What Is a Roth Option?
Although Black-Scholes option pricing model has many advantages, its derivation process is difficult to accept. In 1979, Rose et al. Used a relatively simple method to design an option pricing model, called the Binomial Model or Binomial Tree. The Binomial Option Pricing Model is an option pricing model proposed by JCCox, SAross, M. Rubinstein, and Sharpe. It is mainly used to calculate the value of American options. The advantage is that it is relatively straightforward and can be applied without much mathematical knowledge.
Binary tree option pricing model
- Binomial
- In 1973,
- 1: Advantages and disadvantages of the Black-Scholes equation model:
- Advantages: For European options, there is an accurate pricing formula;
- Disadvantages: For American options, there is no precise pricing formula, it is impossible to find a solution expression, and the mathematical derivation and solution process is difficult to accept and master in the financial world.
- 2: Thought:
- The assumptions are maturity and there are only two possibilities, and the assumptions of 10% rise and fall are rough. Amended as follows: T is divided into many small time intervals t, and at each t, the stock price changes from S to Su or Sd. If the probability of a price rise is p, then the probability of a fall is 1-p.
- 3: Determination of u, p, d:
- The Black-Scholes equation tells us that the market can be assumed to be risk neutral. That is, the expected stock return is equal to the risk-free interest rate r, so:
- Black-Scholes equation
- Because the stock price changes conform to the Brownian motion, so
- use
- get
- In order to ensure that the node prices of different routes can overlap, the rise and fall of the stock price should meet:
- From (1), (3), (4) can be solved:
- among them:
- 4 Conclusion:
- In equal sufficiently small t periods, regardless of the stock price at the beginning. U, d and p determined by (1) ~ (4) are all constants. (That is, it is only related to t, , r, and has nothing to do with S).