Greeks, Taxi Drivers and Options Pricing!

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More than 90% of Indian exchange volumes happen in Options trading and the largest of investors participate via Options markets. Therefore, while Infrequent Options traders often aren’t very sure about the concept of premia or the “Greeks” and leave the terrain to the advantage of those who are willing to understand just a bit more, a basic knowledge of options is very essential!

Funnily, we have multiple scenarios in our daily lives that essentially teach us what these are. And given below is a basic attempt to address this without going through very lengthy courses or videos on youtube! (Disclaimer: No guarantee you will follow the matter below either!)

Options – An Everyday Event

When we buy an insurance policy, we are essentially buying an option to “kick the bucket and leave money behind for family”.  Now, this doesn’t come free!  The insurance company charges a premium for writing this option/  policy for you – and the premium will depend on a wide variety of factors like probability, time available at the time of writing policy and additional risks. Remember – one bought the right – one isn’t forced by the insurance company to kick the bucket, as it were!

Stock or Currency options work much the same way – suppose you want “the right but not the obligation to buy or sell a stock at a particular price”- Lets say you want to sell Nifty at 12000, the writer of the contractor insurance will charge you a premium for doing so which will again, similar to the above. Remember the markets are at 11300 odd so the right to sell at 12000 (Called Put or Right to Sell Options) must be expensive like how the right to buy at 10500 must be (Called Call Options or Right to Buy Options)! These valuable options are called In the Money because they are extremely profitable if you bought and sold them immediately – its like you had the right to buy at Rs 11300 and immediately sell back at 12000- making a quick 700 bucks in the process. Options, where immediate exercise don’t make any money, are essentially called worthless – or Out of Money.

Determining Premium

Surely there is a premium to be charged, right? But what will it depend on? Similar to the insurance policy above, the writer of the option now has given you a very valuable right so of course he or she will take into account the following

  • The minimum he or she will charge for the right is how much you can make if you immediately exercised it (if you can make Rs 700 why will she not charge 700 at least?)- This is called Intrinsic Value
  • There is a long time between now and the end  of the contract – so its possible that the markets may do much above 12000 (magnifying losses for the writer as he or she may have to honor commitment to you even if the market was 14000!) or much below (before the contract comes to a close and the writer has earned the premium and finally gets a peaceful sleep). Since there is a probability of much higher profit as well, there has to be an additional charge for giving this right – there are ways to arrive at this through an assessment of what is called time value.

So when you buy this right – you are in essence paying for what you will anyway make plus sometimes called time value!

Its much like your Kaali Peeli (Black Yellow?) taxi cab on a day-long hold – he waits for you but keeps the meter on in essence giving you the right to come back into the cab at any point of time as long as it is within 8 hours right?

The Greeks

The time value component hides a lot behind its simplicity – remember, it had multiple ingredients which went to this additional “charge”- the taxi driver has to worry about when you might or might not come back / leave the ride within the 8 hours limit (Probability or Volatility), the opportunity cost of having other passengers instead of waiting for you (equivalent to the Interest Rates for the financial markets ) and of course, the length of the wait (called Time to expiration for us and the 8 hours for the taxiwallah). The taxiwallah, therefore, used a rule of thumb in the morning when you hitched the ride and gave you a BlackYellow Cab estimate for waiting charges in addition to travel charges. This was a “fixed” charge.

If you were in financial markets, you might have told him saying that instead of his rudimentary calculation based on a whole lot of nothingness, you are instead armed with a precise calculation for all this using what is called the Black Scholes Model! After all, some very knowledgeable people won a Nobel prize for this in 1997!

This is where the Kaali Peeli cabbie scratches his head and you teach him the following using the “Black Scholes Model”!

So ask him the following questions which would also tell you about the biggest three “Greeks”:

  • Assume there was a large demand for his taxi while he waited downstairs and people were willing to offer him twice as much to break his contract with you. Would the location of the cab matter to his pricing? Of course, it would! This is called the “Delta” in options – meaning how much the premium would change once the asset became more valuable (or in Options lingo as the option traveled from Out Of Money / Worthless to becoming In the Money)
  • Then ask him his – and this is critical! Would he change pricing even if everything remained the same as he anticipated but suddenly his wife called and asked him to report home or else!. Meaning that the “opportunity cost” of the agreement has increased – and not charging extra may be calamitous! In options as well, also interest rates changing have an impact on options pricing and if they go up, options prices move up and vice versa. Measuring the change in the pricing of options versus interest rates is measured via something called “Rho”.
  • Finally, ask him this – you may ask him to change his routes frequently and not the same route that he had thought of when he gave you the charges in the morning. Would he charge you more if you did this? Of course, he would be mad to say no! The impact on prices as a result of the change in volatility of the contract is measured by something called “vega”!

Since winning Nobel Prizes need complicated math, the math doesn’t end here with these 3 greeks! Each of the above three doesn’t remain constant, they in turn also change in response to the underlying situation and therefore there are some more Greeks around the corner but that’s for a later day!

Now if you have understood how 1) vagueness of the contract, 2) volatility of the route and 3) interest rates can impact the value of the taxi charges, you have probably also earned how they impact prices of options.

And if you want to show your cabbie how the “fair price” of the option can be determined, all you need to do is to show him the PL Mobile App where you have the Options Calculator as well!

And yes, the above example is for illustrative purposes only –not to be used for complex derivative trading immediately. For that, you might want to attend our PL Academy sessions (www.plindia.com/placademy or talk to our officers across the country (www.plindia.com/contactus.aspx)!

 

 

 

 

 

 

 

 

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