Composite Contract Profit and Loss at Expiration#

In this lecture we analyze the payoff and profit diagrams of composite option contracts, which are composed of combinations of put and call options, at expiration.

General composite contracts#

Call and put contracts can be combined to develop composite contract structures with interesting payoff diagrams. Let’s limit our focus to contracts that have the same underlying asset and the same expiration date (Definition 12):

Definition 12 (Composite contract payoff and profit)

Let a composite option contract be composed of the set of \(d\) legs (individual contracts) \(\mathcal{C}\) where each leg \(i\in\mathcal{C}\) is written with respect to the same underlying stock XYZ and has the same expiration date. Then, the overall payoff of the composite contract \(\hat{V}(S(T),K_{1},\dots,K_{d})\) is given by:

(31)#\[\hat{V}(S(T),K_{1},\dots,K_{d}) = \sum_{i\in\mathcal{C}}\theta_{i}n_{i}V_{i}(S(T),K_{i})\]

where \(K_{i}\) denotes the strike price of contract \(i\in\mathcal{C}\). The overall profit of the composite contract \(\hat{P}\) is given by:

(32)#\[\hat{P}(S(T),K_{1},\dots,K_{d}) = \sum_{i\in\mathcal{C}}\theta_{i}n_{i}P_{i}(S(T),K_{i})\]

where \(\theta_{i}\) denotes the direction of contract \(i\): if contract \(i\) is short (sold), then \(\theta_{i}=-1\), otherwise \(\theta_{i}=1\), the quantity \(n_{i}\) denotes the copy number of contract \(i\), \({V}_{i}(S(T),K_{i})\) denotes the payoff of contract \(i\), and \(P_{i}(S(T),K_{i})\) denotes the profit of contract \(i\).

For those interested in more advanced cases, e.g., combining contracts with different expiration dates, check out calendar spreads, or diagonal spreads which combine different experation dates and strike prices.

Implementation#

We compute the payoff and profit of a composite contract by summing the payoff and profit of each leg of the contract.

Listing 9 Function to compute the Profit of a composite contract#
 1function profit(contracts::Array{T,1}, 
 2    S::Array{Float64,1})::Array{Float64,2} where T <: AbstractContractModel
 3
 4    # initialize - 
 5    number_of_underlying_prices = length(S);
 6    number_of_contracts = length(contracts);
 7    profit_array = Array{Float64,2}(undef, number_of_underlying_prices, number_of_contracts+2);
 8
 9    # main loop -
10    for i ∈ 1:number_of_underlying_prices
11
12        # get the underlying price -
13        Sᵢ = S[i];
14
15        # compute the payoff -
16        profit_array[i,1] = Sᵢ;
17
18        # loop over the contracts -
19        for j ∈ 1:number_of_contracts
20
21            # get the contract, and data associated with it -
22            contract = contracts[j];
23            sense = contract.sense |> Float64;
24            copy = contract.copy |> Float64;
25            premium = contract.premium;
26
27            # compute the payoff -
28            profit_array[i,j+1] = (copy*sense)*(_payoff(contract, Sᵢ) - premium)
29        end
30    end
31
32    # compute the sum -
33    for i ∈ 1:number_of_underlying_prices
34        profit_array[i,end] = sum(profit_array[i,2:end-1]);
35    end
36
37    # return -
38    return profit_array;    
39end

Vertical Spreads#

Vertical spreads, a defined risk directional strategy, involve buying and selling the same type of option with different strike prices and the same expiration date. This creates two legs, a long leg (the option purchased by the investor) and a short leg (the option sold by the investor). The investor can use the strategy to take a position on whether the share price of the underlying stock, such as XYZ, will increase or decrease.

Vertical spreads are defined risk because the maximum possible gain or loss is known when the contract is sold, meaning investors know how much they can make or lose before entering the trade.

Note

It is important to note that the future share price of XYZ is unknown when the investor opens the trade. Thus, the investor is making a directional assumption when trading a vertical spread about the future movement of the share price.

Put vertical spreads#

There are two types of vertical spreads that can be made with put contracts, each with a different directional assumption.

  • Thebull put credit spread assumes that the share price of the underlying asset, in this case, XYZ, will increase by the time of expiration.

  • In contrast, the bear put debit spread assumes that the share price of XYZ will decrease by the time of expiration.

When investors choose the bullish credit spread, they receive a credit upfront, which is the maximum profit. However, when they choose the debit spread, they incur a net debit to their account. The trade can become profitable over time if the directional assumption is correct.

