Question

4.You are given the following information: stock price is $33, strike price is $30, volatility is 25% (annual), risk free interest rate is 8% (annual), dividend yield is 0%, T is 180 days. Calculate specifically the following:

1. European Call Option Price
2. Market maker’s 1-day gain/loss on 10 shares if the stock price went up to $34. Assume market maker is short call options. Assume C₁ = 5.67

Answer 1

Part – A

European Call Option Price?

Particular	Values
Price of the Underlying Security (P0)	$33
Strike Price (X)	$30
Volatality (V)	25%
Risk-Free Rate (r)	8%
Time Until Expiry	0.5
d1	0.4099727
d2	0.233196
Using Black-Scholes Formula d1 = [ln(P0/X) + (r+v2/2)t]/v √t
d2 = d1 – v √t

From Normal Distribution Table
N(d1)	0.65908701
N(d2)	0.59219539
N(d1) = Normsdist(d1) Function in Excel
Price of European Call Option	$4.68
Price Call = P0 * N(d1) – X * e^(-rt) * N(d2)

Part -B

Market maker’s 1-day gain/loss on 10 shares if the stock price went up to $34. Assume market maker is short call options. Assume C1 = 5.67

Solution -:

Since the price of the stock increases by one dollar, the loss has been increased for market maker (writer) by one dollar. Market maker can only make profit from short call if the price of the stock decrease from the strike price of 30$ and will have unlimited loss if the price keeps on increasing from 30$.

Option price that the market maker will get: 5.67 x 10 shares = 56.7$

Amount at which buyer will buy from the market maker: 30 x 10 shares = 300$

Amount at which market maker will sell it to the buyer: 34 x 10 shares = 340

Therefore, the loss/gain that the market maker have to bear is:

=300$ + 56.7$ - 340$

=16.7$ gain