Risk Neutral World

Risk-Neutral valuation is the most important but still most confusing topic. I was pretty surprised when our professor derived the Black-Scholes-Merton differential equation for option pricing. There was no expected return terms in the equation instead there was risk free interest rate. Then I was introduced to the world of Risk-Neutral world. So what is this risk-neutral world. When you are pricing derivatives you assume that investors are risk neutral. It means that the value of derivative doesn't depend upon the risk preference of the investor. To find the value of any derivative you can assume a risk neutral world and then calculate the expected payoff at the expiration time and then discount it using risk free rate. Now the question is why should this work.
Aren't people looking for some kind of premium to take some risk. The answer is yes. In real world, you can't expect people to be risk neutral. You need to pay more for risky assets. Then does it mean that Balck Scholes equation is wrong. What is the catch???
Answer is risk neutral valuation is just a tool to find the value of option. The investors aren't isk neutral. Actually the price of derivative depends upon its stock value. And the stock price itself contains the risk information. So if the stock is risky , its value will fluctuate accordingly and the derivative price is proportional to stock price and hence you dont get mu factor in the derivative prices.
Thumb Rule : You can safely use risk neutral valuation tool. It simplifies the derivative world.

One more thing: When you move from risk neutral world to real world two things happen. The expected growth rate in the stock price changes and the discount rate that must be used for any payoffs from the derivative changes. These two changes always offset each other.

Note: Though putting down the BS equation would have been a better idea but then I would have to used equation editor and then paste it here as an image. I wish blogger provided equation editor as well :-)