Question

You observe a stock is priced at $165. This stock’s option expirations are July 15, August 20 and October 15. The risk-free rates associated with the option expirations are 5 percent, 5.35 percent and 5.7 percent. The standard deviation is 21 percent. The stock’s option prices are stated in the table below.

	Calls			Puts
Strike	Jul	Aug	Oct	Jul	Aug	Oct
160	6.00	8.10	11.10	0.75	2.75	4.50
165	2.70	5.25	8.10	2.40	4.75	6.75
170	0.80	3.25	6.00	5.75	7.50	9.00

Required:

(a) Construct a bear spread using October calls.  

(b) Determine the profits for the holding period indicated if the stock price is at $150, $155, $160, $165, $170, $175 and $180 at the end of the holding period. Plot a graph for this result.

(c) Compute the breakeven stock price at the expiration.

(d) Identify the maximum and minimum profit.

(e) Justify your answers above.  

Answer 1

Holder of call option will have right to buy underlying asset at the agreed price ( Strike Price). As he is receiving right, he needs to pay premium to writer of call option.
He will exercise the right, when expected spot price > Strike Price. Then writer of option has to sell at the strike Price.

Bear spread with call option: Person holds a call option with high strike price and writes a call with low strike price.
Part a)

Particulars	Amount
Strike Price of Call (Low)_Write	$ 160.00
Strike price of call (High)_Hold	$ 170.00
Value of Call (Low)_Write	$   11.10
Value of call (High)_Hold	$      6.00

Note: The call with lower strike price will have higher premium than call with higher strike Price.

Part b)

( A)	( B )	( C )	( D) = ( B ) - ( C )	( E )	( F )	(G) = ( E) - (F)	(H) = (D) + (G)
FSP	Call Option_LSP	Call Option_LSP	Call Option_LSP	Call Option_HSP	Call Option_HSP	Call Option_HSP	Bear spread with call Payoff
Vc_Low_strk	Premium Recd	Payoff	Vc_High Strk	Premium paid	Payoff
$ 150.00	$                         -	$                  11.10	$                  11.10	$                          -	$                     6.00	$                    -6.00	$                     5.10
$ 155.00	$                         -	$                  11.10	$                  11.10	$                          -	$                     6.00	$                    -6.00	$                     5.10
$ 160.00	$                         -	$                  11.10	$                  11.10	$                          -	$                     6.00	$                    -6.00	$                     5.10
$ 165.00	$                   -5.00	$                  11.10	$                    6.10	$                          -	$                     6.00	$                    -6.00	$                     0.10
$ 170.00	$                -10.00	$                  11.10	$                    1.10	$                          -	$                     6.00	$                    -6.00	$                    -4.90
$ 175.00	$                -15.00	$                  11.10	$                   -3.90	$                     5.00	$                     6.00	$                    -1.00	$                    -4.90
$ 180.00	$                -20.00	$                  11.10	$                   -8.90	$                   10.00	$                     6.00	$                     4.00	$                    -4.90

Part c) Break even stock Price at expiration = 165.10

At this price we have to pay 5.10 to the call option holders (he will excercise the option and buy the share for 160) and we have already recived the premium of 11.1. The net profit is 11.1-5.1 = 6.

We have purchased one call option at strike price of 170 which will be lapsed. we lose the amount we paid towards call option premium i.e. 6.

The net pay off is 0

Part d)

From the above table we can see we have maximum profit of 5.1 and minimum profit is not guarenteed but maximum loss can be restricted to 4.9

Part e)

Bear call spreads are considered limited-risk and limited-reward because traders can contain their losses or realize reduced profits by using this strategy. The limits of their profits and losses are determined by the strike prices of their call options.