Options and Economics

(Note: The examples used in this answer were constructed using May 1st, 2020 options for NFLX, with the spot price as of Friday April 3rd close of trade, 4:00pm EDT)

(finance.yahoo.com, 2020)

A bear put spread is a variation of vertical spread strategy, with a bearish market outlook on the underlying stock price of NFLX shares, when a trader expects a moderate decline in the price of the security. This strategy profits if the underlying share price of NFLX stocks decreases & involves the simultaneously taking a long position in put options, & a short position in the same number of puts at a lower strike, with the same expiration date & the same underlying asset, whereby a trader:

· Goes long on a put option with a high strike (K2), &

· Goes short on a put option with a lower strike (K1)

This strategy offers limited risk & limited profit potential. It is often considered a cheaper & less aggressive alternative to a naked long put option. The inherent trade off of the strategy is that the cap on profit potential is compensated by a reduced premium, as the trade offsets any high initial premium costs involved with the long position by earning a credit on the short position. The trade is still a net debit, meaning the initial cash flow is negative when opening the position, & the trader still holds a net long position, as the value of the long puts are generally higher (Hull, 2015, p.261).

The tabular payoff matrix for a bear put spread can be seen below, where we can identify the value of our position, depending upon at what price the underlying asset (shares of NFLX stock) will settle, at expiration:

(Hull, 2015, p.261).

This example is constructed using the following May 1st, 2020 options data for NFLX shares:

A bull call strategy is a bullish strategy which seeks to profit from an increase in the underlying price of an asset, where the trader expects a moderate rise in price. The position consists of two call options (buy low, sell high) & represents a debit spread. This is since the trader pays a higher price for a lower strike call that is ITM. It is another variation of vertical spread strategy, with same underlying & expiration date. The strategy limits the upside potential of the trade but reduces the net premium spent when opening the position compared to buying a naked call option outright, by selling higher strike calls against those purchased. The objective is for S to increase so that the long call option will be ITM by an amount that will offset the initial cost, & lead to a profit on the position (Hull, 2020, p.259).

The tabular payoff matrix for a bull call spread can be seen below:

(Hull, 2020, p.259

This example is constructed using the following May 1st, 2020 options data for NFLX shares:

A long straddle strategy is used when an investor simultaneously takes a long position in the same number of call & put options on the same underlying, with the same strike price & expiration date. A trader will use this strategy if they believe the underlying price will move significantly & experience extreme volatility, but they are unsure what direction the price will move. The trade has theoretically unlimited upside, while risk is limited. It is a non-directional long volatility strategy. The strategy profits when the trader’s expectation are correct & NFLX stock price experiences a big move in either direction. It is unimportant what direction price moves, only that the deviation is greater than the total premium paid. A loss is achieved if the price remains relatively close to the at-the-money (ATM) strike the options are bought at (Hull, 2015, p.267).

An ATM strike is chosen for both the call & put options, which is as close to current spot price ($361.76) as possible. In our example, we choose the ATM strike of $362.25, & this is done to balance directional exposure by eliminating directional. Since both options have the same strike price, only one is ever ITM at any one time, & one can always be exercised for some gain, which we hope will be enough to cover initial cost of position & result in a profit. The underlying price generally needs a substantial move in order for the trade to be profitable, due to the high initial cost & wide window of losses, even though we don’t have to worry about direction of volatility

The tabular payoff matrix for a long straddle can be seen below:

(Hull, 2015, p.267).

This example is constructed using the following May 1st, 2020 options data for NFLX shares:

This is a similar strategy to long strangle in virtually every characteristic as it is a non-directional, long volatility strategy, with limited risk & theoretically unlimited upside. The main difference is that the call & puts option have different strike prices in a strangle, meaning the initial cost, & therefore maximum losses, are lower, but size of the move necessary to profit is more extreme due to the difference between the strikes A long strangle involves simultaneously taking a long position in the same number of put & call options, where the calls have a higher strike price than the puts. Once again, the trader believes there will be significant volatility in the underlying price but is unsure of which direction. Only one option is ever ITM at any one time, & if its value exceeds initial cost of opening the position then trade makes a profit. If volatility doesn’t materialise & S stays between or near the strikes, trade makes a loss. Normally, the strikes are equidistant from S at time of opening the strike, to minimise directional bias, & this strategy will almost always be less expensive than straddles, because options are purchased OTM. The price you pay for the luxury of not having to predict price direction is that there is a large jump required due to the distance between the strikes (Hull, 2020, p. 269).

