1. Underlying stock price: The current market price of the underlying stock.

2. Strike price: The predetermined price at which the option can be exercised.

3. Time to expiry: The remaining time until the option expires.

4. Volatility: The expected fluctuations in the underlying stock's price.

5. Risk-free interest rate: The current interest rate of risk-free investments, such as government bonds.

6. Dividend yield: The dividend payment rate of the underlying stock.

These factors interact with each other in complex ways, making option pricing a fascinating and challenging task. We'll delve into the details of each factor and explore how they influence option prices.

Strike price. 

The strike price has a direct impact on the option premium.

For Call Options:

• A lower strike price means a higher premium, as the option gives the holder the right to buy the underlying stock at a lower price.

• Example: INFY call with a strike price of Rs. 1000 has a premium of Rs. 20, while a call with a strike price of Rs. 960 has a higher premium of Rs. 24.

For Put Options:

• A higher strike price means a higher premium, as the option gives the holder the right to sell the underlying stock at a higher price.

• Example: A put option with a higher strike price will have a higher premium, as it gives the holder the right to sell the stock at a higher price.

So, the relationship between strike price and premium is:

• Inverse for Call Options: Lower strike price = Higher premium

• Direct for Put Options: Higher strike price = Higher premium

The spot price of the underlying stock.

The spot price of the underlying stock has a significant impact on the option premium.

Here's a summary of the relationship between spot price and option premium:

For Call Options:

• A higher spot price means a higher premium, as the option is more likely to expire in-the-money.

• Example: If the spot price of the underlying stock is high, the call option that is in-the-money will have a higher value.

For Put Options:

• A higher spot price means a lower premium, as the option is less likely to expire in-the-money.

• Example: If the spot price of the underlying stock is high, the put option that is out-of-the-money will have a lower value.

So, the relationship between spot price and premium is:

• Direct for Call Options: Higher spot price = Higher premium

• Inverse for Put Options: Higher spot price = Lower premium

Time to expiry

Time to expiry is a crucial factor in option pricing.

The more time remaining until expiry, the higher the probability of the option moving in-the-money, making the option more valuable. As a result, the premium increases with the time to expiry.

Here's a summary:

For both Call and Put Options:

• More time to expiry means a higher premium.

• Example: A three-month option contract will have a higher premium compared to a one-month option contract.

The relationship between time to expiry and premium is direct for both Call and Put Options:

• More time to expiry = Higher premium

The volatility of the underlying stock

Volatility is a crucial factor in option pricing, and it affects both call and put options similarly.

When the underlying stock price is highly volatile, the chances of the option expiring in-the-money increase, making the option more valuable. As a result, the premium rises with volatility.

Here's a summary:

For both Call and Put Options:

• Higher volatility of the underlying stock price means a higher premium.

• Example: If the stock price is highly volatile, the option holder has a higher chance of making a profit, and the option writer faces greater risk, resulting in a higher premium.

The relationship between volatility and premium is direct for both Call and Put Options:

• Higher volatility = Higher premium

Risk-free rate 

The risk-free interest rate also impacts option pricing.

When the risk-free interest rate increases:

• The present value of the strike price decreases, making the option more attractive, and thus increasing the premium for call options.

• The present value of the strike price decreases, making the option less attractive, and thus decreasing the premium for put options.

Here's a summary:

For Call Options:

• Higher risk-free interest rate = Higher premium

For Put Options:

• Higher risk-free interest rate = Lower premium

Dividends

Dividends also impact option pricing.

When dividends are declared:

• The stock price decreases, making the put option more valuable and increasing its premium.

• The stock price decreases, making the call option less valuable and decreasing its premium.

Here's a summary:

For Call Options:

• Higher dividend = Lower premium

For Put Options:

• Higher dividend = Higher premium

You've now covered all the major factors that affect option pricing! These factors are used in option pricing models, such as the Black-Scholes model, to estimate the value of options contracts before expiry.