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CFA Level 1
Derivatives

European Call Option Pricing with Black-Scholes

Very Hard Derivative Pricing And Valuation Options

A trader is analyzing a European call option on a stock currently trading at $50. The call option has a strike price of $55 and expires in 6 months. The risk-free interest rate is 2% per annum, and the stock's volatility is estimated at 20%.

The trader uses the Black-Scholes formula to calculate the option's price. According to the Black-Scholes model, the price of a European call option can be determined with the following formula:

C = S0 * N(d1) - X * e^(-rT) * N(d2)

where:

S0 = spot price of the stock
X = strike price of the option
r = risk-free rate
T = time to expiration in years
N(d) = cumulative distribution function of the standard normal distribution
d1 = (ln(S0/X) + (r + (σ²/2))T) / (σ√T)
d2 = d1 - σ√T

Given the information above, what is the value of the call option?

Hint

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