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Unformatted text preview: Question 3.9. The strategy of buying a call (or put) and selling a call (or put) at a higher strike is called call (put) bull spread. In order to draw the profit diagrams, we need to find the future value of the cost of entering in the bull spread positions.We have: Cost of call bull spread: _$120 . 405 − $93 . 809_ × 1 . 02 = $27 . 13 Cost of put bull spread: _$51 . 777 − $74 . 201_ × 1 . 02 = − $22 . 87 The payoff diagram shows that the payoffs to the put bull spread are uniformly less than the payoffs to the call bull spread. There is a difference, because the put bull spread has a negative initial cost, i.e., we are receiving money if we enter into it. The difference is exactly $50, the value of the difference between the two strike prices. It is equivalent as well to the value of the difference of the future values of the initial premia. Yet, the higher initial cost for the call bull spread is exactly offset by the higher payoff so that the profits of both strategies are the same. It is easy to show this with equation (3.1), the putcallparity. PayoffDiagram: Profit diagram: Question 3.15. a) Profit diagram of the 1:2 950, 1050strike ratio call spread (the future value of the initial cost of which is calculated as: _$120 . 405 − 2 × $71 . 802_ × 1 . 02 = − $23 . 66): b) Profit diagram of the 2:3 950, 1050strike ratio call spread (the future value of the initial cost of which is calculated as: _2 × $120 . 405 − 3 × $71 . 802_ × 1 . 02 = $25 . 91. c) We saw that in part a), we were receiving money from our position, and in part b), we had to pay a net option premium to establish the position. This suggests that the true ratio n/m lies between1:2 and 2:3. Indeed, we can calculate the ratio n/m as: n × $120 ....
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 Winter '09
 Adam
 Interest Rates, net option premium

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