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Chapter 15 15.1 (i)

X

Xiaoran Gao

Member
Hi,

I'm struggling on this question:

"A building society issues a one-year bond that entitles the holder to the return on a weighted-average share index (ABC500) up to a maximum level of 30% growth over the year. The bond has a guaranteed minimum level of return so that investors will receive at least x% of their initial investment back. Investors cannot redeem their bonds prior to the end of the year.

Explain how the building society can use a combination of call and put options to prevent making a loss on these bonds."

I completely understand that the building society should purchase a put option with a strike price of xS_t, since if the share price goes down below xS_t, the society can exercise the option to prevent loss. Also the society should sell something to cover the premium of this put option.

But why should the society sell a call option with a strike price of 1.3S_t?

Thanks!
 
Hi. The reason for selling the call is because of the phrase "up to a maximum level of 30% growth over the year". If the share price exceeds 1.3S_t the holder shouldn't receive any additional return (ie the payout diagram should be a flat line after 1.3S_t), and this shape is achieved by selling the call option.
 
Steve Hales said:
Hi. The reason for selling the call is because of the phrase "up to a maximum level of 30% growth over the year". If the share price exceeds 1.3S_t the holder shouldn't receive any additional return (ie the payout diagram should be a flat line after 1.3S_t), and this shape is achieved by selling the call option.
Click to expand...

Hi, Steve. Thank you for the response! But I'm still a little bit confused. As per my understanding, selling the call with a strike price of 1.3S_t means that if the buyer exercises the option (when the share price exceeds 1.3S_t), the seller of the option must sell the underlying asset, ie the share, at the strike price which is 1.3S_t. Does this indicate that the society is actually selling the share at a lower price? Wouldn't it be loss-making for the society?
 
Yes, you're correct, they would make a loss on the sale of the call option if the share price is above 1.3S_t. However, the society will also have invested in the underlying shares. So for every unit that the share price rises above the strike price, the short call will lose them one unit but the share holding will be worth one unit more. These two cancel out leaving a flat, horizontal, payoff function.
 
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