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What is the price of a European call option on a non-dividend-paying stock when the stock...

What is the price of a European call option on a non-dividend-paying stock when the stock price is $60, the strike price is $60, the risk-free interest rate is 10% per annual, the volatility is 20% per annual, and the time to maturity is 1 year. Round d1 and d2 to two decimal points.

Show all work. Do not use an online option price calculator.

Solutions

Expert Solution

We use Black-Scholes Model to calculate the price of the call option.

The price of a call option is:

C = (S0 * N(d1)) - (Ke-rT * N(d2))

where :

S0 = current spot price

K = strike price

N(x) is the cumulative normal distribution function

r = risk-free interest rate

T is the time to expiry in years

d1 = (ln(S0 / K) + (r + σ2/2)*T) / σ√T

d2 = d1 - σ√T

σ = standard deviation of underlying stock returns

First, we calculate d1 and d2 as below :

  • ln(S0 / K) = ln(60 / 60). We input the same formula into Excel, i.e. =LN(60 / 60)
  • (r + σ2/2)*T = (0.10 + (0.202/2)*1
  • σ√T = 0.20 * √1

d1 = 0.60

d2 = 0.40

N(d1) and N(d2) are calculated in Excel using the NORMSDIST function and inputting the value of d1 and d2 into the function.

N(d1) = 0.7257

N(d2) = 0.6554

Now, we calculate the price of the call option as below:

C = (S0 * N(d1))   - (Ke-rT * N(d2)), which is (60 * 0.7257) - (60 * e(-0.10 * 1))*(0.6554)    ==> $7.96

Price of call option is $7.96


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