But there's something that appeals to me. It is called option pricing model (B-S).
As a person living in the real world, we all know that things in life are often more difficult to quantify than things in numbers, because first of all, the transformation matrix of things in different dimensions is uncertain, and risks are often more difficult to quantify, otherwise everyone can eat all over the world by Kelly's law.
The Nobel Prize winner who suffered from the bankruptcy of the Lessons Fund said: "Mathematics is beautiful, but it can't calculate people's hearts."
I think, then you can't calculate people's hearts. You can always work out the numbers.
Let's first look at what the B-S model has calculated:
C- current value of call option;
X- the exercise price of the option;
S-the current price of the subject matter;
T—— Time before the option expires (year);
R—— the annual risk-free interest rate of continuous compound interest;
N(d)- the probability that the deviation in the standard normal distribution is less than d;
E—— the base of natural logarithm, which is about 2.7 183.
The purpose of this formula is to calculate the current price of an option, but often the price is determined by the market, so the usage of this formula may be to have the price first, and then calculate the implied volatility through the price in turn. The implied volatility here is Nd 1 and Nd2.
The higher the implied volatility, the greater the future amplitude of warrants.
Although this concept should be more popular, in case I mention normal distribution, the normal distribution here refers to a distribution model with the current price as the center of symmetry, the mathematical expectation of μ and the variance of σ 2, which is widely used in engineering, physics, statistics and other fields.
In the calculation of option yield, I think lognormal distribution should be used (I have not verified this, but I have probably calculated it). The current price is often used as the point of 0%, and the x-axis is the fluctuation range. Assuming that the current price is 100, the probability values on both sides will be (0.9lg)-( 1/0.9)lg. That is to say, the probability of falling to 90 is equal to rising to11.1.
The following is a European option, which is also the pricing calculation method of the option for delivery at maturity.
C- current price, needless to say, is actually a known quantity although it is on the left side of the equation.
X- option exercise price, the price due for delivery, the higher the option exercise price, the lower the call option price.
The current price of S standard is different from the futures price delivered every month. The target of the option is the futures price of the corresponding month, and the 06 option corresponds to June. The higher the current price, the higher the corresponding option price.
T-the time before the option expires (year), which can be calculated by the expiration time and the current time.
R-the annual risk-free interest rate of continuous compound interest. Risk-free interest rate generally refers to interbank lending rate, which can be found in Shanghai shibor interest rate interface/view/0d895a50ad02de80d40c6.html.