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When the non-dividend paying stock price is $20, the strike price is $20, the risk-free rate is 6%, the volatility is 20% and the time to maturity is 3 months which of the following is the price of a European call option on the stock? A. 19.7N(0.2) –20N(0.1) B. 19.7N(0.1) –20N(0.2) C. 20N(0.2) –19.7N(0.1) D. 20N(0.1) –19.7N(0.2)

Question

When the non-dividend paying stock price is 20,thestrikepriceis20, the strike price is 20, the risk-free rate is 6%, the volatility is 20% and the time to maturity is 3 months which of the following is the price of a European call option on the stock?

A. 19.7N(0.2) –20N(0.1)

B. 19.7N(0.1) –20N(0.2)

C. 20N(0.2) –19.7N(0.1)

D. 20N(0.1) –19.7N(0.2)

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Solution

Apologies for the confusion, but it seems like there's no text provided in a different language. However, to answer the question about the price of a European call option:

The correct answer is:

A. 19.7N(0.2) –20N(0.1)

Here's the reasoning behind this choice:

The Black-Scholes formula for a European call option on a non-dividend paying stock is:

C = S0N(d1) - Xe^(-rt)*N(d2)

where:

  • C is the call option price
  • S0 is the current stock price
  • N is the cumulative standard normal distribution function
  • d1 and d2 are variables calculated as follows:
    • d1 = [ln(S0/X) + (r + σ^2/2)t] / (σsqrt(t))
    • d2 = d1 - σ*sqrt(t)
  • X is the strike price
  • r is the risk-free interest rate
  • t is the time to expiration (in years)
  • σ is the volatility of the stock price

In this case, S0 = 20,X=20, X = 20, r = 6% (or 0.06), σ = 20% (or 0.20), and t = 3 months (or 0.25 years).

So, d1 = [ln(20/20) + (0.06 + 0.20^2/2)0.25] / (0.20sqrt(0.25)) = 0.2 And, d2 = 0.2 - 0.20*sqrt(0.25) = 0.1

Therefore, the price of the call option is:

C = 20∗N(0.2)−20*N(0.2) - 20e^(-0.060.25)N(0.1) = 19.7∗N(0.2)−19.7*N(0.2) - 20N(0.1)

So, the correct answer is 19.7N(0.2) –20N(0.1), as stated in option A.

This problem has been solved

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