Question

The following prices are available for call and put options on a stock priced at $50. The risk-free rate is 6 percent and the volatility is 0.35. The March options have 90 days remaining and the June options have 180 days remaining. The Black-Scholes model was used to obtain the prices.

	Calls		Puts
Strike	March	June	March	June
45	6.84	8.41	1.18	2.09
50	3.82	5.58	3.08	4.13
55	1.89	3.54	6.08	6.93

long box spread using the June 50 and 55 option

What is the profit if the stock price at expiration is $52.50?

Answer 1

			CALLS		PUTS
			A	B	C	D
		Strike	March	June	March	June
		45	6.84	8.41	1.18	2.09
		50	3.82	5.58	3.08	4.13
		55	1.89	3.54	6.08	6.93
	LONG BOX STRATEGY:
	1.BUY ONE BULL VERTICAL CALL SPREAD
	2. BUY ONE BEAR VERTICAL PUT SPREAD
	1.BUY ONE BULL VERTICAL CALL SPREAD	Cash Flow
	a. Buy one June Call Option With Strike 50	-$5.58
	bSell One June Call Option With Strike 55	$3.54
	2. BUY ONE BEAR VERTICAL PUT SPREAD
	c. Buy one Put Option with Strike 55	-$6.93
	d.Sell One Put Option with Strike 50	$4.13
	NET COST FOR THE LONG BOX	-$4.84
	CALL OPTION PAYOFF :
	Payoff for Buying an option With Strike Price =St and Price at Expiration =52.5
	Payoff =Max((52.5-St),0)
	Payoff for Selling an option With Strike Price =St and Price at Expiration =52.5
	Payoff =Min.((St-52.5),0)
	PUT OPTION PAYOFF:
	Payoff for Buying an option With Strike Price =St and Price at Expiration =52.5
	Payoff =Max((St-52.5),0)
	Payoff for Selling an option With Strike Price =St and Price at Expiration =52.5
	Payoff =Min.((52.5-St),0)
	CALCULATION OF PROFIT
	Present Value of Future Cash Flow
	Interest Rate =6%=0.06, Time =60 days =2/12 Years	0.166667	Years
	PV =(Cash flow)/(e^(0.06*0.1667)
	PROFIT FOR CALL OPTIONS VERTICAL SPREAD
	Price at Expiration =52.5		A	B	C=A+B
		Price	Payoff	Payoff	Net
		at Expiration	Buy Call Strike =50	SELL Call Strike=55	Payoff
		52.5	2.5	0	2.5
	PROFIT FOR PUT OPTIONS VERTICAL SPREAD
			A	B	C=A+B
		Price	Payoff	Payoff	Net
		at Expiration	Buy PUT Strike =55	SELL PUT Strike=50	Payoff
		52.5	2.5	0	2.5
	Total Payoff from LONG BOX =2.5+2.5=	$5
	Present Cost of Strategy	$4.84
	Future Value of Cost after 180 days=4.84*(e^(.06*0.5)	$4.99
	Interest Rate =6%=0.06
	Number of years in future =180/360=0.5
	Profit FOR LONG BOX STRATEGY =$5-$4.99=	$0.01