Question

To hedge its exposure to the price of oil, an airline buys a call option on oil with the exercise price Kc and sells a put option with the exercise price Kp (Kp < Kc). Both contracts have the same size chosen such as to hedge the entire exposure, and their premiums are equal. On a diagram, show

a) The unhedged exposure as a function of the future spot price of oil

b) The gain from the call option as a function of the future spot price of oil

c) The gain from the put option as a function of the future spot price of oil

d) The hedged exposure as a function of the future spot price of oil

Answer 1

					Assume Kc=$100, Buy (long) call strike price=100
					Kp=$95, Sell(Short) put at strike price=95
					Since both premium are equal,
					Net premium cost=$0
				a)	Unhedged exposure as a function of
					future spot price of oil
					Long Call:If spot price at expiration(Ep)>Kc(100), Gain=(Ep-Kc), otherwise gain/loss=0
					Short Put: If spot price at expiration (Ep) <Kp, Loss=(Kp-Ep), Otherwise gain/loss=0
					Ep	A	B	C=A+B
		SpotPrice at Expiration(Ep)	Net gain/(loss)(Unhedged)		SpotPrice at expiration(Ep)	Gain/(loss) on long call	Gain/(loss) on short put	Net gain/(Loss)
		$90	($5)		$90	$0	($5)	($5)
		$91	($4)		$91	$0	($4)	($4)
		$92	($3)		$92	$0	($3)	($3)
		$93	($2)		$93	$0	($2)	($2)
		$94	($1)		$94	$0	($1)	($1)
		$95	$0		$95	$0	$0	$0
		$96	$0		$96	$0	$0	$0
		$97	$0		$97	$0	$0	$0
		$98	$0		$98	$0	$0	$0
		$99	$0		$99	$0	$0	$0
		$100	$0		$100	$0	$0	$0
		$101	$1		$101	$1	$0	$1
		$102	$2		$102	$2	$0	$2
		$103	$3		$103	$3	$0	$3
		$104	$4		$104	$4	$0	$4
		$105	$5		$105	$5	$0	$5
					It may be noted that there is no loss or gain
					if future spot price is >Kp and <Kc
			(b)		Gain from call option
					SpotPrice at expiration(Ep)	Gain/(loss) on long call
					$90	$0
					$91	$0
					$92	$0
					$93	$0
					$94	$0
					$95	$0
					$96	$0
					$97	$0
					$98	$0
					$99	$0
					$100	$0
					$101	$1
					$102	$2
					$103	$3
					$104	$4
					$105	$5
					There will be gain , if spot price in future> Kc
				.(c)	Gain from Put Option
					SpotPrice at expiration(Ep)	Gain/(loss) on short put
					$90	($5)
					$91	($4)
					$92	($3)
					$93	($2)
					$94	($1)
					$95	$0
					$96	$0
					$97	$0
					$98	$0
					$99	$0
					$100	$0
					$101	$0
					$102	$0
					$103	$0
					$104	$0
					$105	$0
					There will be loss if spot price in future is<Kp
				(d)	Hedged exposure
					Assume current spot price is =$97.5
					Ep	C	D=97.5-Ep	E=C+D
	SpotPrice at expiration(Ep)	Net gain/(loss) on hedged exposure			SpotPrice at expiration(Ep)	Gain/(loss)from option	Gain/loss without hedging	Net gain/(loss) on hedged exposure
	$90	$2.50			$90	($5)	$7.50	$2.50
	$91	$2.50			$91	($4)	$6.50	$2.50
	$92	$2.50			$92	($3)	$5.50	$2.50
	$93	$2.50			$93	($2)	$4.50	$2.50
	$94	$2.50			$94	($1)	$3.50	$2.50
	$95	$2.50			$95	$0	$2.50	$2.50
	$96	$1.50			$96	$0	$1.50	$1.50
	$97	$0.50			$97	$0	$0.50	$0.50
	$98	($0.50)			$98	$0	($0.50)	($0.50)
	$99	($1.50)			$99	$0	($1.50)	($1.50)
	$100	($2.50)			$100	$0	($2.50)	($2.50)
	$101	($2.50)			$101	$1	($3.50)	($2.50)
	$102	($2.50)			$102	$2	($4.50)	($2.50)
	$103	($2.50)			$103	$3	($5.50)	($2.50)
	$104	($2.50)			$104	$4	($6.50)	($2.50)
	$105	($2.50)			$105	$5	($7.50)	($2.50)
					Loss or gains are limited by hedging