Generally, the profit for a put vertical spread depends on the strike prices and the cost of each leg of the composite contract (Definition 13):

Definition 13 (Profit Put Vertical spread)

Let contract \(j\) have a strike price of \(K_{j}\) and premium \(\mathcal{P}_{j}\). The share price at expiration is given by \(S(T)\). Finally, let contract 1 be the short leg \(\theta_{1} = -1\) and contract 2 be the long leg \(\theta_{2} = 1\). Then, the profit for a single Put vertical spread \(P_{12}\) at expiration is given by:

\[\hat{P} = -P_{1}+P_{2}\]

which, after substitution of the profit functions for a put contract, gives:

\[ \hat{P}(S(T),K_{1},K_{2}, \mathcal{P}_{1}, \mathcal{P}_{2}) = \max\left(K_{2} - S(T),0\right) - \max\left(K_{1} - S(T),0\right) + \left(\mathcal{P}_{1} - \mathcal{P}_{2}\right)\]

The first term is the net payout of the two legs of the spread, while the second term is the net cost of the two contracts. The maximum possible profit, loss, and breakeven conditions are given by:

  • The maximum possible profit of \(\left(\mathcal{P}_{1} - \mathcal{P}_{2}\right)\) will occur when \(S\geq{K_{1}}\).

  • The maximum possible loss of \(K_{2} - K_{1} + \left(\mathcal{P}_{1} - \mathcal{P}_{2}\right)\) will occur when \(S\leq{K_{2}}\).

  • The vertical put spread will breakeven when \(S = K_{1}+\left(\mathcal{P}_{2} - \mathcal{P}_{1}\right)\).

Definition 13 has many exciting behaviors. It is much more complex than it might first appear as the cost of each contract \(\mathcal{P}_{j}\) is a non-linear function of many variables including the current share price of the underlying asset \(S\), the strike price of the contract, the number of days the contract has before expiration, and the implied volatility.

Credit spreads#

A bull put credit spread is a composite contract that combines a short put and a long put, providing the investor with a credit upon opening the trade. This strategy has a directional bias (bullish) and a defined risk, with the short put strike price \(K_{1}\) being lower than the current share price \(S_{\circ}\) but higher than the long put strike price \(K_{2}\) (i.e. \(S_{\circ}>K_{1}>K_{2}\)). The long put serves to limit potential losses, but it also restricts potential gains due to its cost (Fig. 22).

../../_images/Fig-put-vertical-spread-credit-bull.svg

Fig. 22 The payoff and profit for a bull put credit spread on XYZ with 56-DTE. Parameters: \(K_{1}=60.0\) USD/share, \(K_{2}=50.0\) USD/share, \(S_{\circ}=64.69\) USD/share, \(\mathcal{P}_{1}=1.39\) USD/share, \(\mathcal{P}_{2}=0.23\) USD/share, \(T=56\) days, and \(r=0.04\).#

A bear put debit spread is a composite contract that combines a short put and a long put, providing the investor with a debit upon opening the trade. This strategy has a directional bias (bearish) and a defined risk, with the short put strike price \(K_{1}\) being higher than the current share price \(S_{\circ}\) but lower than the long put strike price \(K_{2}\) (i.e. \(S_{\circ}<K_{1}<K_{2}\)). The long put serves to limit potential losses, but it also restricts potential gains due to its cost (Fig. 23).

../../_images/Fig-put-vertical-spread-debit-bear.svg

Fig. 23 The payoff and profit for a bear put debit spread on XYZ with 56-DTE. Parameters: \(K_{1}=65.0\) USD/share, \(K_{2}=75.0\) USD/share, \(S_{\circ}=64.69\) USD/share, \(\mathcal{P}_{1}=3.30\) USD/share, \(\mathcal{P}_{2}=10.70\) USD/share, \(T=56\) days, and \(r=0.04\).#

Straddles and Strangles#

Straddles and Strangles are neutral trades, i.e., they do not make a directional assumption. Thus, an investor can benefit in these trades if the share price of the underyling asset increases, decreases or potentially (depending upon how the trade was initialized) not move at all. The primary difference between a straddle and a strangle is that the strike prices of the contracts are different in a strangle while they are the same in a straddle.

