# What Are Derivatives, How Should We Trade Them?

In conventional terms, derivatives are financial instruments whose values are derived from an underlying. For instance, the value of Nifty Futures is derived from Nifty Spot. On paper, the concepts of derivatives are uniform for stocks and indices. However, from a trading perspective, there are significant differences between Nifty options and stock options. While stocks are traded both in the cash and futures market, the same does not apply for an Index.

**Index Options Vs Stock Options **

The price of an index option depends on 3 factors.

1. The market risk (Volatility)

2. Time to expiry

3. Risk-free rate

In Stock options, there is a slight deviation in this model as the market risk stemming from the volatility can be hedged by building positions in the cash segment as well. Because volatility is rarely the same at two different points on the time curve, we shall use the lognormal calculations to derive the price of an option.

curve, we shall use the lognormal calculations to derive the price of an option.

**The Log Normal Model**

Let us assume, the underlying price of a stock is “P” and “C” is the call option strike whose value we need to determine. The time to maturity of this option is “T” and the volatility is estimated to be “V”. We assume that the risk-free rate is “r”. Keeping in mind that the stock does not pay any dividend, we can calculate the value of the call option using the formula below:

Step 1

PN(d1)-{CN(d2)}/e^(rT)

Step 2

Derive the value of d1 and d2. Here we need to keep in mind N(d1) is the probability distribution with a mean value of 0 and a standard deviation of 1. (d1)= {natural log (P/C)+(r+V^2/2)T}/V(square root of T)

(d2)= d1- {V(square root of T)}

**Executing This Model**

The lognormal model generates the price of an option with extreme levels of accuracy. The tact lies in incorporating the correct volatility during live markets. As we had mentioned earlier, volatility is rarely the same at two different points on the time curve. In general, Volatility is caused by the arrival of new information or the uncertainty caused due to the lack of information. In both cases, it results in rapid shifts in the option price. This is why it is extremely important to be aware of real-time volatility while trading stock or Nifty options to maintain high levels of accuracy and consistency.