You are given the following information concerning options on a particular stock

Question

You are given the following information concerning options on a particular stock: Stock price = $67 Exercise price = $60 Risk-free rate = 4% per year, compounded continuously Maturity = 3 months Standard deviation = 40% per year a. What is the intrinsic value of each option? (Leave no cells blank - be certain to enter "0" wherever required. Do not round intermediate calculations.) Value Call option $ Put option $ b. What is the time value of each option? (Do not round intermediate calculations and round your final answers to 2 decimal places (e.g., 32.16).) Value Call option $ Put option $

Explanation / Answer

Intrinsic Value of Call Option = Underlying Price – Strike Price
=> $67 - $60 = $7

Intrinsic Value (Put) = Strike Price – Underlying Price
=> The Put Option has no intrinsic value, since it is out of the money. Only in-the-money options has an intrinsic value.

Value of Options: Black-Scholes formula

Put Option:

P = Xe-rt * N(-d2) – S0 e-rt * N(-d1)

The formulas for d1 and d2 are:

S0 = underlying price (USD per share)

X = strike price (USD per share)

= volatility (% p.a.)

r = continuously compounded risk-free interest rate (% p.a.)

q = continuously compounded dividend yield (% p.a.)

t = time to expiration (% of year)

d1 = {ln(67/60) + 0.25[(0.04 – 0)+(0.16/2)}/ 0.4*(0.251/2) = 5.613922287
d2 = 5.613922287 - [0.4*(0.251/2)] = 5.588922287

P = 60e-(04*0.25) * N(-5.588922287) + 67e-(0.4*0.25) * N(-5.613922287)
P = 0.143

So, value of the put option is $0.143

Call Option:

C = S0 e-rt * N(-d1) - Xe-rt * N(-d2)

The formulas for d1 and d2 are:

C = 67e-(0.4*0.25) * N(-5.613922287) - 60e-(04*0.25) * N(-5.588922287)
C = 7.731

So, value of the Call option is $7.731

Time Value = Premium – Intrinsic Value

Time value of Put Option = $0.143 - $0 = $0.143

Time value of Call Option = $7.731 - $7 = $0.731

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