Appendix: The Black–Scholes Formula
There are a number of assumptions underlying the formula:
- There are no transaction costs and no taxes.
- The risk-free rate is constant for the life of the option.
- The market operates continuously (day and night).
- The stock price moves continuously, with no sudden jumps.
- The stock pays no cash dividends.
- The option can be exercised only at the expiration date.
- The underlying stock can be sold short without penalty.
- The distribution of returns on the underlying security (the common stock) is lognormal.
Based on these assumptions, it is possible to derive their
C = P × N(d1)-EX×e-rt×N(d2),
C = the value ...