Straddles#

A straddle is a neutral strategy constructed by simultaneously buying (or selling) a put and a call option on the same underlying asset XYZ, with the same expiration, and the same strike price (Definition 14):

Definition 14 (Profit and loss of a straddle)

Let \(K_{j}\) denote the strike price of contract \(j\) (USD/share), and let \(\mathcal{P}_{j}\) denote the price of contract \(j\) (USD/share). Finally, let index \(j=1\) denote the put contract, \(j=2\) denote the call contract; for a straddle \(K_{1} = K_{2}\equiv{K}\) (both legs have the same strike). The profit for a single straddle contract \(\hat{P}\) at expiration is given by:

\[\hat{P} = \theta\cdot\left(P_{1}+P_{2}\right)\]

where \(\theta_{1}=\theta_{2}\equiv\theta\) denotes a direction parameter: \(\theta=-1\) if each leg is sold (short), \(\theta=1\) otherwise. After substitution of the profit functions for a put and a call contract, the overall profit \(\hat{P}\) is given by:

\[\hat{P} = \theta\cdot\Bigl[(K-S)^{+}+(S-K)^{+}-(\mathcal{P}_{1}+\mathcal{P}_{2})\Bigr]\]

where \(V_{p} = (K-S)^{+}=\max(K-S,0)\) is the payoff function for the put contract, and \(V_{c} = (S-K)^{+} = \max(S-K,0)\) is the payoff function for the call contract. The profit (or loss) of a straddle has three regimes given by:

\[\begin{split} \hat{P} = \begin{cases} \theta\cdot\Bigl[(S-K)-\left(\mathcal{P}_{1}+\mathcal{P}_{2}\right)\Bigr] & S>K \\ -\theta\cdot\Bigl[\mathcal{P}_{1}+\mathcal{P}_{2}\Bigr] & S=K \\ \theta\cdot\Bigl[(K-S)-\left(\mathcal{P}_{1}+\mathcal{P}_{2}\right)\Bigr] & S<K \end{cases} \end{split}\]

Finally, a straddle has two possible breakeven points denoted as \(S^{+}\) and \(S^{-}\):

  • If \(S>K\): a straddle will breakeven at \(S^{+} = K + \left(\mathcal{P}_{1}+\mathcal{P}_{2}\right)\)

  • If \(S<K\): a straddle will breakeven at \(S^{-} = K - \left(\mathcal{P}_{1}+\mathcal{P}_{2}\right)\).

Investors can initiate a straddle either for a credit or a debit, depending on whether they buy or sell both legs. This strategy has the potential for unlimited profit or loss. A long straddle is initiated for a debit and has unlimited profit potential but limited loss potential. On the other hand, a short straddle is initiated for a credit and has limited profit potential but unlimited loss potential.

Long straddle#

For a long straddle, we purchase (are long) both the put and the call contracts in the straddle, thus \(\theta = 1\). Let’s contruct the profit diagram for a long straddle for AMD with the parameters:

  • Underlying: AMD has S(0) = 117.50 USD/share, the average implied volatility for AMD options with DTE = 31 days is IV = 51.75%.

  • Leg 1: The strike price for the long put leg is given by \(K_{1}\) = 120 USD/share with DTE = 31 days. The premium for this contract is \(\mathcal{P}_{1}\) = 7.85 USD/share.

  • Leg 2: The strike price for the long call leg is given by \(K_{2}\) = 120 USD/share with DTE = 31 days. The premium for this contract is \(\mathcal{P}_{2}\) = 6.30 USD/share.

../../_images/Fig-AMD-long-straddle-DTE-31d.svg

Fig. 24 Profit for a long straddle on AMD with DTE = 31 days until expiration. The strike price for both legs is \(K = 120\) USD/share. The premium for the put leg is \(\mathcal{P}_{1} = 7.85\) USD/share and the premium for the call leg is \(\mathcal{P}_{2} = 6.30\) USD/share.#

Short straddle#

For a short straddle, we sell (are short) both the put and the call contracts in the straddle, thus \(\theta = 1\). Let’s contruct the profit diagram for a long straddle with the parameters:

  • Underlying: AMD has S(0) = 117.50 USD/share, the average implied volatility for AMD options with DTE = 31 days is IV = 51.75%.

  • Leg 1: The strike price for the short put leg is given by \(K_{1}\) = 120 USD/share with DTE = 31 days. The premium for this contract is \(\mathcal{P}_{1}\) = 7.85 USD/share.

  • Leg 2: The strike price for the short call leg is given by \(K_{2}\) = 120 USD/share with DTE = 31 days. The premium for this contract is \(\mathcal{P}_{2}\) = 6.30 USD/share.

