Stochastic Processes · 免费预览
两个简单的例子
将利率设为零时，一期看涨期权的标的股票价格升至 120 或降至 80，该期权存在唯一的无套利价格 5，可通过复制得到；由鞅测度概率也会得到同样的数值；而两期二叉树给出的价格为 10，并附有明确的对冲方案。
1. Pricing without probabilities
Pricing without probabilities
2. The martingale measure
The martingale measure
3. A two-period tree
A two-period tree
4. Replication, the Wall Street view
Replication, the Wall Street view
5. What arbitrage means
What is an arbitrage opportunity in a market model?
6. The five-dollar verdict
Why must the call option on the 90-stock cost exactly 5?
7. The other face of pricing
What is a martingale measure for a market?
8. Computing the bookkeeping probabilities
The stock moves up 30 or down 10. What probabilities make it a martingale?
9. Trees price by branch
In the two-period tree, how are the martingale probabilities found?
10. Replication pins the price
Why does finding a replicating portfolio determine the option's price exactly?
11. The squeezed price
A stock at 90 moves to 120 or 80, and a call struck at 100 pays 20 or 0. Using the no-arbitrage argument, compute the option price c in dollars and write the number.
12. The bookkeeping probability
For the same stock with moves of plus 30 and minus 10, find the up-move probability that makes the stock a martingale, and write the answer as a fraction or decimal.
13. Pricing the tree
In the two-period tree, the four terminal payoffs of the call struck at 100 are 40, 15, 20, 0 with martingale path probabilities 1/15, 4/15, 1/6, 1/2. Compute the option value and write the number of dollars.