Binomial models in finance by John van der Hoek, Robert J Elliott

By John van der Hoek, Robert J Elliott

This publication bargains with many themes in glossy monetary arithmetic in a manner that doesn't use complicated mathematical instruments and indicates how those types may be numerically applied in a pragmatic manner. The e-book is aimed toward undergraduate scholars, MBA scholars, and managers who desire to comprehend and practice monetary types within the spreadsheet computing environment.

The easy development block is the one-step binomial version the place a recognized cost at the present time can take one in all attainable values on the subsequent time. during this easy state of affairs, danger impartial pricing may be outlined and the version should be utilized to cost ahead contracts, alternate fee contracts, and rate of interest derivatives. the straightforward one-period framework can then be prolonged to multi-period versions. The authors exhibit how binomial tree types should be built for numerous functions to lead to valuations in step with industry costs. The booklet closes with a singular dialogue of actual options.

From the reviews:

"Overall, this is often an outstanding 'workbook' for practitioners who search to appreciate and practice monetary asset expense versions by way of operating via a accomplished number of either theoretical and dataset-driven numerical examples, follwoed via as much as 15 end-of-chapter workouts with elaborated components taht aid make clear the mathematical and computational facets of the chapter." Wai F. Chiu for the magazine of the yankee Statistical organization, December 2006

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44 3 The Binomial Model for Other Contracts We shall price this option in the one-step binomial asset pricing model. Write X for the price of the European call contingent premium Option. Let α be the contingent premium. Then X(0) = 0, as nothing is paid at time t = 0. Assume S(1, ↓) < K < S(1, ↑). At expiry (t = 1), the payoff is X(1, ↑) = S(1, ↑) − K − α X(1, ↓) = 0. Then 1 [πX(1, ↑) + (1 − π)X(1, ↓)] R π 1 = π [S(1, ↑) − K] − α R R 0 = X(0) = so α= R C(0), π where C(0) = π [S(1, ↑) − K] R is the price of the vanilla call.

100 million USD). For 3 months time EXP will not know the CAD value of the payments. ). Then EXP will be guaranteed at least 100 · K million CAD for the exports. 9 (Forward exchange rate contract). Again we have long and short contract, depending on whether one is buying or selling. If you hold a long forward exchange rate contract, then you have the obligation to buy a specified amount F USD at a specified exchange rate K at time T , no matter what the actual exchange rate is at time T. No payment is made initially, and the profit at time T is F [X(T ) − K], which can be negative.

Under these circumstances we saw that it is not optimal to exercise an American call option early, as it is more profitable to sell the option than to exercise it. So the early exercise feature under these circumstances provides no extra value. We shall discuss later what happens when there are dividend payments. 34 (Call options are decreasing functions of their time to expiration). Suppose there are two calls which are identical except they have different expiration times T1 and T2 , with T1 > T2 .

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