Explain the differences between Shorting selling call and pu

Explain the differences between Shorting (selling) call and puts, not just in definition, but in actual workings of the option, price changes, time value, the Greeks, strategic use in a portfolio, risk management etc. Give an example of a company, and one call and one put for the company and explain the pricing differences and why they are?

Solution

A call option gives the buyer option to purchase at a certain pre-determined price (strike price) the underlying asset at or within certain period of time (expiry date) without the obligation to buy. A put option gives the buyer option to sell a certain pre-determined price (strike price) the underlying asset at or within certain period of time (expiry date) without the obligation to sell. On the other hand, the seller or writer of the options is obligated in case of a call to sell to the call buyer at strike price and in case of put to buy at strike price. The option writer sell the rights to the option buyer for a certain price which is called the option premium and is dependent upon the time to expiry, interest rates, underlying asset volatility and any other related costs (like storage costs for physical assets).

The option writer is taking a view that in case of call option the price of the underlying asset will not go beyond the strike price (plus premium) by the expiry date and conversely for put the price of the asset will not go below strike price (plus premium). The value of the option is impacted by various factors as below:

a. Time Value : Longer the time to expiry, more is the time left for the asset price to move unfavourably for the option writer, hence the premium charged will be higher. However, as the option nears the expiry, the out of money options loose money exponentially

b. Price changes : Option writers delta is opposite of that of option buyers that is negative for selling calls and positive for selling puts. When the asset prices move up, the probability of loss on calls sold by them increases and when the asset prices decline the probability of loss on puts increase.

c. Use in portfolio : Generally the options are written to enhance the portfolio yields or for hedging against short term risks. Like an investor holding an asset where they expect short term negative reaction but still not significant enough to warrant a sell on the asset can sell out of the money calls. In case the call are not exercised i.e. investor expectation of short term negative price action is realised they make extra money (yield) from premium collected but incase the price moves up they will end up selling the asset though at a higer price. Coversely for selling put options, where in let us assume a trader is short on the stock and the asset prices have declined and they expect more decline but lower probability than earlier, they can hedge and reduce their delta by selling out the money puts - in this case if the asset prices decline further they may make less money but if the asset prices were to increase they can be covered by the premium earned on short puts.

In general, the puts and calls at same strike price, expiry date and asset will follow the put call parity which states:

C + PV(Strike Price) = P + S₀ - in real life also this should hold but adjusted for the transaction costs.