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Probability in Finance

Probability in Finance

Super Learner
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I am unable to understand the whole concept of option pricing and the calculation 

2 Answers

365 Team
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Hi Samir,
thanks for reaching out and sorry for the delayed response. Could you share which course and which lecture you’re referring to? Thank you in advance!
Best, 
365 Eli

Probability section under The 365 Data Science Program course. The title for the lecture was Probability in Finance.

1 month

Super Learner
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Hi Samir,
 
I really liked the example provided in the lecture so I’ll stick with it in order to try to explain what option pricing is and how to calculate if calling or not calling is favorable.
 
Option pricing is an agreement between parties for the price of a stock or item at a future point in time. 
 
So let’s say you’ve got 10 google stocks and you want to sell them to me 1 week from today at $1100 a piece (their actual stock price) plus a premium of $100. It would be good if I bought them with these terms a week from now and the stocks’ unit price happened to rise from $1100 to $1200, because I’d be buying them at the lower price of $1100, hence ending up paying $11100 ($1100 x 10) + premium instead of $12000, making a net profit of $900. 
 
However, the chance of the stock price increasing is lower than that of it decreasing (0.4 against 0.6). So in order to make a choice, I calculate the expected value of both of the “best case scenarios” for me, which are:

  • calling the deal and the stock price increasing (net profit = $900)
  • not calling the deal and the stock price decreasing (net profit = -$100)

 
If the resulting expected value of these payoffs is positive, I should take the deal. Else I probably shouldn’t, so I calculate it by multiplying each payoff’s probability with its value (because we’re looking at the expected value of numerical outcomes) and adding them up:
 
E(P) = 0.6 * (-$100) + 0.4 * $900 = $300.
 
The thing is that you also know all of this, so you would try to increase the premium so that the deal is either fair or disadvantageous for me (and therefore advantageous to you). It’s a matter of making decisions that, on average, maximize profit and minimize loss. Hope this helps!