Question

BIC owns 51,750 shares of Smith & Oates. The shares are currently priced at $69. A call option on Smith & Oates with a strike price of $70 is selling at $3.50 and has a delta of .69. What is the number of call options necessary to create a delta-neutral hedge?

Answer 1

To create a delta-neutral hedge, you would need approximately 75,000 call options.

Step-by-step explanation:

To create a delta-neutral hedge, we need to determine the number of call options required to offset the delta of the owned shares.

The delta of a call option represents the change in the option's value in relation to the change in the underlying stock price. In this case, the call option has a delta of 0.69, which means that for every $1 increase in the stock price, the option's value will increase by $0.69.

To calculate the number of call options needed, we divide the number of owned shares (51,750) by the delta of the call option (0.69):

1. 
   
3. Number of call options needed = Number of owned shares / Delta of the call option
4. 
   
6. Number of call options needed = 51,750 / 0.69
7. 
   
9. Number of call options needed ≈ 75,000

Therefore, approximately 75,000 call options would be necessary to create a delta-neutral hedge.

Answer 2

To create a delta-neutral hedge, BIC needs to sell approximately 750 call options on Smith & Oates with a delta of .69. Since each option contract represents 100 shares, the number of options needed is determined by dividing the total delta of the shares by the product of the option's delta and 100.

Step-by-step explanation:

Delta-Neutral Hedging

To create a delta-neutral hedge for BIC's holding of Smith & Oates shares, we need to calculate the number of call options required. Delta of a call option indicates how much the price of the option is expected to change for a $1 change in the price of the underlying stock. Since the delta of the call option is .69, this means for every option contract (representing 100 shares), the position's value will change by $69 for a $1 change in the stock price.

To hedge 51,750 shares of Smith & Oates, we calculate the number of options needed to offset the delta of the shares. The delta of the shares is 1 per share as they will change dollar for dollar with the stock. Therefore, BIC would need to sell call options to create a delta-neutral hedge.

To find the total delta of the shares, we multiply 51,750 shares by the delta per share (1), which equals 51,750. To create a delta-neutral position, we need to offset this by the total delta of the options we sell. Since each call option has a delta of .69 and represents 100 shares, we divide the total delta of the shares by the product of the option's delta and the number of shares each option contract represents (51,750 / (.69 x 100)). This gives us approximately 750 call options, which BIC needs to sell in order to establish a delta-neutral hedge.