Question

1. Consider the following table for calls and puts

	Call Delta	Put Delta
Strike price of 40	0.60	- 0.40

1. Betty and Bob buy 1000 shares of stock and sell 12 calls. Algebraically find their Equivalent Share Position.
2. Algebraically find how many Puts should they buy or sell to be Delta Neutral.

Answer 1

a. Each share of a stock has a delta of 1.

Buying 1000 shares have a delta of 1,000

Each call option is for 100 shares of the underlying.

Selling 12 calls has a delta of 12 * 100 * -0.6 = -720

Since we are selling call options, we have used a negative sign for Call Delta.

The total delta of buying 1000 shares and selling 12 calls = 1,000 - 720

The total delta of buying 1000 shares and selling 12 calls = 280

The Equivalent Share position = Owning 280 shares of stock.

b. Since we are long 280 shares of stock. We need to buy put options to make the position delta neutral.

Number of put option contracts to buy = Delta of 280 shares/(Delta of Put * 100)

(Ignore the negative sign)

Number of put option contracts to buy = 280/(0.4 * 100)

Number of put option contracts to buy = 7

Let's verify: Delta of each put option is -0.4

The delta of 7 put option contracts = 7 * 100 * -0.4 = -280

Now the position is delta neutral: 280 - 280 = 0