Question

Draw a diagram showing the profit and loss of a natural gas put option (for March 2018) with a strike price of $3.10/MMBtu and the premium of $0.2. Make sure to show how the profit/loss situation depends on the gas price at the time of the option maturity. Under what circumstances will the holder of the option make a gain? Under what circumstances will the option be exercised?

Answer 1

As Put option provide right to sell to the holder of option , which indicate the pay off from PUT option ,

Max (0, X-S) or detailed pay off with premium paid Max( -premium , Strike - Spot price - premium) ,

Spot price(S)	Strike Price(X)	Premium	Payoff
$0	$3.10	($0.20)	$2.90
$0.25	$3.10	($0.20)	$2.65
$0.50	$3.10	($0.20)	$2.40
$0.75	$3.10	($0.20)	$2.15
$1	$3.10	($0.20)	$1.90
$1.25	$3.10	($0.20)	$1.65
$1.50	$3.10	($0.20)	$1.40
$1.75	$3.10	($0.20)	$1.15
$2	$3.10	($0.20)	$0.90
$2.25	$3.10	($0.20)	$0.65
$2.50	$3.10	($0.20)	$0.40
$2.75	$3.10	($0.20)	$0.15
$2.89	$3.10	($0.20)	$0.01
$2.90	$3.10	($0.20)	$0.00
$3	$3.10	($0.20)	($0.10)
$3.25	$3.10	($0.20)	($0.20)
$3.50	$3.10	($0.20)	($0.20)
$3.75	$3.10	($0.20)	($0.20)
$4	$3.10	($0.20)	($0.20)
$4.25	$3.10	($0.20)	($0.20)
$4.50	$3.10	($0.20)	($0.20)
$4.75	$3.10	($0.20)	($0.20)
$5	$3.10	($0.20)	($0.20)
$5.25	$3.10	($0.20)	($0.20)
$5.50	$3.10	($0.20)	($0.20)
$5.75	$3.10	($0.20)	($0.20)

From the above excel calculation , it is clear that the Put Holders will be in profit till price of

a natural gas is less than of equal to $ 2.90 /MMBTU at time of maturity of option. The option holder will be in loss with increase of price limited to premium paid.

Pay off diagram,