Question

Use the following data from 2023-10-14 for a group of Jun $406 options on futures contracts

Current futures price: $405
Expiration: 2024-06-01
Risk-free rate: 5% (discrete)
Call market price: $13.15
Put market price: $10.2
Assume a standard deviation of 20% and use the Black 76 model to determine if the options are correctly priced.
Note: The table of cumulative normal distribution is on the Moodle site. If you are using Excel, you need to round dk to 2 digits and N(dk) to 4 digits.

a. What is the value of d1 ?

Round your answer to two decimal places.

Answer 1

The value of d1 is calculated using the Black 76 model formula. Input the futures price, strike price, standard deviation, time to expiration, and risk-free rate into the formula, compute d1, and then round it to two decimal places.

Step-by-step explanation:

To calculate the value of d1 using the Black 76 model, we use the formula:

d1 = (ln(F/K) + (sigma^2/2) * T) / (sigma * sqrt(T))

Where:

F = current futures price

K = strike price of the option

sigma = standard deviation or volatility

T = time to expiration in years

r = risk-free interest rate

Given:
F = $405

K = $406

sigma = 20% = 0.20

T = (2024-06-01 - 2023-10-14) / 365

r = 5%

Please calculate T based on the exact number of days between the current date and the expiration date and then compute the value of d1 accordingly. Since you have access to Excel and are required to round figures, after computing d1, round it to two decimal places.

Remember to use the natural logarithm (ln) for the calculation, and ensure that the standard deviation (sigma) and time to expiration (T) are expressed in the same time units (years).