../../_images/Fig-AMD-short-straddle-DTE-31d.svg

Fig. 25 Profit for a short straddle on AMD with DTE = 31 days until expiration. The strike price for both legs is \(K = 120\) USD/share.#

Strangles#

A strangle position is a neutral strategy constructed by simultaneously buying and selling a put and a call option on the same underlying asset XYZ, with the same expiration but with different strike prices (Definition 15):

Definition 15 (Profit and loss of a strangle)

Let \(K_{j}\) denote the strike price of contract \(j\) (USD/share), and let \(\mathcal{P}_{j}\) denote the price of contract \(j\) (USD/share). Finally, let index \(j=1\) denote the put contract, \(j=2\) denote the call contract; for a strangle \(K_{1}<K_{2}\). The profit for a single strangle contract \(\hat{P}\) at expiration is given by:

\[\hat{P} = \theta\cdot\left(P_{1}+P_{2}\right)\]

where \(\theta_{1}=\theta_{2}\equiv\theta\) denotes a direction parameter: \(\theta=-1\) if each leg is sold (short), \(\theta=1\) otherwise. After substitution of the profit functions for a put and a call contract, the overall profit \(\hat{P}\) is given by:

\[\hat{P} = \theta\cdot\Bigl[(K_{1}-S)^{+}+(S-K_{2})^{+}-(\mathcal{P}_{1}+\mathcal{P}_{2})\Bigr]\]

where \(V_{p} = (K_{1}-S)^{+}=\max(K_{1}-S,0)\) is the payoff for the put contract, and \(V_{c} = (S-K_{2})^{+} = \max(S-K_{2},0)\) is the payoff for the call contract. The profit (or loss) of a strangle has three regimes given by:

\[\begin{split} \hat{P} = \begin{cases} \theta\cdot\Bigl[(S-K_{2})-\left(\mathcal{P}_{1}+\mathcal{P}_{2}\right)\Bigr] & S>K_{2} \\ -\theta\cdot\Bigl[\mathcal{P}_{1}+\mathcal{P}_{2}\Bigr] & K_{1}\leq{S}\leq{K_{2}} \\ \theta\cdot\Bigl[(K_{1}-S)-\left(\mathcal{P}_{1}+\mathcal{P}_{2}\right)\Bigr] & S<{K_{1}} \end{cases} \end{split}\]

A strangle has two break-even points \(S^{+}\) and \(S^{-}\) where \(K_{2}<S^{+}\) and \(S^{-}<K_{1}\). The low break-even point \(S^{-}\) is given by:

\[S^{-} = K_{1} - \left(\mathcal{P}_{1}+\mathcal{P}_{2}\right)\]

while the high break-even point \(S^{+}\) is given by:

\[S^{+} = K_{2} + \left(\mathcal{P}_{1}+\mathcal{P}_{2}\right)\]

Depending upon the choice of the strike prices and whether an investor buys or sells both legs, a strangle can be initiated as a credit or debit and can potentially have undefined profit or loss.

Long strangle#

For a long strangle, we purchase (are long) both the put and the call contracts in the straddle, thus \(\theta = 1\). Opening this trade results in a debit, where the investor profits when the trade is closed. Let’s contruct the profit diagram for a long straddle with the parameters:

  • Underlying: AMD has S(0) = 117.50 USD/share, the average implied volatility for AMD options with DTE = 31 days is IV = 51.75%.

  • Leg 1: The strike price for the short put leg is given by \(K_{1}\) = 105 USD/share with DTE = 31 days. The premium for this contract is \(\mathcal{P}_{1}\) = 1.95 USD/share.

  • Leg 2: The strike price for the short call leg is given by \(K_{2}\) = 135 USD/share with DTE = 31 days. The premium for this contract is \(\mathcal{P}_{2}\) = 2.20 USD/share.

../../_images/Fig-AMD-long-strangle-DTE-31d.svg

Fig. 26 Profit for a long strangle on AMD with DTE = 31 days until expiration. The strike price for the put leg \(K_{1} = 105\) USD/share, while the strike price for the call leg \(K_{2} = 135\) USD/share.#

Short strangle#

For a short strangle, we sell (are short) both the put and the call contracts in the straddle, thus \(\theta = 1\). Let’s contruct the profit diagram for a long straddle with the parameters:

  • Underlying: AMD has S(0) = 117.50 USD/share, the average implied volatility for AMD options with DTE = 31 days is IV = 51.75%.

