scholarly journals Option Pricing, Zero Lower Bound, and COVID-19

Risks ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 167
Author(s):  
Giacomo Morelli ◽  
Lea Petrella
Keyword(s):  
Lower Bound ◽  
Interest Rates ◽  
Quantitative Assessment ◽  
Zero Lower Bound ◽  
European Options ◽  
Equity Options ◽  
Put Options ◽  
American Put Options ◽  
Federal National Mortgage Association ◽  
American Put

This paper provides a quantitative assessment of equity options priced at the Zero Lower Bound, i.e., when interest rates are set essentially to zero. We obtain closed form formulas for American options when the Zero Lower Bound policy holds. We perform numerical implementation of American put options written on the stock Federal National Mortgage Association (FNMA) and of related bounds for the optimal exercise. The results show similarities with the corresponding European options priced at the Zero Lower Bound during the COVID-19 crisis.

scholarly journals Accuracy Tests Of American Put Valuation Models For Pharmaceutical Equity Options

2011 ◽  
Vol 6 (2) ◽  
Author(s):  
Yong H. Kim ◽  
Sangwoo Heo ◽  
Peter Cashel-Cordo ◽  
Yong S. Jang
Keyword(s):  
Option Prices ◽  
Equity Options ◽  
Forecasting Accuracy ◽  
Put Options ◽  
True Value ◽  
Black Scholes Model ◽  
American Put Options ◽  
Black Scholes ◽  
Variance Estimate ◽  
American Put

This study compares the performance of the Macmillan (1986), Barone-Adesi and Whaley (1987) MBAW model, Ju and Zhong (1999) MQuad model, Black-Scholes model and Put-Call Parity in pricing American put options of pharmaceutical companies. These are evaluated using actual option prices for three companies over 2000 to 2005, as opposed to the previous use of generated binomial option pricing data. We compare the forecasting accuracy by maturity, moneyness, and variance estimate. Contrary to Ju and Zhong (1999), we find that the MBAW outperforms the other models for at-the-money, and out-of-the-money options. The MQuad model performs best for in-the-money options. However, in this case both the MBAW and MQuad models estimates are very similar. Our results are consistent irrespective of option maturities and volatility estimates. These findings raise questions regarding the practice of using actual prices as the true value, compared to the previous results that use simulated prices.

scholarly journals Estimating the Early Exercise Premium of American Put Index Options

2009 ◽  
Author(s):  
Ako Doffou
Keyword(s):  
Interest Rates ◽  
Test Results ◽  
Quality Test ◽  
Index Options ◽  
Put Options ◽  
Early Exercise ◽  
Accuracy Test ◽  
American Put Options ◽  
American Put ◽  
Early Exercise Premium

This paper examines empirically the value of early exercise by testing the ability of two American put valuation models to predict the early exercise premium for the S&P 100 American put options. An accuracy test and a quality test are performed on (1) the MacMillan and Barone-Adesi and Whaley model, and (2) the Carr, Jarrow and Myneni model. The test results show that early exercise premium is significant regardless of moneyness. Moreover, consistent with the theory, the value of early exercise is significantly negatively related to moneyness and interest rates and significantly positively related to time to maturity and to the volatility of the underlying index. Both American put valuation models examined do not fully capture the value of early exercise embedded in American put prices.  

scholarly journals Pricing Perpetual American Put Options with Asset-Dependent Discounting

2021 ◽  
Vol 14 (3) ◽  
pp. 130
Author(s):  
Jonas Al-Hadad ◽  
Zbigniew Palmowski
Keyword(s):  
Value Function ◽  
Asset Price ◽  
Stopping Times ◽  
Martingale Measure ◽  
Put Options ◽  
American Put Options ◽  
Exact Calculations ◽  
Negative Exponential ◽  
American Put ◽  
The Value Function

The main objective of this paper is to present an algorithm of pricing perpetual American put options with asset-dependent discounting. The value function of such an instrument can be described as VAPutω(s)=supτ∈TEs[e−∫0τω(Sw)dw(K−Sτ)+], where T is a family of stopping times, ω is a discount function and E is an expectation taken with respect to a martingale measure. Moreover, we assume that the asset price process St is a geometric Lévy process with negative exponential jumps, i.e., St=seζt+σBt−∑i=1NtYi. The asset-dependent discounting is reflected in the ω function, so this approach is a generalisation of the classic case when ω is constant. It turns out that under certain conditions on the ω function, the value function VAPutω(s) is convex and can be represented in a closed form. We provide an option pricing algorithm in this scenario and we present exact calculations for the particular choices of ω such that VAPutω(s) takes a simplified form.

An Early-Exercise-Probability Perspective of American Put Options in the Low-Interest-Rate Era

2014 ◽  
Vol 35 (12) ◽  
pp. 1154-1172 ◽  
Author(s):  
Daniel Wei-Chung Miao ◽  
Yung-Hsin Lee ◽  
Wan-Ling Chao
Keyword(s):  
Interest Rate ◽  
Put Options ◽  
Early Exercise ◽  
American Put Options ◽  
American Put
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