I need help with #2

1. Using the information in this module, please compute the Black Scholes Merton price of a European Call Option (BY HAND) with the following characteristics:

S = 50 K = 50 Sigma = 30% r = 1.00% T = 6 months D = 0 (Answered)

For a European call option, the Black Scholes Merton price is C = S0N(d1) - Ke-rtM(d2), where S0 is the stock price k is the price at which you may buy a stock. The risk-free interest rate is r. sigma is the volatility and t is the maturation period of the investment.

Explanation: A European call option's Black Scholes Merton price may be calculated using the following formula:

S0N(d1) - Ke (d2)

where

In the stock market, S0 is the share price.

This price is known as the strike price, abbreviated as K.

Risk-free rate r is defined as: Sigma measures the degree of uncertainty.

It is time to reach maturation

The normal cumulative distribution functions N(d1) and N(d2) are standard.

In our situation,

S0 is equal to a value of 50.

K is equal to 50.

r is equal to 1%.

Sigma is equal to 30%

t = six months

N(d1) = (1/sqrt(2*pi))*integral(-infinity to d1) of e^-(x^2/2)dx

N(d2) = (1/sqrt(2*pi))*integral(-infinity to d2) of e^-(x^2/2)dx

We now have to figure out d1 and d2.

In this example, we use the formula

d1 = (ln(S0/K) + (r + sigma2/2)*T/sigma*sqrt(t))/sigma.

d2 = d1 - sigma*sqrt(t)

Now that we have the data, we can put them in and get C.

C = 50N(d1) - 50e^-0.01*6N(d2)

C = 50N(0.2570) - 50e-0.06N - 0.2570 = 50N (-0.0398)

C is equal to $15.37

2. For the same option, make a spreadsheet that calculates the BSM option price. Please verify that the price is similar to the one you obtained in Part 1 of this assignment. You may also check your Please use DG201 to value the same option using the binomial option price using a tree with 500 steps. Is this price similar to the BSM model?

I have provided a snip of the spreadsheet that I created to calculate Black Scholes options prices. It includes all of the inputs to the model.

The Excel function to calculate N(x) is =NORM.S.DIST(x). Type of Option Call Option Stock Price (So) 75.00 Exercise (Strike) Price (K) 70.00 Time to Maturity (in years) (t) 1.00 Annual Risk Free Rate (r) 1.00% Annualized Volatility (0) 20.00% Option Price $ 9.04 Additional Calculation Parameters In(So/K) 0.069 (r+o?/2)t 0.030 ovt 0.200 d1 0.495 d2 0.295 N(d1) 0.690 1(d2) 0.616 N(-d1) 0.310 N(-d2) 0.384 etrt 0.99005