  • Leg 1: The strike price for the short put leg is given by \(K_{1}\) = 105 USD/share with DTE = 31 days. The premium for this contract is \(\mathcal{P}_{1}\) = 1.95 USD/share.

  • Leg 2: The strike price for the short call leg is given by \(K_{2}\) = 135 USD/share with DTE = 31 days. The premium for this contract is \(\mathcal{P}_{2}\) = 2.20 USD/share.

../../_images/Fig-AMD-short-strangle-DTE-31d.svg

Fig. 27 Profit for a short strangle on AMD with DTE = 31 days until expiration. The strike price for the put leg \(K_{1} = 105\) USD/share, while the strike price for the call leg \(K_{2} = 135\) USD/share.#

Butterflies and Condors#

Iron Butterfly#

An iron butterfly is a neutral strategy that has defined risk constructed by selling put and call options, while simultaneously buying put and call options. All the legs have the same underlying asset XYZ, and the same expiration, but have different strike prices. In particular, the strike prices for the short put and short call contracts are the same, while the strike prices for the long put and long call contracts are different (Definition 16):

Definition 16 (Profit and loss of an Iron Butterfly)

Fill me in

Example#

  • Underlying: AMD has S(0) = 117.50 USD/share, the average implied volatility for AMD options with DTE = 31 days is IV = 51.75%.

  • Leg 1: The strike price for the short put leg is given by \(K_{1}\) = 120 USD/share with DTE = 31 days. The premium for this contract is \(\mathcal{P}_{1}\) = 7.85 USD/share.

  • Leg 2: The strike price for the short call leg is given by \(K_{2}\) = 120 USD/share with DTE = 31 days. The premium for this contract is \(\mathcal{P}_{2}\) = 6.30 USD/share.

  • Leg 3: The strike price for the long put leg is given by \(K_{3}\) = 110 USD/share with DTE = 31 days. The premium for this contract is \(\mathcal{P}_{3}\) = 3.30 USD/share.

  • Leg 4: The strike price for the long call leg is given by \(K_{4}\) = 130 USD/share with DTE = 31 days. The premium for this contract is \(\mathcal{P}_{4}\) = 3.15 USD/share.

../../_images/Fig-AMD-iron-butterfly-DTE-31d.svg

Fig. 28 Profit for an iron butterfly on AMD with DTE = 31 days until expiration. The strike price for the short put and call legs is \(K = 120\) USD/share, while the strike price for the long put leg is \(K_{3} = 110\) USD/share, and the long call leg is \(K_{4} = 130\) USD/share.#

Iron Condor#

An iron condor is a neutral strategy that has defined risk constructed by selling put and call options, while simultaneously buying put and call options. All the legs have the same underlying asset XYZ, and the same expiration, but have different strike prices (Definition 17):

Definition 17 (Profit and loss of an Iron Condor)

Let \(K_{j}\) denote the strike price of contract \(j\) (USD/share), and let \(\mathcal{P}_{j}\) denote the price of contract \(j\) (USD/share). Let index \(j=1\) denote the short put contract, \(j=2\) denote the short call contract, \(j=3\) denote the long put contract and \(j=4\) denote the long call contract. For an iron condor \(K_{3} < K_{1} < S(0) < K_{2} < K_{3}\), where \(S(0)\) denotes the current share price of the underlying asset. Then, the profit for a single iron condor contract \(\hat{P}\) at expiration is given by:

\[\hat{P} = \theta_{1}P_{1} + \theta_{2}P_{2} + \theta_{3}P_{3} + \theta_{4}P_{4}\]

where \(\theta_{1}=\theta_{2} = -1\) (short legs) and \(\theta_{3}=\theta_{4} = 1\) (long legs). After substitution of the profit functions for put and call contracts, the overall profit \(\hat{P}\) is given by:

\[\hat{P} = -(K_{1}-S)^{+} - (S-K_{2})^{+} + (K_{3} - S)^{+} + (S-K_{4})^{+} + \left(\mathcal{P}_{1} + \mathcal{P}_{2} - \mathcal{P}_{3}-\mathcal{P}_{4}\right)\]

where \(V_{p,\star} = (K_{\star}-S)^{+}=\max(K_{\star}-S,0)\) is the put payoff, and \(V_{c,\star} = (S-K_{\star})^{+} = \max(S-K_{\star},0)\) is the call payoff. The profit (or loss) of an iron condor has several important regimes:

