Question

0. After a detailed analysis on the risks and returns of the stock market and Stock XYZ (current price=€50), you conclude that the price of XYZ is unlikely to change a lot during the course of the next 3 months. You decide to bet on this analysis and establish a short straddle position, by simultaneously writing 100 puts and 100 calls with maturity of 3 months and a strike price of €50. The premium you receive for writing each put/call is €2.50.

   •  What is the maximum profit of your position? What should the stock price be, in order to realize this maximum gain?

   •  Report the lower and higher bounds for XYZ’s price 3 months from now that provide you with a non-negative return on your position.

   •  Draw a profit diagram separately for your a) short position on puts, b) short position on calls, and c) total position

Answer 1

	Cash Flow from writing 100 put/call=100*2.50*2	€   500.00
	Price at expiration =S
	Payoff from writing Put with Strike 50
	Payoff=Min((S-50),0)
	Profit/(Loss)=Payoff+2.5
	Payoff from writing Call with Strike 50
	Payoff=Min((50-S),0)
	Profit/(Loss)=Payoff+2.5
	Maximum Profit:
	There will be maximum profit at S=50
	Payoff =0
	Profit =$500
	Non Negative Return:
	Lower Bound of Price at expiration=50-5	€     45.00
	If Price at expiration is 45
	Payoff from Put option per Straddle =	€     (5.00)
	Payoff from Call option per Straddle =	0.00
	Net Payoff	€     (5.00)
	Amount received for each short straddle	€       5.00
	Return	0.00
	Upper Bound of Price at expiration =50+5	€     55.00
	Payoff from Put option per Straddle =	0.00
	Payoff from Call option per Straddle =	€     (5.00)
	Net Payoff	0.00
	Amount received for each short straddle	€       5.00
	Return	0.00
	PROFIT DIAGRAM
			100*(payoff+2.5)
		Price at expiration	Profit/(Loss) from Put Option	Profit/(Loss) from Call Option	Total Profit/(Loss) from Straddle
		€           40	€        (750)	€          250	€        (500)
		€           42	€        (550)	€          250	€        (300)
		€           44	€        (350)	€          250	€        (100)
		€           46	€        (150)	€          250	€          100
		€           48	€             50	€          250	€          300
		€           50	€          250	€          250	€          500
		€           52	€          250	€             50	€          300
		€           54	€          250	€        (150)	€          100
		€           56	€          250	€        (350)	€        (100)
		€           58	€          250	€        (550)	€        (300)
		€           60	€          250	€        (750)	€        (500)