Question

please show steps and formula. thanks.

10 6 Q F R F G H K Enter C V B Shift Alt Alt cate A) LIBOR B) 17%CLIBOR+ 1% D) LIBOR-1% 18) The current stock price of Alcoco is $70, and the stock does not pay dividends. The instantaneous risk-free rate of return is 6%. The instantaneous standard deviation of Alcoco's stock is 40%. You want to purchase a put option on this stock with an exercise price of $75 and an expiration date 30 days from now. According to the Black-Scholes OPM, you should hold re t cate shares of stock per 100 put options to hedge your risk. 18) A) 30 B) 34 C) 69 D) 74 19) Which of the following would not be considered a supply shock? in the price of imported oil 19)

Answer 1

Number of shares to hold = delta of put option * 100 (since we are calculating the number of shares to hold per 100 put options).

The delta of the put option is calculated as below :

Delta of put option = N(d₁) - 1

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

where :

S₀ = current spot price. This is 70.

K = strike price. This is 75.

r = risk-free interest rate. This is 6%, or 0.06.

t is the time to maturity in years. This is 30/365, or 0.0822

σ = standard deviation of underlying stock returns. This is 40%, or 0.40.

N(x) is the cumulative normal distribution function

We calculate d₁ as below :

• ln(S₀ / K) = ln(70 / 75). We input the same formula into Excel, i.e. =LN (70 / 75)
• (r + σ²/2)*T = (0.06 + (0.40²/2)*0.0822
• σ√T = 0.40 * √0.0822

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

N(d₁) = 0.3081.

Delta of put option = N(d₁) - 1

Delta of put option = 0.3081 - 1

Delta of put option = -0.69

Number of shares to hold = delta of put option * 100

Here, we take the absolute value of the delta (without negative sign).

Number of shares to hold = 0.69 * 100 = 69