REFINING THE QUADRATIC APPROXIMATION FORMULA FOR AN AMERICAN OPTION

2001 ◽  
Vol 04 (05) ◽  
pp. 773-781 ◽  
Author(s):  
WOON KWONG WONG ◽  
KAI XU
Keyword(s):  
Approximation Method ◽  
American Options ◽  
American Option ◽  
Quadratic Approximation ◽  
Approximation Formula ◽  
Qualitative Behavior ◽  
Special Case

The aim of this paper is to provide a more refined approximation for the valuation of an American option, based on the quadratic approximation method. We not only show that the result using the old method is the special case of our method, but also investigate the qualitative behavior of American options with respect to a certain new parameter.

Generalized Analytical Upper Bounds for American Option Prices

2007 ◽  
Vol 42 (1) ◽  
pp. 209-227 ◽  
Author(s):  
San-Lin Chung ◽  
Hsieh-Chung Chang
Keyword(s):  
Interest Rates ◽  
American Options ◽  
General Theorem ◽  
Upper Bounds ◽  
American Option ◽  
Option Prices ◽  
Dividend Yield ◽  
Strike Price ◽  
Risky Assets ◽  
The Interest Rate

AbstractThis paper generalizes and tightens Chen and Yeh's (2002) analytical upper bounds for American options under stochastic interest rates, stochastic volatility, and jumps, where American option prices are difficult to compute with accuracy. We first generalize Theorem 1 of Chen and Yeh (2002) and apply it to derive a tighter upper bound for American calls when the interest rate is greater than the dividend yield. Our upper bounds are not only tight, but also converge to accurate American call option prices when the dividend yield or strike price is small or when volatility is large. We then propose a general theorem that can be applied to derive upper bounds for American options whose payoffs depend on several risky assets. As a demonstration, we utilize our general theorem to derive upper bounds for American exchange options and American maximum options on two risky assets.

scholarly journals American options in an imperfect complete market with default

2018 ◽  
Vol 64 ◽  
pp. 93-110 ◽  
Author(s):  
Roxana Dumitrescu ◽  
Marie-Claire Quenez ◽  
Agnès Sulem
Keyword(s):  
Optimal Stopping ◽  
Value Function ◽  
American Options ◽  
American Option ◽  
Stopping Times ◽  
Optimal Stopping Problem ◽  
Nonlinear Expectation ◽  
Portfolio Strategy ◽  
Reflected Bsde ◽  
The Value Function

We study pricing and hedging for American options in an imperfect market model with default, where the imperfections are taken into account via the nonlinearity of the wealth dynamics. The payoff is given by an RCLL adapted process (ξt). We define the seller's price of the American option as the minimum of the initial capitals which allow the seller to build up a superhedging portfolio. We prove that this price coincides with the value function of an optimal stopping problem with a nonlinear expectation 𝓔g (induced by a BSDE), which corresponds to the solution of a nonlinear reflected BSDE with obstacle (ξt). Moreover, we show the existence of a superhedging portfolio strategy. We then consider the buyer's price of the American option, which is defined as the supremum of the initial prices which allow the buyer to select an exercise time τ and a portfolio strategy φ so that he/she is superhedged. We show that the buyer's price is equal to the value function of an optimal stopping problem with a nonlinear expectation, and that it can be characterized via the solution of a reflected BSDE with obstacle (ξt). Under the additional assumption of left upper semicontinuity along stopping times of (ξt), we show the existence of a super-hedge (τ, φ) for the buyer.

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