Question

If a USD 89.83-strike European call on a non-dividend-paying stock with 0.74 years until expiration is trading at USD 1.64 in an economy where the continuously-compounded interest rate is 6.37%/year and an otherwise identical put is trading at USD 1.89, what is the price of the underlying stock in USD?

Answer 1

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As per put call parity

P+ S = present value of X + C

P= value of put option.

S= current price of share

X= strike price

C= value of call option.

Present value of X = X/e^rt

r = risk free rate. 6.37%

t= time period 0.74

Given:

P= value of put option = 1.89

S= current price of share=?

X= strike price = 89.83

Present value of X = 89.83/e^(6.37%×0.74)

C= value of call option = 1.64

1.89+ S = [89.83/e^(6.37%×0.74)]+ 1.64

S= $85.44

Value/Price of Stock =$85.44