Stochastic Processes · 免费预览
美式期权
美式期权可以在任意时刻行权，其价值满足一个递推关系，该关系取行权收益与贴现后的延续价值两者的最大值；同一份看跌期权，作为欧式合约价值为 1.728，而允许提前行权时价值为 2.784；对于无股息股票的看涨期权，则根本不应提前行权。
1. The right to jump the queue
The right to jump the queue
2. A put that strikes early
A put that strikes early
3. The value as an optimal stopping problem
The value as an optimal stopping problem
4. Calls never jump the queue
Calls never jump the queue
5. Reading the max recursion
In the American option recursion V n equal to the max of g n and the discounted continuation, what do the two entries represent?
6. The freedom is worth something
Why must an American option's value be at least its European counterpart's?
7. The crux node
In the American put example, at the time-1 node where the stock is 4, exercise pays 6 and continuing is worth 0.4 times (2.4 + 8) = 4.16. What does the holder do?
8. Why puts like to strike
What economic force makes early exercise attractive for a deep in-the-money put?
9. Calls wait, structurally
Why does the American call on a non-dividend-paying stock never exercise early?
10. Naming the optimal rule
In the American put example, which stopping time achieves the value 2.784?
11. The American premium
For the put struck at 10 on the stock starting at 8, the European value is 1.728 and the American recursion gives max of 2 and 0.4 times (0.96 + 6). Compute the American value and write the number.
12. Cashing in at the bottom
In the same American put, at the time-2 node where the stock has fallen to 2, compute the exercise payoff g equal to (10 - 2)+ and write the number.
13. The price of patience
Compute how much the early-exercise right adds to the put by taking the American value 2.784 minus the European value 1.728, and write the number.