The tabular payoff matrix for a long strangle can be seen below:

(Hull, 2020, p. 269)

This example is constructed using the following May 1st, 2020 options data for NFLX shares:

(Note: The examples used in this answer are constructed using April 24th, 2020 options for V, with the spot price as of Monday April 6th close of trade, 5:27pm GMT)

(finance.yahoo.com, 2020)

A call ratio back-spread is a strategy used by bullish investors who believe the underlying price of the asset will increase significantly over a specified period. It combines the purchase & sale of call options to create a spread with limited loss potential & mixed profit potential. This will allow us to profit if our bullish market expectations are correct, but also protects us from large downside risk, even allowing us to profit if the underlying decreases significantly enough. The strategy involves selling a call option (ITM) & then using the collected premium to purchase a greater number of call options with the same expiration, at a higher strike price (OTM). Upside potential is therefore theoretically unlimited as the trader is holding more long calls than short ones (Murphy, 2019). Call options are bought as the investor believes the underlying price will grow above the higher strike price of the purchased calls, & ideally rise high enough to compensate for any premium paid. The short position in an ITM call is used to pay investor a credit to finance purchase of the higher strike calls. Trade is designed to profit from increases in market volatility i.e. by simultaneously buying/selling calls, traders can hedge their downside risk, while benefiting from the upside as markets gain.

This example is constructed using the following April 24th, 2020 options data for KO shares:

This is a non-directional short volatility strategy used when a trader expects the underlying price to remain stable for the period until expiration. The position consists of four different options with three different strike prices:

· Long position in a put option, with the lowest OTM strike

· Short position in a call put & call option, with a higher, identical ATM strike

· Long position in a call option, with the highest OTM strike

The strategy effectively combines a short strangle (middle strikes), hedged by a long strangle (outer strikes). It has limited upside & downside potential & is also a net credit strategy (Scott, 2020).

This example is constructed using the following April 24th, 2020 options data for KO shares:

This is a non-directional volatility strategy that limits both potential gains & losses but seeks to benefit from high volatility & a sizeable move in the underlying price in either direction. It is a net credit strategy, involving all puts, & represents a combination of a bear & bull put spreads. The combinations of puts involve taking the following positions in strikes in ascending order: short, long (both ITM), & long, short (Both OTM). The objective is to profit from projected high volatility when S moving beyond highest or lowest strikes. All puts have same expiration dates & strikes are equidistant (fidelity.com, 2013).

This example is constructed using the following April 24th, 2020 options data for KO shares:

(Note: The examples used in this answer are constructed using May 1st, 2020 options for TWTR, with the spot price as of Monday April 6th close of trade, 7:21pm GMT)

(finance.yahoo.com, 2020)

Given that we have already discussed the details of a strangle in detail, there is no need for duplication in this regard, so I will continue to describe the example chosen & indicate the results. I began by analysing the viability of both long & short strangle positions, where a short strangle would instead consist of short positions in the call & put options, & in doing so I couldn’t justify using a short strangle for this example, due to the unnecessary risk assumption for the given potential return (Hull, 2015, p.269). (Note :I have constructed my Excel spreadsheet in such a way that a short strangle position can be observed by simply changing the value of positions from 1 to -1). This example will therefore be based on a long strangle.

This example is constructed using the following May 1st, 2020 options data for TWTR shares:

A strip is a trading strategy that is used when a trader expects considerable price movements in the underlying asset & is uncertain of which direction it will move but expects there is a higher probability of a downward movement. The trader is said to be bearish on the underlying security, TWTR stocks, but bullish on volatility. It is a market neutral trading strategy with profit potential on either side of the trade. It represents a slightly modified version of a straddle, but while a straddle provides equal profit potential on either side of the underlying price move i.e. is perfectly neutral, a strip is a bearish market neutral strategy which provides double profit potential on downward price movements, as a higher quantity of puts are purchased. The strategy offers unlimited upside potential & limited downside, where risk is limited to the total premium paid (Hull, 2020, p. 268).

A strip involves simultaneously taking a long position in a call option, & a higher number of put options, all with the same underlying asset & expiration date. It constitutes a net debit position.

This example is constructed using the following May 1st, 2020 options data for TWTR shares:

I applied the same logic for a straddle strategy as I did initially for the strangle strategy in part (i) & concluded to use a long straddle example for the same reason. This example will therefore be based on a long straddle.

This example is constructed using the following May 1st, 2020 options data for TWTR shares:

(Note: The examples used in this answer are constructed using April 24th, 2020 options for KO, with the spot price as of Wednesday April 8th open market, 12:13pm EDT)

(finance.yahoo.com, 2020)

Displayed above is the data, taken from Yahoo Finance, of a $58 strike call option, due to expire on the 24th April 2020. With its last trading price of $0.35 7 current ask price of $0.23. Using the CBOE options calculator to calculate the expected price for this call option we achieve the following results:

(cboe.com)

We can look to the discrepancies in mathematical options pricing models to explain the difference in the CBOE calculated call value of $0.0384, & that market/last traded price of the option at $0.35. These models use certain variables to calculate an option’s theoretical value i.e. an estimate of the fair value of an option, what it should be worth. There are assumptions included in several pricing models which don’t necessarily reflect market realities, for example, the Binomial Pricing Model assumes perfectly efficient markets, the Black-Scholes Model is used only to price European style options & operates under certain assumptions regarding the distribution of the stock price & the surrounding economic environment. Another reason to look to Is that volatility of the underlying asset is a matter of estimation (corporatefinanceinstitute.com, n.d.). While there is volatility implied in the price of the option, this simply represents market expectations & may or may not materialise in practice. Volatility can only be estimated historically or through using the other inputs.

