Question

The price of a non-dividend-paying stock is $51. A six-month European call on the stock with a strike price of $50 is selling for $5. The continuously compounded risk-free rate is 6%. What is the price of a six-month European put on the stock with a strike price of $50?

Answer 1

Put Call Parity Theorm:

It shows the long term equilibrium relation between Value of call with certain exercise price, Value of put with same exercise price, excercise price, exercise date and stock price today.

Vc + PV of Strike Price = Vp + Stock price

Vc = Value of call
Vp = Value of Put

Particulars	Values
Vc	$      5.00
Strike Price	$   50.00
Int rate	6%
Maturity Period in Year	0.5000
Stock Price	$   51.00

Vc = Value of Call
Vp = Value of Put

Vp = Vc + PV of Strike Price - Stock Price

Computation of PV of Strike Price

PV of Strike Price = Strike Price * e^-rt
e - Exponential factor
r - Int Rate per anum
t - Time in Years
= $ 50 * e^-0.06 * 0.5
= $ 50 * e^-0.03
= $ 50 * 0.9704
= $ 48.52

Vp = Vc + PV of Strike Price -Stock Price
= $ 5 + $ 48.52 - $ 51
= $ 2.52