Question

Assume you are holding 1000 shares of XYZ stocks. You are considering using call options to hedge downside risk. The stock is selling at $45 and the following two call options are being considered for writing: an XYZ July 40 (i.e., the strike price is $40, and it expires in July); and an XYZ July 50. You are going to write 10 contracts, and each contract contains 100 options.

Part I.

Your broker provided you with the information about the prices of these two call options, one is $8 and the other is $1. But he forgot to tell you which one was for $8 and which one was for $1. Based on what you have learnt, what is the price for XYZ July 40 call? Briefly discuss, why writing a call option can provide downside protection for your stock holding.

Part II.

Compare two strategies:

Strategy A: write July 40 calls against your holding;

Strategy B: write July 50 calls against your holding.

Both strategies provide some downsize protection. Please explain which strategy offers a higher level of protection in the current case.

Answer 1

I.

Call option strike Price=$40

Stock selling price =$45

Intrinsic Value of Call Option =(45-40)=$5

If the share is bought at the strike price and sold at the market price there will be a gain of $5(In the money option)

Total Value of CallOption with Strike $40 =Intrinsic Value+Time Value=$5+Time Value

Call option strike Price=$50

Stock selling price =$45

Intrinsic Value of Call Option =$0(Out of the money option)

If a share is bought at the strike price and sold at the market price there will be no gain.

Total Value of Call Option with Strike $50 =$0+Time Value=Time Value

Hence, the Call option with Strike $40 will have a higher price =$8

A call option with Strike $50 will have a Lower price =$1

If price at expiration =S and Strike price =X,

The payoff for writing a call option =Min. ((X-S),0)

If prices move up, there will be a negative payoff. If prices go down, the payoff will be zero. But the premium received will be the profit. Writing Call option at strike $40 will give downside protection to the extent of the premium received ($8)

Part II.

July 40 call gives higher protection because the premium received is higher.