Question

I have an asset that can be sold for 200 mil in the market. If in one year depending on the state of the economy the price can either go up to 400 mil or down to 100 mil how could i determine the price of the put option to prevent loss?

Answer 1

According to the Black Scholes model, following factors impact the price of an option:

• Market Price of the Stock: An increase in the stock price positively impacts the call option value but negatively impacts the put option value
• Strike Price of the Stock: A shift to higher strike prices reduces the value of a call option but increases the value of a put option
• Interest rates: An increase in the interest rates reduces the present value of the strike price and makes the call option more valuable and the put option less valuable
• An reduction in the time to maturity or time to expiry reduces the value of a call option and also the put option

An increase in the volatility of the stock increases the value of the call options and also of the put option.
As can be seen from the above points, it is only volatility that impacts call and put options in the same direction. The case is the same for time to expiry but that is a subset of volatility since longer time to expiry builds greater expectations of volatility. But why is it that volatility impacts calls and puts in the same direction.

The reasons are not far to seek. An option (both calls and puts) are non-symmetric. That means, the buyer of the option will only exercise the option when it is favorable and choose to forego the premium when the price movement is negative. This rule applies to call options and to put options. Higher volatility means higher upside risk or higher downside risk. When there is downside risk, the buyer of the call option will forego the premium. When there is upside risk, the buyer of the call option will rake in the profits. The same rule applies to put options too. That is why higher volatility makes call options and put options more valuable.

The break-even point is quite easy to calculate for a put option:

Break-even Stock Price = Put Option Strike Price – Premium Paid

Profits or losses on a put option uses the following simple formula:

Put Option Profit/Loss = Breakeven Point – Stock Price at Expiration