Question

You short 200 contracts of a call option on Stock XYZ. The contract multiplier is 100, i.e. each contract is on 100 shares of the stock.

In addition, you hold the following positions as of the end of previous trading day: 15,559 shares of the underlying stock; and $809,608 in debt.
The XYZ stock price is $51 right now. The risk-free interest rate is 4% per year. There are 252 trading days in a year.
Using the Black-Scholes model, you establish that the total delta of your option position is
-13,495
You adjust your hedge to bring your shareholding to match the new option delta. Which of the following is correct for your DEBT account, after you make the necessary adjustments?
a. $809,608 - (15,559 – 13,495)*51 = 704,344
b. $809,608e(0.04*1/252) + (15,559 – 13,495)*51 = 915,000
c. $809,608e(0.04*1/252) – (15,559 – 13,495)*51 = 703,932
d. $809,608 + (15,559 – 13,495)*51 = 914,872

Answer 1

c. $809,608e(0.01*1/252) - (15,559 - 13,495) *51 = 703,932

Step-by-step explanation:

Black Scholes Model is a mathematical model for pricing a contract of an option. It is best suited for dynamic financial market. The model determines the price of an option contract after incorporating the effects of volatility. In the given scenario there are 200 contracts of a call option. The trading days are 252 in the year and risk free interest rate is 4% prevailing in the market.