The original derivation process of 1 BS formula adopts partial differential equation, geometric Brownian motion property in stochastic process (describing the underlying assets) and Ito formula. If you haven't studied stochastic and partial differential estimation, only Martians can explain it to you. If you want this form, look at the binary tree model. Binary tree model is easy to understand and can be deduced by itself. The limit of binary tree model (infinite fine time division) is BS formula. If you really want to know the formula of BS model, you can look at Jiang's Mathematical Model and Method of Option Pricing. It is enough to select the European option from chapter 1 to chapter 5.
2. In this model, five risk interest rates must exist in the form of continuous compound interest. Simple risk-free interest rate or discontinuous risk-free interest rate is generally calculated once a year, and R is required to be continuous compound interest. R0 must be converted into r to be substituted in the above formula. The transformation relationship between them is: r = ln (1+R0) or R0 = exp (r)- 1. For example, if R0 = 0.06, then r = ln( 1+0.06) = 0.0583, that is, 100 will get 583% continuous compound interest investment of 106 in the second year, which is consistent with the direct calculation of R0 = 0.06.
3.BS option pricing model: b-s-m model assumes that stock prices fluctuate randomly and obey lognormal distribution; During the validity period of the option, the risk-free interest rate, expected return variables and price volatility of stock assets are constant; There is no friction in the market, that is, there is no tax and transaction cost; Stock assets do not pay dividends and other benefits during the validity period of the option (this assumption can be abandoned); Option is a European option, that is, it cannot be exercised before the option expires; There is no risk-free arbitrage opportunity in the financial market; The transaction of financial assets can continue; All financial assets can be used for short selling.
: Futures options refer to options in futures contracts. A futures option contract refers to a futures contract that buys and sells a certain number of specific commodities or assets at an agreed price on or before the expiration date of the option. Futures options are based on commodity futures contracts. When a futures option contract is executed, it is not the commodity represented by the futures contract, but the futures contract itself.