It is the volatility implied/contained/priced into the price of the option itself. It represents the volatility you pay for in the option. It is the future volatility expected by the option’s market i.e. it is the volatility that traders expect the option to realise in the period until expiration. For example, we see implied volatility based on the last/market price of an April 24th KO call option with a strike of $58, i.e. $0.35, is equal to 75.96%, which reflects the volatility the market expects of the underlying price of KO to experience from now until expiration. All other factors being equal, a higher implied volatility will mean a higher option price. The relationship between the option’s price & volatility is measured by Vega, which is the first derivative of the option’s price with respect to volatility. We use the CBOE calculator as there is no options pricing model which can be used to derive a direct formula to determine implied volatility.

The role of the Greeks in options pricing is to measure risk & quantify how an option’s value would change under various possible market developments (Chen, 2020). This allows us to choose the most suitable options strategy, suitable number of contracts a trade should consist of, make adjustments to their positions, & plan for different scenarios.

The amount the price of an option will change in response to a corresponding 1% change in the price of the underlying security. Delta measures the sensitivity of an option’s premium to changes in price of the underlying security. It is the first derivative of the option price with respect to the underlying asset price. For example, a Delta value as show above of 0.0222 means when the price of KO increases by $1, the option’s price will increase by $0.02. Delta is only accurate for small price changes, as Delta itself will also change as the underlying price does, as measured by Gamma. Therefore, for large changes in underlying price, the actual option price change may be different than projected by Delta (Hull, 2015, p. 285). Delta is closely related to option moneyness, whereby ITM options are generally more sensitive to underlying price changes, & vice versa. One interpretation of Delta for traders is that it’s absolute value can indicate the approximate probability the option expiring ITM i.e. 0.0222 would indicate a 2.22% chance of the option expiring ITM.

Delta can also be interpreted as a hedge ratio i.e. if a trader has a is worried about downside market price risk & wants to hedge against this downside risk, they can do so by aiming to eliminate total Delta & make it equal to zero (Hull, 2015, p.402). For example, if Delta = 0.40 (40 Delta), a trader would ideally take a short position in 40 shares to hedge against the downside risk of the underlying security. It allows a trader to immediately know the number of shares to short. In our example above, we would short 2 or 3 shares of KO, meaning we would either be under or over hedged, but this would protect against downside price risk. This is more helpful when investing in a portfolio of a large number of stocks, given that Delta is additive, so we try to make total Delta equal to zero. But once again this is only appropriate for small changes in underlying price, therefore successful hedging requires constant monitoring & rebalancing.

The change in Delta divided by the dollar change in the price of the underlying security’s price. It measures the rate of change in an option’s price with respect to the underlying security. Gamma is closely related to Delta, as both measure an option’s security, but do so in different ways. Gamma measures how much Delta will change if the underlying price increases by $1. Therefore, while Delta is the speed of option price change, Gamma is the acceleration of price change. It is the first derivative of Delta, or the second derivative of option price with respect to underlying price (Hull, 2015, p.411). Gamma is at its highest, or Delta is changing at the fastest rate, when the option is near, or ATM. Gamma is therefore close to zero for far OTM options & deep ITM options. Options ATM with little time to expiration are the most instable & have the highest Gamma. The greatest benefit of Gamma is that it reveals hidden risk exposures which Delta cannot identify. In our example above, Gamma is equal to 0.0109, meaning Delta will increase by 0.0109 for every $1 increase in underlying price.

The derivative of the option’s premium with respect to volatility. Vega is the measure of change in an option’s price in response to a percentage change in volatility. Options generally benefit from rising volatility, but the extent varies between options. Vega measures an option’s sensitivity to volatility & tells us by how much will the option premium change if implied volatility increases, all else being equal (Hall, 2020). For example, if the market becomes increasingly uncertain regarding KO’s future price & implied volatility rises by 1%, our call option’s price will increase by the value of Vega, 0.0052 in our example above. It is the ratio of price change ($) to volatility change (%) i.e. dollars per percentage point. Volatility & Vega affect only the time value & have no effect on intrinsic value, therefore, options with more time value will have a higher Vega (Hull, 2015, p.415). Therefore, ATM options have the highest Vega, as they have the greatest time value.