Stochastic Processes · 免费预览
具体示例
在 u 等于 2、d 等于二分之一、r 等于四分之一的便捷模型中，后向归纳法将路径依赖的回调期权定价为 1.376；看跌看涨平价关系通过折现执行价与现货价格之差把任意一对看跌期权和看涨期权联系起来；敲出障碍对期权价值的削减量恰好等于被淘汰路径的贡献。
1. The convenient model and a lookback
The convenient model and a lookback
2. The put, and the hedging underneath
The put, and the hedging underneath
3. Put-call parity
Put-call parity
4. Knockout barriers
Knockout barriers
5. Reading a callback
The callback option pays max of past prices minus the final price. Which payoff is correct for the path visiting 4, 8, 16, 8?
6. Checking the recursion by hand
At the node reached by up-up in the callback tree, the two child values are 0 (up-up-up) and 8 (up-up-down). What is the node's value under the recursion V n = 0.4 (V_up + V_down)?
7. Why put hedges are mild
For puts, every hedge ratio along the tree lies between minus one and zero. Why?
8. Parity in one line
What does put-call parity say about a call and a put with the same strike K and expiry N?
9. When the twins coincide
In the model with u = 3/2, d = 2/3, r = 1/6, a stock starts at 36. For which strike do the two-period call and put have equal time-0 values?
10. What a barrier buys the seller
In the knockout example, the barrier at 20 erased exactly one path that would have paid 8, reducing the option's value from what it would be without the barrier to 8.660. What is the seller's saving?
11. Pricing the callback
In the convenient model the eight callback payoffs are 0, 8, 0, 6, 0, 2, 2, 3.5 with risk-neutral probability 1/2 per branch and r equal to 1/4. Compute V_0 and write the number.
12. The parity gap at the root
A stock starts at 36, interest is r equal to 1/6 per period, and a two-period call and put share the strike 49. Compute V_P minus V_C at time 0 and write the number.
13. What the barrier saved
For the knockout call, the erased path contributes (6/7) cubed times (0.6) squared times 0.4 times 8. Compute this number, the seller's saving, and write it to four decimal places.