baccarategg| Option pricing theory in stock market

Talking about the stock market.BaccarateggWhen the theory of option pricing based onBaccarateggFirst of all, we should understand that an option is a special type of financial derivative that gives the holder the right to buy or sell an asset at a specific price at a specific time in the future. The core goal of option pricing theory is to determine the reasonable value of this right.

Basic concept

Option pricing theory is based on several basic concepts: contract type, exercise price, maturity date, market volatility, risk-free interest rate and expected rate of return. Options can be call options (Call Option) or put options (Put Option). The exercise price is the price at which the holder can buy or sell the asset. The expiration date is the time when the option contract expires, and the market volatility is an index to measure the degree of asset price volatility. The risk-free interest rate is usually the interest rate of treasury bonds, and the expected return is the expected rate of return on assets.

Black-Scholes model

Black-Scholes model is the most famous and widely used model in option pricing theory. The model was proposed by Fischer Black and Myron Scholes in 1973. The Black-Scholes formula is as follows:\ [C = rT 0 N (diter1)-X e ^ {- rT} N (dumb2)\]\ [P = X e ^ {- sq0} N (- dumb2)-slug 0N (- dumb1)\] where: -\ (C\) and\ (P\) are the theoretical values of call and put options, respectively. Production price -\ (X\) is exercise price -\ (r\) is risk-free interest rate -\ (T\) is remaining maturity time -\ (N (\ cdot)\) is cumulative distribution function of standard normal distribution -\ (dwind1\) and\ (dwind2\) are intermediate variables in the model-Black-Scholes model assumes that asset prices follow geometric Brownian motion. The market is efficient, there are no arbitrage opportunities, and transaction costs and taxes are negligible.

Binomial option pricing model

Binomial option pricing model is a discrete-time option pricing method, which was proposed by Cox, Ross and Rubinstein in 1979. Compared with the Black-Scholes model, the binomial model assumes that asset prices have two possible outcomes at each time step: up or down. The model simulates the path of asset price by building a binary tree, then calculates the value of options under different paths, and finally calculates the average value to get the theoretical price of options.

Monte Carlo simulation

Monte Carlo simulation is an option pricing method based on simulation, which estimates the theoretical value of options by simulating a large number of asset price paths. Compared with binomial model, Monte Carlo simulation can deal with more complex option pricing problems, such as path dependent options and nonlinear options. However, the cost of Monte Carlo simulation is high, and the accuracy of the results depends on the number of simulations.

Factors affecting option pricing

The following are some key factors that affect option pricing: 1. Asset price volatility: the greater the volatility, the higher the option value. two。 Remaining expiration time: the longer the maturity time, the higher the option value. 3. Risk-free interest rate: for call options, the higher the risk-free interest rate is, the higher the option value is; for put options, the impact of risk-free interest rate is smaller. 4. Exercise price: for call options, the lower the exercise price, the higher the option value; for put options, the higher the exercise price, the higher the option value. 5. Expected return: the higher the expected return, the higher the option value. These factors affect the price of options market by affecting the actual value and theoretical value of options.

Summary

Option pricing theory is an important field in finance, which involves the determination of option value and the formulation of option strategy. There are three kinds of Black-Scholes model, binomial option pricing model and Monte Carlo simulation.