66
6 The Greeks and Risk Management
Fig. 6.6 Profit diagram of bull-spread (left) and bear-spread (right)
small initial probability, as per Black-Scholes theory, to be exercised at maturity. It
thus is inexpensive, but pays off big-time in times of market crashes.
It should be obvious that the financial constructions are equivalent to betting on
an expected performance of some share. If we wish to bet on a rising market, called a
bull market, we can sell a call option with a high strike price K 2 and buy another with
a smaller strike price K 1 < K 2 . This is called a bull-spread and its profit diagram
is shown on the left-hand side in Fig. 6.6. The profit lines of the two options are
shown as dashed lines in red and magenta and the sum of both is shown as the solid
black line. Note that the cash flow of selling and purchasing the two options nearly
balances and requires little extra funds. The profit, on the other hand, shown by
the solid black line, is distinctly favoring higher share values, hence this financial
instrument implements betting on a rising market.
The converse mechanism, namely betting on a falling market, also called a bear
market, is achieved by a bear-spread where a call option with a high strike price is
purchased and one with lower strike price sold. The corresponding profit diagram is
shown on the right-hand side in Fig. 6.6.
In a similar fashion one can bet on a stable market by creating a Butterfly spread
where two options with an intermediate strike price K 2 are sold and one option is
bought with strike price K 1 < K 2 below K 2 and one with K 3 above K 2 < K 3 . The
option with K 2 is at the money and likely to be rather profitable to sell, but the two
options are far away from the present share price and rather inexpensive. Provided
the market does not move much, the option seller will be able to keep the difference
as profit.
The complementary strategy, namely betting on a varying market, is accomplished
by purchasing one call and one put option with the same strike price. This is called
a straddle and the profit diagram is shown in the top left plot in Fig. 6.7. We see
that the put and call options rise if the share prise S is significantly different from
the strike price. Note, however, that the options are purchased at the money and are
likely to be expensive. If the speculator is reasonably certain that the market is very
volatile and the stock market varies significantly, the straddle can be “pulled apart”
6 The Greeks and Risk Management
Fig. 6.6 Profit diagram of bull-spread (left) and bear-spread (right)
small initial probability, as per Black-Scholes theory, to be exercised at maturity. It
thus is inexpensive, but pays off big-time in times of market crashes.
It should be obvious that the financial constructions are equivalent to betting on
an expected performance of some share. If we wish to bet on a rising market, called a
bull market, we can sell a call option with a high strike price K 2 and buy another with
a smaller strike price K 1 < K 2 . This is called a bull-spread and its profit diagram
is shown on the left-hand side in Fig. 6.6. The profit lines of the two options are
shown as dashed lines in red and magenta and the sum of both is shown as the solid
black line. Note that the cash flow of selling and purchasing the two options nearly
balances and requires little extra funds. The profit, on the other hand, shown by
the solid black line, is distinctly favoring higher share values, hence this financial
instrument implements betting on a rising market.
The converse mechanism, namely betting on a falling market, also called a bear
market, is achieved by a bear-spread where a call option with a high strike price is
purchased and one with lower strike price sold. The corresponding profit diagram is
shown on the right-hand side in Fig. 6.6.
In a similar fashion one can bet on a stable market by creating a Butterfly spread
where two options with an intermediate strike price K 2 are sold and one option is
bought with strike price K 1 < K 2 below K 2 and one with K 3 above K 2 < K 3 . The
option with K 2 is at the money and likely to be rather profitable to sell, but the two
options are far away from the present share price and rather inexpensive. Provided
the market does not move much, the option seller will be able to keep the difference
as profit.
The complementary strategy, namely betting on a varying market, is accomplished
by purchasing one call and one put option with the same strike price. This is called
a straddle and the profit diagram is shown in the top left plot in Fig. 6.7. We see
that the put and call options rise if the share prise S is significantly different from
the strike price. Note, however, that the options are purchased at the money and are
likely to be expensive. If the speculator is reasonably certain that the market is very
volatile and the stock market varies significantly, the straddle can be “pulled apart”