Introduction to Corporate Finance

8: Options

We can see a similar relationship by looking at Table 8.3, which shows what happened to the prices

of March Charybdis options during the week 11–18 February 2016. During that week, Charybdis shares

fell $3.26. All the call prices in Table 8.3 declined during the week, but all the put prices increased. In

response to the $3.26 decline in Charybdis shares, call prices dropped between $0.44 and $2.80, and

put prices rose between $0.80 and $3.20. Combining the lessons of the last few paragraphs, we can say

that call prices increase and put prices decrease when the difference between the underlying share price and

the exercise price (S – X) increases.

Finally, to isolate the most important, and the most subtle, influence on option prices, examine

Table 8.4, which compares the prices of March options on two different shares, Charybdis and Dubbo

Phosphates, a producer of phosphate and potash crop fertilisers. On 18 February 2016, these two shares

traded at nearly the same prices, with Charybdis at $83.44 compared to Dubbo Phosphates’ $83.02.

We might expect options on Charybdis and on Dubbo Phosphates with similar characteristics – the

same expiration date and strike price – to trade at nearly identical prices, but Table 8.4 shows that

this was not the case. Looking at March call options with a $85 strike price, we see that Charybdis’

call sold for $2.15 while Dubbo Phosphates’ was worth 26% more at $2.71 (despite Dubbo Phosphates’

share price trading for $0.42 less than Charybdis’). For contracts with a slightly higher strike price, $90,

Dubbo Phosphates’ call was worth 46% more than Charybdis’ ($1.24 versus $0.85). Why were Dubbo

Phosphates’ call options worth so much more, even though its share price was trading at a lower price

than that for Charybdis’ shares?

TaBle 8.4 PRICES OF OPTION CONTRACTS ON TWO COMPANIES, 18 FEBRUARY 2016

On 18 February 2016, call options on Dubbo Phosphates were trading for more than Charybdis calls (holding the strike
prices and expiration dates equal). Dubbo Phosphates options were more valuable, in part, because Dubbo Phosphates
shares were more volatile.

Expiration Strike Dubbo Phosphates call Charybdis call

March $85 $2.71 $2.15

March 90 1.24 0.85

Dubbo Phosphates share price = $83.02

Charybdis share price = $83.44

History offers a clue about what makes Dubbo Phosphates options so valuable. The weekly price

movements in the two shares reveal that the fluctuations in the share price for Dubbo Phosphates were

often larger than Charybdis’ movements. Dubbo Phosphates is a much smaller company than Charybdis,

and its cash flows are very sensitive to movements in agricultural commodity prices (which are themselves

notoriously volatile). Perhaps, then, it is not too surprising that Dubbo Phosphates’ shares are more volatile

than Charybdis’. But why should Dubbo Phosphates’ higher volatility lead to higher option prices?

The answer lies in the asymmetry of option payoffs. When a call option expires, its payoff is zero, for

a wide range of share prices. Whether the share price falls below the option’s strike price by $1, $10 or

$100, the call payoff is zero. On the other hand, as the share price rises above the strike price, the call

option’s payoff increases. A similar relationship holds for puts. The value of a put at expiration is zero

if the share price is greater than the strike price. Whether the share price is just above or far above the

strike price, it does not change the payoff. However, the put option has a larger payoff the lower the

share price falls, once it falls below the strike price. In summary, call and put option prices increase as the

volatility of the underlying share price increases.