Final answer:
To calculate the European Call Option Price, we use the Black-Scholes Model, substituting the given values into the formula. For the Market Maker's 1-day gain/loss on 10 shares if the stock price went up to $34, the Market Maker would have a gain of 10 * ($34 - $30).
Step-by-step explanation:
To calculate the European Call Option Price, we can use the Black-Scholes Model. The formula for calculating the European Call Option Price is:
C = S * N(d1) - X * e^(-r * T) * N(d2)
Where:
C = Call Option Price
S = Stock Price
X = Strike Price
r = Risk-Free Interest Rate
T = Time to Expiration (in years)
N(x) = Cumulative Standard Normal Distribution Function
d1 = (ln(S/X) + (r + (v^2)/2) * T) / (v * sqrt(T))
d2 = d1 - v * sqrt(T)
Using the given values, we have S = $33, X = $30, r = 8% (0.08), T = 180/365 (approximately 0.493), and v = 25% (0.25).
Substituting these values into the formula, we get:
C = $33 * N(d1) - $30 * e^(-0.08 * 0.493) * N(d2)
We can use a standard normal distribution table or a calculator to find the values of N(d1) and N(d2) corresponding to the given volatility and time to expiration. Once we have these values, we can calculate the European Call Option Price.
For part b) Market maker's 1-day gain/loss on 10 shares if the stock price went up to $34:
If the stock price went up to $34, and the Market Maker is short call options, the Market Maker will have to buy 10 shares at the increased price of $34 and sell them at the strike price of $30. Therefore, the Market Maker's 1-day gain/loss would be 10 * ($34 - $30).