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

Suppose you closed the spread 60 days later. What will be the profit if the stock price is still at $50?

              

Answer 1

			CALLS		PUTS
			A	B	C	D	E=B-A	F=D-C
		Strike	March	June	March	June	Call Spread Net PresentCost	Put Spread Net Present Cost
		45	6.84	8.41	1.18	2.09	1.57	0.91
		50	3.82	5.58	3.08	4.13	1.76	1.05
		55	1.89	3.54	6.08	6.93	1.65	0.85
	As Per Calender Spread Strategy,
	June Options will be bought and March option will be sold
	For buying an option, you need to pay
	For Selling and option you will get premium
	CALL OPTION PAYOFF :
	Payoff for Buying an option With Strike Price =St and Price at Expiration =50
	Payoff =Max((50-St),0)
	Payoff for Selling an option With Strike Price =St and Price at Expiration =50
	Payoff =Min.((St-50),0)
	PUT OPTION PAYOFF:
	Payoff for Buying an option With Strike Price =St and Price at Expiration =50
	Payoff =Max((St-50),0)
	Payoff for Selling an option With Strike Price =St and Price at Expiration =50
	Payoff =Min.((50-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 CALENDER SPREAD
			A	B	C=A+B	D=C/(e^(0.06*0.1667)	E	F=D-E
		Strike	Payoff	Payoff	Net	Present	Net Cost	Profit On Call Option
			March Call(Sell)	June Call(Buy)	Payoff	Value		Calender Spread
		45	-5	5	0	0	1.57	-1.57
		50	0	0	0	0	1.76	-1.76
		55	0	0	0	0	1.65	-1.65
	PROFIT FOR PUT OPTIONS CALENDER SPREAD
			A	B	C=A+B	D=C/(e^(0.06*0.1667)	E	F=D-E
		Strike	Payoff	Payoff	Net	Present	Net Cost	Profit On PUT Option
			March PUT(Sell)	June PUT(Buy)	Payoff	Value		Calender Spread
		45	0	0	0	0	0.91	-0.91
		50	0	0	0	0	1.05	-1.05
		55	-5	5	0	0	0.85	-0.85