B. Grundy, Option prices and the underlying asset's return distribution, J. Finance 46 (1991), 1045--1069.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....lognormal distribution. For related work, see Dupire [6] and Derman and Kani [5] Closer to the theme of this paper are the papers by Lo [15] who derives best possible closed form bounds on the price of a European call option given the mean and variance of the underlying stock price, by Grundy [9], who extended Lo s work for the case when the first and the kth moments of the stock price are known, and by Boyle and Lin [3] who use semidefinite optimization to find an upper bound on the price of a European call option on the maximum of a number of assets, given the means, variances and ....

....X Gamma k) subject to E [X ] V ar [X ] oe 2 : Z 1 0 (x)dx = 1 (x) 0: The closed form solution for this optimization problem is due to Scarf [21] in the context of an inventory control problem. Lo [15] observed the direct application of Scarf s result to option pricing. Grundy [9] introduced as open problems several of the problems that we solve here: using known option prices, find sharp upper and lower bounds on the moments of the stock price, and on the price of an option with a different strike price. These problems can be formulated as follows: max = min E [X ] or ....

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B. Grundy. Option prices and the underlying asset's return distribution. Journal of Finance, 46(3):1045--1070, July 1991.

....2 ; k k 2 2 2 ; if k 2 2 2 : This bound is due to Scarf [31] in the context of an inventory control problem. Lo [20] observed the direct application of Scarf s result to option pricing. For a new proof, based on optimization techniques, see Popescu [27] Grundy [10] extended Lo s work for the case when only the rst and the kth moments of the stock price are known. He also proposed as open problems some of the questions studied in this paper, such as the problem of nding bound on stock price moments, when prices q i of European call options with di erent ....

B. Grundy. Option prices and the underlying asset's return distribution. Fournal of Finance, 46(3):1045-1070, July 1991.

....the lognormal distribution. For related work, see Dupire [6] and Derman and Kani [5] Closer to the theme of this paper are the papers byLo[15] who derives best possible closed form bounds on the price of a European call option given the mean and variance of the underlying stockprice,by Grundy [9], who extended Lo s work for the case when the first and the kth moments of the stock price are known, and byBoyle and Lin [3] who use semidefinite optimization to find an upper bound on the price of a European call option on the maximum of a number of assets, given the means, variances and ....

....maximize E [max(0#X; k) subject to E [X] Var [X] oe 2 : Z 1 0 (x)dx =1 (x) 0: The closed form solution for this optimization problem is due to Scarf [21] in the context of an inventory control problem. Lo [15] observed the direct application of Scarf s result to option pricing. Grundy [9]introduced as open problems several of the problems that we solve here: using known option prices, find sharp upper and lower bounds on the moments of the stock price, and on the price of an option with a different strike price. These problems can be formulated as follows: max = min E [X] or E ....

[Article contains additional citation context not shown here]

B. Grundy. Option prices and the underlying asset's return distribution. Journal of Finance, 46(3):1045--1070, July 1991.

....of volatility parameters from the options and the time series. A close similarity between the two parameter sets would indicate that market prices do incorporate some regime switching information. While this analysis assumes that option prices are generated 7 See related discussions in Grundy (1991), Lo and Wang (1995) and Bates (1996) 20 by the regime switching model, traders may be incorporating regime switching information simply by adjusting the volatility that they use in the modified Black Scholes model. The second part of the in sample analysis investigates the correspondence ....

Grundy, B.D., 1991, Option prices and the underlying asset's return distribution, Journal of Finance 46, 1045-1069.

....Theorem 2 implies that the first term on the RHS of (6) is non positive for all s and t. Proposition 2 implies that Omega Gamma s; t) 1. Since r(t) 0 for all t, the second term on the RHS of (6) is non positive for all s and t. Since the RHS of (6) is non positive, so is the LHS of (6) 11 Grundy (1991) shows that option prices contain information not only about the riskneutralized distribution of the underlying asset, but also about its true distribution, provided the underlying asset follows a one dimensional diffusion and the risk premium on the option can be bounded. Proposition 1 has ....

Grundy, Bruce D., 1991, Option prices and the underlying asset's return distribution, Journal of Finance 46, 1045-1069.

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B. Grundy, Option prices and the underlying asset's return distribution, J. Finance 46 (1991), 1045--1069.

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B. GRUNDY. Option prices and the underlying asset's return distribution. J. Finance, 46(3):1045-- 1070, July 1991.

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