BS model, namely BS option pricing model, refers to Black-Scholes-Merton option pricing model. Bs model can price interest rate options, exchange rate options, swap options and options of forward interest rate agreements, and can also arbitrage between forward and options of corresponding varieties. These arbitrages are also very popular in overseas OTC derivatives markets.

BS option pricing formula

The pricing formula of BS option is: c = s n (d 1)-x exp (-r t) n (D2).

Parameter estimation of BS model

1, estimation of risk-free interest rate

Term requirement: the risk-free interest rate should be the same as the expiration date of the option in treasury bill rate. If the same time is not available, treasury bill rate with the nearest time should be selected.

Treasury bill rate here refers to its market interest rate (yield to maturity calculated according to the market price), not coupon rate.

The risk-free interest rate in the model is calculated by continuous compound interest, not the common annual compound interest.

Continuous compound interest assumes that interest is paid continuously, and the frequency of interest payment is greater than per second 1 time.

2. Estimation of standard deviation

Basic assumptions of BS model

1. During the validity period of the option, the underlying stock of the buyer's option does not pay dividends or make other distributions;

2. Any securities purchaser can borrow any amount of funds at a short-term risk-free interest rate;

3. The short-term risk-free interest rate is known and will remain unchanged during its life;

4. There is no transaction cost for buying and selling stocks or options;

5. Short selling is allowed, and short sellers will immediately get funds at the current price of short selling stocks;

6. All securities transactions are continuous, and stock prices wander randomly;

7. The option is a European option and can only be executed on the expiration date;

8. The stock price obeys lognormal distribution.