Option Strategies

Go to the companion website for more details (see Options Simulator under Chapter 16 Examples).

The Excel workbook titled options simulator contains examples of several options strategies that can be simulated and their payoffs graphed. The option spreadsheet in this workbook consists of several lattices for pricing up to three independent call options and two put options along with a Black-Scholes pricing model that provides a continuous time check against the discrete form lattices. The Black-Scholes-Merton pricing model is derived in Chapter 17. These options are linked to the payouts provided on the Strategy spreadsheet (columns A to G). For example, consider a six-month call option on a share with current spot price at $100 and with annual volatility 20 percent. The strike price of the call is and with annual risk-free rate of 5 percent. This option is priced at $13.44, using the lattice, and $13.50, using Black-Scholes. The profit schedule for this call is given in column C on the strategy spreadsheet. Columns D through G contain profit positions corresponding to various spot prices (given in column A) for two more calls and two puts ranging over three strikes (K₁, K₂, K₃). These five basic options strategies can be used to generate the profit schedules for the more sophisticated strategies given in columns I through O. Let's examine these now.

An investor may wish to bet on share prices falling. One strategy that places such a bet is to take a short position in the call by selling call options. By doing so, the investor is exposed to unlimited risk should prices rise sufficiently. Short positions, in general, have exposure to unlimited losses and somewhat appropriately carry the moniker naked shorts. To hedge this risk, investors cover their short calls by holding a share of stock. Thus, we have the covered call payout, which is the net profit to selling a call and simultaneously buying a share. As we can see from the profit schedule given in Figure 16.12, this payout is maximized at $3.44 because at some point the call will be exercised (at in this case).

Figure 16.12 Covered Call

Thus, the long position in the stock hedges the risk of having to buy a share at some future point in time at a price greater than $90 if the call is exercised, but at a cost, which in this case limits any profit to $3.44. This is a rather extreme case. In reality, the investor will not hedge the entire short position. Doing so would completely offset his belief that prices are more likely to fall than rise. The concept, however, is constructive in that it illustrates the natural hedging characteristics of covered short positions.

Similarly, a long put position hedges downside risk. A protective put (column J) allows the investor to also participate in the upside by holding a share. As shown in Figure 16.13, the profit schedule for this strategy indeed limits the downside loss while allowing the investor to participate in the gains should share prices rise instead. In the early years of options trading, there were no puts. Investors created synthetic puts instead by holding a portfolio consisting of a short position in the stock and a long position in a call.

Figure 16.13 Protective Put

Spread strategies limit profits to a targeted range of spot prices while capping losses and gains. These are profitable strategies if the investor's spot price forecast is fulfilled. If, for example, the spot price is currently below $90 and we believe that over the life of the option that prices will stay in the range of $90 to $100, then we could buy a call with strike $90 and sell a call with strike $100. If prices rise above $90, we exercise the call and should they continue to rise, we book a profit until the price reaches $100, at which time the short call is exercised. We then deliver the share that we bought earlier at $90, which limits our gain. The profit schedule is therefore range-bound between the two strike prices. This strategy is referred to as a bull spread, and is depicted in Figure 16.14.

Figure 16.14 Bull Spread

As the name would suggest, a bear spread is a strategy that counts on prices falling but not too far. Buying a put at strike and selling another at a lower strike , pockets the profit from the short position but limits the gain should prices continue to fall below $90. If prices do fall below K₁ then the gain from the long put is used to buy the share when the short put is exercised by the counterparty. The profit schedule is shown in Figure 16.15. (We will exclude the contributing legs from here on out—refer to the spreadsheet if you want this information as well.) Again, we clearly see that this strategy provides limited gains in the region bounded by the strike prices.

Figure 16.15 Bear Spread

Suppose an investor buys a share and a put with strike price and sells a call option with strike price . This is identical to a long put and a covered call. What does this strategy achieve? First, the put provides downside protection. The long position in the stock allows the investor to participate in the upside movements in price as well but only if price does not exceed K₂. In that event, the long position in the stock covers the short call. This strategy therefore provides a capped profit should prices rise and limits losses should prices fall. It is called a collar and is illustrated in Figure 16.16.

Figure 16.16 Collar

A collar clearly limits participation in both the upside as well as the downside and therefore limits the effects of market volatility.

A butterfly spread is a bet on stock prices being range-bound. In Figure 16.17, we see the profit on a long position in a share combined with a call at and two short calls at . The two short calls offset the out-of-pocket costs of the investment in the share and the long call when price is low. As the share price rises toward $100, the profit from the short position is added to the price appreciation on the share until the short calls are exercised at K₂. If price continues to rise, the investor offsets the short call losses by exercising the long call at K₃.

Figure 16.17 Butterfly Spread

The profit opportunity is potentially very large, depending on how we scale our positions. The long position in the share combined with the long call hedge the risk on the short calls. Thus, profits are range-bound and losses, though limited, are realized outside of the range of forecasted price. This is an aggressive strategy.

Suppose it is earnings season and we are anticipating a firm's earnings announcement. Earnings announcements, especially as they deviate from consensus expectations, result in earnings surprises and hence the possibility of rather large movements in share prices in either direction. If we anticipate a large movement in price but are unsure of the direction, we could purchase a put and a call with the same strike price and expiration date. This strategy is called a long straddle and its profit schedule is given in Figure 16.18. This particular straddle has a strike price of $100. Though these two options are priced at the money (ATM), they are not required to be.

Figure 16.18 Long Straddle

A straddle is a volatility strategy that is direction-neutral with unlimited reward. Its payoff dependence on volatility should be obvious from the figure. If we allow for these two options to have different strike prices (but still impose the same expiration date), then the strategy is called a strangle.Figure 16.19 illustrates the profit schedule for a strangle with a long put with strike price and a long call with strike price . Both options are out of the money (OTM).

Figure 16.19 Long Strangle

These examples provide a useful introduction to more sophisticated strategies. The spreadsheet can be used to simulate almost any combination of options strategies and to graph their profit schedules. The parameter settings can be changed on the option sheet to produce options prices for various volatility, strike prices, discount rates, and time horizons. These are automatically linked to the strategy sheet. Although the lattices are restricted to six nodes, it is straightforward to expand the number of nodes using the current spreadsheet as a template.