Question

Suppose Sarah's stock price is currently $50. In the next six months it will either fall to $45 or rise to $70. What is the option delta of a call option with an exercise price of $65?

Answer 1

The option delta of a call option with an exercise price of $65 is 1.33.

Step-by-step explanation:

The option delta of a call option represents the sensitivity of the option price to changes in the underlying stock price. It measures the change in the option price for a $1 change in the stock price.

To calculate the option delta, we need to determine the probability-weighted average change in the stock price. In this case, the stock price can either fall to $45 or rise to $70, with equal probabilities of 0.5.

So the average change in the stock price is (0.5 * ($70 - $50)) + (0.5 * ($45 - $50))

= $10 - $2.5 = $7.5.

Since the exercise price of the call option is $65, which is higher than the current stock price of $50, the option delta would be positive.

The option delta can be calculated as ($65 - $50) / $7.5 = 1.33.