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Options: Get to Know and Valuation

Photo by Wendell Shinn via Unsplash

Options are not something new in town, people heard multiple times before. Yet most of them are confused by overwhelming definition and complexity of mathematical model. We will be discussing about options and try to avoid the nitty-gritty of the definition and math, but instead simple explanation in analogy to get the overall picture.

Options divided into European-style and American-style. American-style allows investor to exercise even before expiration date while European-style can’t. This article, will only be focusing on European-style.

Let me tell you a story of Bob and Ash. Bob works as a sparkling maker and Ash owns acres of vineyard. Bob needs grapes for his sparkling factory and Ash needs costumer to keep operating. Due to multiple factors such as weather, ripeness, and structure of soil, the price of grape are volatile throughout the years. It’s hard for Bob to maintain production as price of raw material is uncertain.

After couple sleepless nights, Bob came with the idea of ‘call options’ for securing the price of grape and ready to propose the idea to Ash. Bob will give Ash a ‘premium’ as a right to have an ‘options’ and a ‘strike price’ as an agreed price. Ash agreed and continue to talk about ‘expiration date’ or the day of ‘options’ can be exercised. When price of grape is higher than ‘strike price’ at market, Ash will be paid based on ‘strike price’ and obligated to supply Bob’s factory. However, if price of grape in market lower than ‘strike price’, Bob will not require to buy from Ash and Ash can keep the ‘premium’ on his pocket. Sounds fair right?

FIg-1 | Exercised Call Options Mechanism

Table are turned now, as Ash looking for customer to keep in business. Ash offered Bob a ‘put options’ and Bob agreed the idea. Ash will give Bob a ‘premium’ as a right to have an ‘options’ and a ‘strike price’ as an agreed price. They discussed further about ‘expiration date’ or the day of ‘options’ can be exercised. When price of grape is higher than ‘strike price’ at market, Ash will not require to sell to Bob and Bob can keep the ‘premium’. If price of grape in market lower than ‘strike price’, Bob is obligated to buy from Ash at given ‘strike price’. So, ‘put options’ is a reverse of ‘call options’.

FIg-2 | Exercised Put Options Mechanism

After understanding the basic mechanism of options, either call or put, now you are ready to dive in to next step. In order to understand the value of options, we will be discussing option valuation with Black-Scholes Option Pricing Model.

Black-Scholes Options Valuation

  1. History

The Black-Scholes (1973) Option Pricing Model, developed by Myron Scholes along with Robert Merton for his work with Fischer developing initial Option Pricing Model, adjusts for risk with two risk variables. N(d1) is the risk adjustment factor to the current stock price and N(d2) is the risk adjustment factor to the present value of the exercise price. The invention led to Nobel prize in 1997.

2. Assumptions

Key assumptions that underlie the Black-Scholes model include:

  • Return are normally distributed
  • Underlying asset pays no income
  • No transaction cost and taxes
  • Risk-free rate is known and constant
  • Underlying asset volatility is known and constant
  • Options can only be exercised at expiration date; which only suitable for European-style options

3. Model

Fig-3 | Black-Scholes Formula

ct = Long call value

Pt = Long put value

K = Strike price

T-t = Years between valuation date and expiration date

St = Underlying asset on the valuation date

rt = Continuously risk-free rate on the valuation date

σt = Underlying volatility on the valuation date

N( )= Standard normal cumulative distribution function

4. Example

I know the math seems intimidating, now let’s take a look on example. We will use McDonald’s Corporation (MCD) as example.

Fig-4 | Black-Scholes Model on Python
Fig-5 | MCD Long Call Value

That’s it, done in second with Python.


Options may confusing a bit at glance, fortunately, after you read the story of Bob and Ash in the beginning, and take a deep dive into Black-Scholes Options Valuation, now you are completely understand the fundamentals of options.



This material has been prepared for general informational purposes only and is not intended to be relied upon as professional advice. The information is being presented without consideration of the investment objectives, risk tolerance or financial circumstances .




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