# An Example of a Bull Put Spread Option Strategy - How to Analyze Delta, Gamma, Theta, Vega and Rho

Updated: Aug 22, 2023

When trading vertical spreads, traders must feel comfortable dealing with numbers and have a deep understanding of the Delta and the other Greeks.

This tutorial explains in depth how the five Greeks Delta, Gamma, Theta, Vega and Rho work and, consequently, provide you with a numerical example of a Bull Put Spread strategy. By the end of this article, you should be able to understand how to manage the Greeks in order to trade this type of vertical spread successfully.

## An Example of a Bull Put Spread Option Strategy

### The Delta

In a bull put spread (long option strategy), the delta is a positive number included between 0 and +1 because the position is bullish. The Delta is at its highest speed when:

The stock price is between the two strike prices;

Options get closer to the expiration date.

A high-speed delta reflects a situation of uncertainty and, consequently, a higher risk. In fact, the highest is the delta speed of options, the more dependent from the underlying price it becomes. That is why each single dollar of movement in the stock involves a highest changing of the option price.

In such a situation, the position may move dramatically involving a high degree of risk for the trader becoming either profitable or unprofitable with a small changing in the stock price.

Conversely, a low speed delta may reflect a relative situation of calmness and a lower risk for the trader. In such context, the option position is less dependent on the price of the underlying and it is unlikely to move considerably if conditions do not change.

In a bull put spread strategy, the moneyness of options works as follow:

ATM options, the delta is here at its fastest rate and gets faster as your position come closer to the expiration date. As a result, time decay may have a relevant impact on ATM options.

ITM options, the delta slows down its speed and becomes a number close to 0 for deep in-the-money options. As a result, the impact of time decay becomes lower as options get deeper ITM.

OTM options, the delta slows down its speed and becomes a number close to 0 for deep out-of the-money options. As a result, the impact of time decay becomes lower as options get deeper OTM.

### The Gamma

In this strategy, gamma is negative when the position is profitable and positive when the position is unprofitable, while delta is always positive (long position).

If the stock raises, the negative gamma has a positive impact on delta decreasing its value, whilst if the stock falls the positive gamma has a negative impact on delta increasing its value. Gamma reaches its greatest positive value below the lower strike (the one purchased) and its greatest negative value above the higher strike (the one sold).

The closer to the expiration date you get, the higher is the level of risk if the position is still ATM or close. Gamma, as well as theta, becomes more significant as options approach expiration.

### The Theta

As you sell and buy put options simultaneously (long position - net credit), theta is positive when the position is profitable and negative when the position is unprofitable.

It means that time decay helps you when the position is OTM (stock price higher than the strike prices traded) and is against you when the position is ITM (stock price lower than the strike prices traded). Whatâ€™s more, theta is not a linear value. The less time an option has until expiration, the faster that option is going to lose its value. In a bull put spread this means that, as the expiration date come closer, theta will increase its positive value (positive leverage) when the position is profitable (OTM) and will increase its negative value (negative leverage) when the position is unprofitable (ITM).

As a result, it can be extremely dangerous to be stuck in positions that are experiencing a loss, because in the last days before expiration time decay decreases dramatically and can badly harm your position. Theta, as well as gamma, becomes more significant as options approach expiration.

### The Vega

As the bull put spread is a long position and a net credit strategy (you sell options premium), Vega is negative when the position is profitable and positive when the position is unprofitable.

It means that an increase in implied volatility is harmful to your position when it is OTM and helpful when your position is ITM.

Vega is greatest for options far from expiration and becomes less important while options approach expiration. As a result, the effect of implied volatility on the bull put spread, which is a strategy to trade on a short-term basis, becomes minimal.

### The Rho

#### In a bull put trade rho is positive, meaning that higher interest rates are helpful to your position (you make money when interest rates increase and lose money when they decrease). In fact, higher interest rates would increase the value of the naked puts.

The bull put spread is a short-term strategy and, as rho decreases in value when options get closer to expiration, rho will likely be a low value in the 0.010 range, meaning that options are expected to rise by only $0.01 with a 1% increase in interest rates. This makes its impact on this vertical spread non considerable.

### Appendix - Why rho is a positive number in a Bull Put Spread

When interest rates rise, there is more convenience to keep money in your bank account then investing it on shares. However, when you choose to control the same amount of shares using a much lower amount of money through the sale of put options (or purchase of call options), the remaining cash continues to earn interest in your bank account.

As a result, when interest rates rise, the sale of put options (or purchase of call options) becomes more attractive than the purchase of shares and the increasing demand justifies a slightly higher price as measured by the options rho value.