P. Carr, R. Jarrow, and R. Myneni. Alternative characterizations of American put options. Journal of Mathematical Finance, 2:87--106, 1992.  Home/Search   Document Details and Download   Summary   Related Articles   Check

.... When M = 1; 2 we will use the simpler notation L( jS; K;T ) and L 2 ( jS; K;T ) The bounds we present are for the put option on a dividend paying stock, the price of the corresponding call option, C(S; K;T ; r; can be computed using a put call symmetry relationship, for example [14, 13], C(S; K;T ; r; P (K; S; T ; r; 8) Using this relationship, the lower bound for put options is easily converted into a lower bound for call options. 2 RESULTS We evaluate the integral in (2) for any e(t) of the form given in (4) In so doing we compute a 3M 1 parameter family of ....

P. Carr, R. Jarrow, and R. Myneni. Alternative characterizations of american put options. Mathematical Finance, 2:87--106, 1992.

....and Whaley #1987#, is to divide the price of an American option into that of a similar European option and the early exercise premium. This approach was further developed and speci#c results were obtained for the case of the log normal underlying price process by Kim #1990#, Jacka #1991#, Carr, Jarrow and Myneni #1992#, and Ho, Stapleton and Subrahmanyam #1997a#. Speci#cally, an American option can be considered as a sum of two sets of cash #ows using the decomposition approach: the value of the terminal cash #ow at expiration and the value of the intermediate cash #ows between the valuation date and ....

....results. These problems make it desirable, whenever possible, to derive quasi analytical models for non standard American options. Our research shows that in many cases, such formulae can be derived, at least for some cases of exotic options, extending the work of Kim #1990#, Jacka #1991# and Carr, Jarrow and Myneni #1992#. We are able to derive quasi analytical formulae for the prices and hedge ratios in the case of barrier options #and #capped options#. The formulae are implemented using analytic approximations of the optimal exercise boundary and Richardson extrapolation. Our results indicate that our method ....

Carr, P., R. Jarrow and R. Myneni, 1992, #Alternative Characterizations of American Put Options," Mathematical Finance, 2, 87-106.

....In the context of American options under the exponential L evy model, X.L. Zhang (1995) 23] 1998) 25] extended the approach of McMillan [18] and H. Pham [20] extended the representation of the American early exercise premium due to Kim [11] Jacka [12] and Carr, Jarrow and Myneni [3]. Gerber and Shiu (1998) 10] showed that analytical formulas for the exercise barrier of perpetual options may be obtained under certain exponential L evy models, since they depend on knowing the Laplace transform of the value function rather than on the value function itself. Their rst results ....

P. Carr, R. Jarrow, R. Myneni (1992), \Alternative characterizations of American put options", Mathematical Finance, 2, 87 - 105.

....In the context of American options under the exponential Levy model, X.L. Zhang (1995) 23] 1998) 25] extended the approach of McMillan [18] and H. Pham [20] extended the representation of the American early exercise premium due to Kim [11] Jacka [12] and Carr, Jarrow and Myneni [3]. Gerber and Shiu (1998) 10] showed that analytical formulas for the exercise barrier of per 4 We expect that even these simple approximations might have a quite significant impact on pricing American options in practice, since we believe that taking advantage of the superior numerical fit of ....

P. Carr, R. Jarrow, R. Myneni (1992), "Alternative characterizations of American put options", Mathematical Finance, 2, 87 -- 105.

....options. The curve x = s(t) 0 t T is known as the optimal exercise boundary representing the asset price above which American calls are exercised optimally. No explicit analytic solution exists for the valuation of American options despite the effort by McKean [19] Carr, Jarrow, and Myneni [10], and Jacka [12] in the search for a closed form expression on w = w(x; t) Therefore, numerical methods are indispensable in the study of option pricing. The existing numerical schemes of Brennan and Schwartz [7, 8] 1991 Mathematics Subject Classification. 90A09, 65K10, 35R35, 60G40, 35K55, ....

P. Carr, R. Jarrow, and R. Myneni, Alternative characterizations of American put options, Mathematical Finance, 2 (1992), 87--106.

....methods or numerical methods. In the analytical approach, attempt has been made in the search for a simple characterization of the optimal exercise curve. For example, closed form solutions in terms of exogenous variables and the optimal exercise boundary are presented by Carr, Jarrow, and Myneni [9], Jacka [11] and Kim [13] The method of variational inequalities was employed by Bensoussan and Lions [4] and Jaillet, Lamberton, and Lapeyre [12] for a study in the solution uniqueness and existence. In the numerical methods, implicit finite difference methods of Brennan and Schwartz [6, 7] and ....

P. Carr, R. Jarrow, and R. Myneni, Alternative characterizations of American put options, Mathematical Finance, 2 (1992), 87--106.

....K fl ffl (pK Gamma pKR) S K: 12) The first line of our formula (8) represents the randomized version of a decomposition of the American put value into the European put value and the early exercise premium. This decomposition also holds in the fixed maturity setting as shown previously in Carr, Jarrow, and Myneni (1992), Jacka (1991) and Kim (1990) Note that the formula (9) for the randomized value of the European put is simpler than the Black Scholes formula in that it does not use any special functions such as the normal distribution function. On the other hand, 9) holds only for out of the money values ....

Carr, P., R. Jarrow, and R. Myneni, 1992, "Alternative Characterizations of American Put Options, " Mathematical Finance, 87--106.

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P. Carr, R. Jarrow, and R. Myneni. Alternative characterizations of American put options. Journal of Mathematical Finance, 2:87--106, 1992.

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Carr, P., R. Jarrow, & R. Myneni (1992): "Alternative Characterizations of American Put Options", Journal of Mathematical Finance, 2, 87-106.

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Carr, P., R. Jarrow and R. Myneni (1992) Alternative Characterizations of American Put Options, Mathematical Finance, 2, 87106.

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