Scholes formula for the European Put Option

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Using the Black-Scholes formula for the European Call Option, and the Put- Call Parity deduce the Black-Scholes formula for the European Put Option.

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Answer:

C = N(d1)S-N(d2)Ke-rT

Put-Call Parity

P = Ke-rt -S -C

P =  Ke-rt -S - N(d1)S-N(d2)Ke-rT

P = Ke-rt -N(d2)Ke-rT -S - N(d1)S

P = (1-N(d2))Ke-rT -( 1- N(d1))S

P = N(-d2)Ke-rT -N(-d1)S

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