\[\begin{split} \hat{P} = \begin{cases} K_{2} - K_{4} + \Bigl(\mathcal{P}_{1} + \mathcal{P}_{2} - \mathcal{P}_{3}-\mathcal{P}_{4}\Bigr) & S>K_{4} \\ K_{2} - S + \Bigl(\mathcal{P}_{1} + \mathcal{P}_{2} - \mathcal{P}_{3}-\mathcal{P}_{4}\Bigr) & K_{2}<S<K_{4} \\ \Bigl(\mathcal{P}_{1} + \mathcal{P}_{2} - \mathcal{P}_{3}-\mathcal{P}_{4}\Bigr) & K_{1}\leq{S}\leq{K_{2}} \\ S - K_{1} + \Bigl(\mathcal{P}_{1} + \mathcal{P}_{2} - \mathcal{P}_{3}-\mathcal{P}_{4}\Bigr) & K_{3}<S<K_{1} \\ K_{3} - K_{1} + \Bigl(\mathcal{P}_{1} + \mathcal{P}_{2} - \mathcal{P}_{3}-\mathcal{P}_{4}\Bigr) & S<K_{3} \end{cases} \end{split}\]

An iron condor has two break-even points. The low break-even point \(S^{-}\) occurs when \(K_{3}<S^{-}<K_{1}\) while the high break-even point \(S^{+}\) occurs when \(K_{2}<S^{+}<K_{4}\):

\[\begin{split} \begin{eqnarray} S^{-} &=& K_{1} - \Bigl(\mathcal{P}_{1} + \mathcal{P}_{2} - \mathcal{P}_{3}-\mathcal{P}_{4}\Bigr)\\ S^{+} &=& K_{2} + \Bigl(\mathcal{P}_{1} + \mathcal{P}_{2} - \mathcal{P}_{3}-\mathcal{P}_{4}\Bigr) \end{eqnarray} \end{split}\]

An investor holding an iron condor profits if the share price of XYZ remains between the strike prices of the two short options (like a short strangle). However, unlike strangles, an iron condor is a defined risk strategy. The long options limit possible losses, but they also restrict potential gains (because of their cost).

Example#

  • Underlying: AMD has S(0) = 117.50 USD/share, the average implied volatility for AMD options with DTE = 31 days is IV = 51.75%.

  • Leg 1: The strike price for the short put leg is given by \(K_{1}\) = 105 USD/share with DTE = 31 days. The premium for this contract is \(\mathcal{P}_{1}\) = 1.95 USD/share.

  • Leg 2: The strike price for the short call leg is given by \(K_{2}\) = 135 USD/share with DTE = 31 days. The premium for this contract is \(\mathcal{P}_{2}\) = 2.20 USD/share.

  • Leg 3: The strike price for the long put leg is given by \(K_{3}\) = 100 USD/share with DTE = 31 days. The premium for this contract is \(\mathcal{P}_{3}\) = 1.10 USD/share.

  • Leg 4: The strike price for the long call leg is given by \(K_{4}\) = 140 USD/share with DTE = 31 days. The premium for this contract is \(\mathcal{P}_{4}\) = 1.57 USD/share.

../../_images/Fig-AMD-iron-condor-DTE-31d.svg

Fig. 29 Profit for an iron condor on AMD with DTE = 31 days until expiration. The strike price for the short put leg is \(K_{1} = 105\) USD/share, the short call leg has strike \(K_{2} = 135\) USD/share, the long put leg has strike \(K_{3} = 100\) USD/share, and the long call leg has strike \(K_{4} = 140\) USD/share.#

Summary#

In this lecture we analyzed the payoff and profit diagrams of composite option contracts at expiration. In particular, we introduced general composite contracts, then focused on composite contracts that have a directional bias, and concluded with contracts that are neutral to the direction of the underlying asset.

  • General composite contracts are constructed by combining two or more option contracts to generate a new composite contract with some desired payoff and profit properties. For now, we limit our analysis to contracts that have the same underlying asset and the same expiration date.

  • Vertical spreads are composite contracts that have a directional bias. They are constructed by combining a single long and and single short option contract with the same expiration date but different strike prices.

  • Straddles and Strangles are composite contracts that are neutral to the direction of the underlying asset. They are constructed by combining two long or two short options contracts with the same expiration date and strike price.

  • Butterflies and Condors are composite contracts that are neutral to the direction of the underlying asset. They are constructed by combining two short and two long option contracts with the same expiration date but different strike prices.