A new evaluation of mean value for fuzzy numbers and its application to American put option under uncertainty

This paper focuses primarily on pricing an American put option with a fixed term where the price process is geometric mean-reverting. The change of measure is assumed to be incorporated. Monte Carlo simulation was used to calculate the price of the option and the results obtained were analyzed. The option price was found to be $94.42 and the optimal stopping time was approximately one year after the option was sold which means that exercising early is the best for an American put option on a fixed term. Also, the seller of the put option should have sold $0.01 assets and bought $ 95.51 bonds to get the same payoff as the buyer at the end of one year for it to be a zero-sum game. In the simulation study, the parameters were varied to see the influence it had on the option price and the stopping time and it showed that it either increases or decreases the value of the option price and the optimal stopping time or it remained unchanged.

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A Note on a Moving Boundary Problem Arising in the American Put Option

Studies in Applied Mathematics ◽

10.1111/1467-9590.00183 ◽

2001 ◽

Vol 107 (2) ◽

pp. 157-183 ◽

Cited By ~ 16

Author(s):

Charles Knessl

Keyword(s):

Boundary Problem ◽

Moving Boundary ◽

Moving Boundary Problem ◽

American Put Option ◽

Put Option ◽

American Put

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THE EARLY EXERCISE PREMIUM IN AMERICAN OPTIONS BY USING NONPARAMETRIC REGRESSIONS

International Journal of Theoretical and Applied Finance ◽

10.1142/s0219024918500395 ◽

2018 ◽

Vol 21 (07) ◽

pp. 1850039

Author(s):

WEIPING LI ◽

SU CHEN

Keyword(s):

Mean Square Error ◽

Nonparametric Regression ◽

American Options ◽

Mean Square ◽

Early Exercise ◽

American Put Option ◽

Put Option ◽

Out Of Sample ◽

American Put ◽

Early Exercise Premium

The early exercise premium and the price of an American put option are evaluated by using nonparametric regression on the time to expiration, the moneyness and the volatility of underlying assets. In terms of mean square error (MSE), our nonparametric methods of American put option pricings outperform the existing classical methods for both in-the-sample (1 September 2011–31 January 2012) and out-of-sample (1 September 2012–28 February 2013) testings on the S&P 100 Index (OEX). Our methods have better predictions and more accurate approximations. The Greek letters for both the early exercise premium and the American put option are computed numerically.

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