American options for coupon bonds and interest rates

2011 ◽  
pp. 365-398
Author(s):  
Belal E. Baaquie
Keyword(s):  
Interest Rates ◽  
American Options

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 on High Dividend Securities: A Numerical Investigation

Risks ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 59
Author(s):  
Francesco Rotondi
Keyword(s):  
Interest Rates ◽  
American Options ◽  
Least Square Method ◽  
American Option ◽  
Least Square ◽  
Stochastic Interest Rates ◽  
Stochastic Interest ◽  
Black Scholes ◽  
Ill Posed ◽  
European Counterpart

I document a sizeable bias that might arise when valuing out of the money American options via the Least Square Method proposed by Longstaff and Schwartz (2001). The key point of this algorithm is the regression-based estimate of the continuation value of an American option. If this regression is ill-posed, the procedure might deliver biased results. The price of the American option might even fall below the price of its European counterpart. For call options, this is likely to occur when the dividend yield of the underlying is high. This distortion is documented within the standard Black–Scholes–Merton model as well as within its most common extensions (the jump-diffusion, the stochastic volatility and the stochastic interest rates models). Finally, I propose two easy and effective workarounds that fix this distortion.

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