Options

If the option can only be exercised at maturity it is conventionally known as a European call. Else if it can be exercised on or at any time before maturity it is called an American call

position diagrams

Consider an interaction between buyers and sellers of options

Consider 2 ways in which the option owner gets a favorable position on their options

• (a)

  • the option owner has a call with strike price $530

  • suppose the share price turns out to be more than $530

  • the owner has the right to buy the stock at a price($530) which is lower than the market price

    $$(+)\text{Value of call}=\text{market price(S)}-\text{strike price(X)}$$

  • the seller will then be forced to sell the stock at $530 which is lower than the market price

    $$(-)\text{Value of call}=\text{strike price(X)}-\text{market price(S)}$$

  • now suppose instead the stock price falls. In that case the owner simply will not exercise their call as they will be buying at a strike price higher than that of the market price

    $$\text{hence the value of the call for the owner remains at 0 when }S\le X$$

• (b)

  • the option owner has a put with strike price $530

  • suppose the share price turns out to be less than $530

  • the owner has the right to sell the stock at a price($530) which is higher than the market price

    $$(+)\text{Value of put}=\text{strike price(X)}-\text{market price(S)}$$

  • the seller will then be forced to buy the stock at $530 which is higher than the market price

    $$(-)\text{Value of put}=\text{market price(S)}-\text{strike price(X)}$$

  • now suppose instead the stock price rises. In that case the owner simply will not exercise their put as they will be selling at a strike price lower than the market price.

    $$\text{hence the value of the put for the owner remains at 0 when }S\ge X$$

Option Strategies

Consider the following 3 strategies

1. Buy share + Sell Call
   • Say you bought a share at $530.
   • Now because you don't account for the $530 paid for it in a payoff diagram it does not start from zero at S=$530.
   • The value of your stock simply rises and falls together in 1 to 1 relationship with the market stock price as they just the same items.
   • Then now you sell a call with strike price $S=530$.
   • On superposition you gain the no upside graph
2. Buy Share + Buy Put
   • follow similar logic as above
3. Bank Deposit + Buy Call
   • well unlike a stock whose values varies depending on the stock market your deposit remains at the same value at which you deposited(in this case $530) i.e independent stock price
   • follow similar logic again and superimpose to get the downside protection graph