Haipeng Xing Department of Applied Mathematics and Statistics Outline 1 Strategies to be considered 2 Principal-protected notes 3 Trading an option and the underlying asset 4 Spreads 5 Combinations
Strategies to be considered Depending on the trader s judgement about how prices will move and the trader s willingness to take risks, he may choose di erent profit patterns. Bond plus options to create principal protected note An option and the asset underlying the option Two or more options on the same asset Two or more options of di erent types Principal-protected notes Options are often used to create what are termed principal-protected notes for the retail market; see the following example (Hull, 2014; Example 12.1).
Principal-protected notes The attraction of a principal-protected note is that an investor is able to take a risky position without risking any principal. From the perspective of the bank, the economic viability of the structure in the last example depends on the level of interest rates the volatility of the portfolio the level of dividends Trading an option and its underlying (a stock) Figure 1: Profit patterns (a) long position in a stock combined with short position in a call; (b) short position in a stock combined with long position in a call. (Hull, 2014; Figure 12.1).
Trading an option and its underlying (a stock) Figure 2: Profit patterns (c) long position in a stock combined with long position in a put; (d) short position in a stock combined with short position in aput.(hull,2014;figure12.1). Spreads bull spreads A spread trading strategy involves taking a position in two or more options of the same type. A bull spread can be created by buying a European call option on a stock with a certain strike price and selling a European call option on the same stock with a higher strike price. Both options have the same expiration date. Figure 3: Profit from bull spread created using call options (Hull, 2014; Figure 12.2).
Spreads bull spreads Bull spreads can also be created by buying a European put with a low strike price and selling a European put with a high strike price. Figure 4: Profit from bull spread created using put options (Hull, 2014; Figure 12.3). Spreads bear spreads A bear spread can be created by buying a European put with one strike price and selling a European put with a lower strike price. Figure 5: Profit from bear spread created using put options (Hull, 2014; Figure 12.4).
Spreads bear spreads Bear spreads can also be created by buying a call with a high strike price and selling a call with a low strike price. Figure 6: Profit from bear spread created using call options (Hull, 2014; Figure 12.5). Spreads box spreads A box spread is a combination of a bull call spread with strike prices K 1 and K 2 an a bear put spread with the same two strike prices. If all options are European, the payo from a box spread is always K 2 K 1 ; see the following illustration (Hull, 2014; Table 12.3). A box-spread arbitrage only works with European options. If all options are American, traders are liable to lose money.
Spreads butterfly spreads A butterfly spread involves positions in options with three di erent strike prices. (K 2 =(K 1 + K 3 )/2 is usually close to the current stock price) Figure 7: Profit from butterfly spread using call options (Hull, 2014; Figure 12.6). Spreads butterfly spreads A buttfly spread leads to a profit if the stock price stays close to K 2, but give rise to a small loss if there is a significant stock price move in either direction. It is a strategy for an investor who fells that large stock price moves are unlikely; see the following table (Hull, 2014; Table 12.4).
Spreads butterfly spreads Butterfly spreads can also be created using put options. Figure 8: Profit from butterfly spread using put options (Hull, 2014; Figure 12.7). A butterfly spread can be sold by following reverse strategy. Options are sold with strike prices of K 1 and K 3, and an option with the middle strike price K 2 are purchased. Spreads calendar spreads Calendar spreads use options that have the same strike price and di erent expiration dates. Figure 9: Profit from calendar spread using two call options, calculated at time T 1 (<T 2 ) (Hull, 2014; Figure 12.8).
Spreads calendar spreads Calendar spreads can be created with put options as well as call options. The profit pattern is similar to that obtained from using calls. Figure 10: Profit from calendar spread using two put options, calculated at time T 1 (<T 2 ) (Hull, 2014; Figure 12.8). A reverse calendar spread is the opposite to that in Figures 9 and 10. Combinations straddle A combination is an option trading strategy that involves taking a position in both calls and puts on the same stock. A straddle combination involves buying a European call and put with the same strike price and expiration date. The following straddle is referred to as a bottom straddle or straddle purchase. A top straddle or straddle write is the reverse position. Figure 11: Profit from a straddle (Hull, 2014; Figure 12.10 & Table 12.5).
Combinations strips and straps A strip consists of a long position in one European call and two European puts with the same strike price and expiration date. A strap consists of a long position in two European call and one European puts with the same strike price and expiration date. In both a strip and a strap, the investor is betting that there will be a big stock price move. However, in a strip, the investor also bets that a decrease in the stock price is more likely than an increase, and in a strap, the investor also bets that an increase in the stock price is more likely than a decrease. Combinations strips and straps Figure 12: Profit from a strip and a strap (Hull, 2014; Figure 12.11).
Combinations strangles In a strangle, sometimes called a bottom vertical combination, an investor buys a European put and a European call with the same expiration date and di erent strike prices. Figure 13: Profit from a strangle (Hull, 2014; Figure 12.12 & Table 12.6). In a strangle, the investor bets that there will be a large price move, but is uncertain whether it will be an increase or a decrease. The sale of a strangle is sometimes referred to as a top vertical combination, and it is approporiate for an investor who feels that large stock price moves are unlikely.