Journal of Statistical Mechanics: Theory and Experiment
Volume 2007
April 2007
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Miquel Montero J. Stat. Mech. (2007) P04002 doi:10.1088/1742-5468/2007/04/P04002
Volatility and dividend risk in perpetual American options
Miquel Montero
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| Figure 1. Option prices for a perpetual vanilla call under dividend risk. Here we consider the implications of a possible abrupt stoppage in the dividend payment. We represent the price of the option, in terms of the moneyness (S0/K), for different values of λ. We have used typical market values for the parameters: r = 4%, δa = 1.75%, δb = 0% and σa = σb = 25%. We plot as well the pay-off function in a solid (black) line. |
| Figure 2. Option prices for a perpetual vanilla put under volatility risk. We represent the price of the option, in terms of the moneyness (S0/K), for different values of λ. We analyse here the consequences of a sudden increment in the volatility of the stock. We have used the following values for the parameters: r = 4%, δa = δb = 1.75%, σa = 10% and σb = 25%. The pay-off function is depicted in a solid (black) line. |
Figure 3. Option prices for a perpetual vanilla put under volatility risk.
We represent the price of the option, in terms of the moneyness
(S0/K), for different values of λ. We analyse here the consequences of a severe reduction in the volatility of the stock. We have used the following values for the parameters:
r = 4%, δa = δb = 1.75%, σa = 40% and σb = 25%. The previous market conditions lead to the existence of threshold  . We also plot the theoretical limiting case  for which Ha should equal Hb. |
Figure 4. Mean exercise time of a perpetual binary call under drift risk. We
represent the mean lifetime of the option, in terms of the moneyness
(S0/K0), for different values of λ. The values for the parameters are:  ,  and σa = 10%. |
Figure 5. Standard deviation of the exercise time of a perpetual binary call without drift risk. We
represent the variance of the lifetime of the option, in terms of the moneyness
(S0/K0), for different values of λ. The values of the parameters were adjusted in order to keep the drift unchanged:  . |
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Volatility and dividend risk in perpetual American options
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