Background So far in this module we have discussed all the important Option Greeks and their applications. It is now time to understand how to calculate these Greeks using the Black & Sch ..
So far in this module we have discussed all the important Option Greeks and their applications. It is now time to understand how to calculate these Greeks using the Black & Scholes (BS) Options pricing calculator. The BS options pricing calculator is based on the Black and Scholes options pricing model, which was first published by Fisher Black and Myron Scholes (hence the name Black & Scholes) in 1973, however Robert C Merton developed the model and brought in a full mathematical understanding to the pricing formula.
This particular pricing model is highly revered in the financial market, so much so that both Robert C Merton and Myron Scholes received the 1997 Noble Prize for Economic Sciences. The B&S options pricing model involves mathematical concepts such as partial differential equations, normal distribution, stochastic processes etc.
My objective is to take you through the practical application of the Black & Scholes options pricing formula.
Think of the BS calculator as a black box, which takes in a bunch of inputs and gives out a bunch of outputs. The inputs required are mostly market data of the options contract and the outputs are the Option Greeks.
The framework for the pricing model works like this:
On the input side:
Spot price – This is the spot price at which the underlying is trading. Note we can even replace the spot price with the futures price. We use the futures price when the option contract is based on futures as its underlying. Usually the commodity and in some cases the currency options are based on futures. For equity option contacts always use the spot price.
Interest Rate – This is risk free rate prevailing in the economy. Use the RBI 91 day Treasury bill rate for this purpose. You can get the rate from the RBI website, RBI has made it available on their landing page, as highlighted below.
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As of September 2015 the prevailing rate is 7.4769% per annum.
Dividend – This is the dividend per share expected in the stock, provided the stock goes ex dividend within the expiry period. For example, assume today is 11th September and you wish to calculate the Option Greeks for the ICICI Bank option contract. Assume ICICI Bank is going ex dividend on 18th Sept with a dividend of Rs.4. The expiry for the September series is 24th September 2015, hence the dividend would be Rs.4. in this case.
Number of days to expiry – This the number of calendar days left to expiry
Volatility – This is where you need to enter the option’s implied volatility. You can always look at the option chain provided by NSE to extract the implied volatility data.
Let us use this information to calculate the option Greeks for ICICI 280 CE.
On the output side, notice the following –
I’m assuming that by now you are fairly familiar with what each of the Greeks convey, and the application of the same.
One last note on option calculators – the option calculator is mainly used to calculate the Option Greeks and the theoretical option price. Sometimes small difference arises owing to variations in input assumptions. Hence for this reason, it is good to have room for the inevitable modeling errors. However by and large, the option calculator is fairly accurate.
While we are discussing the topic on Option pricing, it perhaps makes sense to discuss ‘Put Call Parity’ (PCP). PCP is a simple mathematical equation which states –
Put Value + Spot Price = Present value of strike (invested to maturity) + Call Value.
The equation above holds true assuming –
For people who are not familiar with the concept of Present value, I would suggest you read through this – (section 14.3).
Assuming you are familiar with the concept of Present value, we can restate the above equation as –
Put Option + Spot Price = Strike + Call options
Underlying = Infosys
Strike = 1200
Spot = 1200
Assume upon expiry Infosys expires at 1100, what do you think happens?
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