Question

Consider a PUT option. If, in a two-state model, a stock can take a price of $300 or $200, what would be the hedge ratio for each of the following exercise prices: $280, $270, $240, $200?  


b. What do you conclude about the hedge ratio as the option strike price becomes progressively more in the money?

- Increases to a maximum of 1.0

- Decreases to a minimum of 1.0

- Increases to a maximum of 0

- Decreases to a minimum of 0

- Increases to a maximum of -1.0

- Decreases to a minimum of -1.0

Answer 1

Hedge Ratio is given by the formula
Hedge Ratio = (Pu - Pd) / (Su - Sd)

Where
Pu and Pd are value of put option at higher and lower stock price respectively and Su and Sd are higher and lower share price respectively.

Pu will always be 0 since exercise price is less than the higher stock price and put option will lapse out of the money.

Pd will be calculated by Exercise Price – Lower Stock Price
Pu = Exercise Price - 200

Calculation of Pu and Pd
Using the formula,

Exercise Price of Option	Pu	Pd
$280	0	$80
$270	0	$70
$240	0	$40
$200	0	$0

Calculation of Hedge Ratio
Su = 300
Su = 200
Su - Sd = 300 – 200 = 100

	Exercise Price of Option = $280	Exercise Price of Option = $270	Exercise Price of Option = $240	Exercise Price of Option = $200
Pu	0	0	0	0
Pd	$80	$70	$40	$0
Pu - Pd	-$80	-$70	-$40	0
Su - Sd	$100	$100	$100	$100
Hedge Ratio	-0.80	-0.70	-0.40	0

As the option strike price becomes more in the money that is exercise price of option increases, hedge ratio increases to a maximum of -1.