This continues from my last post. I will write down some notes on Black-Scholes theory.

1. time value of money.
Basically this is about interest and it represents the 'opportunity cost'. If you choose not to invest money in options, you can receive interest with relatively low or no risk.

Bearing this in mind, it will be different to receive some amount of money today as compared to receive equal amount a year later. Assuming an annual interest of i%, the amount of $Y to be received a year later will be deemed equivalent to the amount $Y/(1+i%) received today. Over here, we have introduced the concept of 'discount factor' (1/(1+i%)) to help to define the effect of time value of the money.

In Black-Scholes theory, with a few important mathematical assumptions made, the discount factor is calculated to be exp(-rT). It is more accurately called 'continuously compound interest'. Although it looked obscured, it does ring a bell for those with engineering background, exponential decay with respect to a period of time T at a factor of r.

Forget about mathematics, let's climb on the giant's shoulders first.

2. when you deposit your money with continuously compound interest r at t0, then at time (t0+t), your money plus interest will be exp(rt).