Analytical pricing of American Put options on a Zero Coupon Bond in the Heath-Jarrow-Morton model
Analytical pricing of American Put options on a Zero Coupon Bond in the Heath-Jarrow-Morton model
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Heath-Jarrow-Morton 模型中零息债券美式看跌期权的分析定价
DOI：
10.1016/j.spa.2014.09.021
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发表时间：
2015
影响因子：
1.4
通讯作者：
Chiarolla M
中科院分区：
文献类型：
--
作者：
Chiarolla M
本文研究了在Heath-Jarrow-Morton（HJM）远期利率模型的Musiela参数化下零息票债券（ZCB）美式看跌期权定价的最优停止问题，首先用概率方法证明了价格函数的正则性。然后，我们找到了一个无限维变分公式的定价问题，通过近似原来的最佳停止问题的有限维的，经过适当的平滑的回报。正如预期的那样，美国债券期权的价格等于收益的第一时间被证明是最优的。
We study the optimal stopping problem of pricing an American Put option on a Zero Coupon Bond (ZCB) in Musiela’s parametrization of the Heath–Jarrow–Morton (HJM) model for forward interest rates.First we show regularity properties of the price function by probabilistic methods. Then we find an infinite dimensional variational formulation of the pricing problem by approximating the original optimal stopping problem by finite dimensional ones, after a suitable smoothing of the payoff. As expected, the first time the price of the American bond option equals the payoff is shown to be optimal.