Question

A digital (European) option is an option which would pay nothing if the option is OTM upon expiration and pays a predetermined constant amount M if the underlying asset finished ITM.

Graph the payoffs of a digital call option (long and short) with strike price X.

Answer 1

	Assume, Amount of Payment M=	$10
	Strike Price X=$100
	Digital Long Call Option
	Assume Price at expiration =S
	If S< or =$100, Payoff =0
	If S>$100, Payoff =$10
	Digital Short Call Option
	Assume Price at expiration =S
	If S< or =$100, Payoff =0
	If S>$100, Payoff =-$10
	LONG CALL OPTION
	S	A
	Price at Expiration	Payoff Long CALL
	$95	$0
	$96	$0
	$97	$0
	$98	$0
	$99	$0
	$100	$0
	$100.01	$10
	$101	$10
	$102	$10
	$103	$10
	$104	$10
	$105	$10
	$106	$10
	$107	$10
	$108	$10
	$109	$10
	$110	$10
	$111	$10
	$112	$10
	SHORT CALL OPTION
	S	A
	Price at Expiration	Payoff SHORT CALL
	$95	$0
	$96	$0
	$97	$0
	$98	$0
	$99	$0
	$100	$0
	$100.01	($10)
	$101	($10)
	$102	($10)
	$103	($10)
	$104	($10)
	$105	($10)
	$106	($10)
	$107	($10)
	$108	($10)
	$109	($10)
	$110	($10)
	$111	($10)
	$112	($10)