Assume the following: 1. All positions held for 6 months 2. Risk free rate = 4%

Question

Assume the following:

1. All positions held for 6 months

2. Risk free rate = 4% per year (2% for six months)

Option prices are:

Strike

Call

Put

$ 950

$120.405

$ 51.777

1000

    93.809

   74.201

1020

    84.470

   84.470

1050

    71.802

101.214

Construct a profit diagram for the purchase of a $1050-strike call and sale of a $950-strike call. Verify that is the same as buying a $1050-strike put and selling a $950-strike put. What is the difference in the initial costs of the positions? Find the Income from (positive number) or cost of (negative number) the put and call spreads.

Strike

Call

Put

$ 950

$120.405

$ 51.777

1000

    93.809

   74.201

1020

    84.470

   84.470

1050

    71.802

101.214

Explanation / Answer

Solution :

All figures in US$ -

Strike Call Put         950 120.405     51.777      1,000     93.809     74.201      1,020     84.470     84.470      1,050     71.802 101.214 1. If a call option is bought for $ 1050 strike price - The price after six months would be 1050 + 2% = $1,071 Therefore profit/loss would be as follows As the price would be more option would be excercised -1050 1071 -71.802 -50.802 Negtive profit 2. If a call option is sold for $ 950 strike price - The price after six months would be 950 + 2% = $ 969 Therefore profit/loss would be as follows As the price would be more option would be excercised by buyer of the option 950 -969 120.405 101.405 Positive profit 3. If a put option is purchased for $ 1050 strike price - The price after six months would be 1050 + 2% = $1,071 Therefore profit/loss would be as follows As the price would be more option would be excercised by seller of the option 1050 -1071 101.214 80.214 Positive profit 4. If a put option is sold for $ 950 strike price - The price after six months would be 950 + 2% = $ 969 Therefore profit/loss would be as follows As the price would be more option would be excercised by buyer of the option -950 969 -51.777 -32.777 Negtive profit

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