How does the probability of price movement affects the price of an option?

Let’s understand this with an example. Suppose SBI is trading at Rs 250. There is 50% probability that its price would move to Rs 280 within this month. The probabilities of the SBI stock price moving to Rs 290, Rs 300, Rs 310 and Rs 320 are 30%, 25%, 20% and 15% respectively.

So, What would be your profits if you choose to buy a call option with a strike price of Rs 300?

If the stock price were to finish at Rs 280, Rs 290 and Rs 300, the contract would expire worthless on the date of expiration. In case, the price of SBI finishes at Rs 310 or Rs 320, you would gain Rs 10 and Rs 20 respectively. Your expected return on the call would be:

(50%*0)+(30%*0)+(25%*0)+(20%*10)+(15%*20) = Rs 5

So, for this SBI option contract, you would like to pay less than Rs 5 and the seller would like to get more than Rs 5 to make a profit.