Whether a position is long or short Theta will depend on both the present value effect and the optionality value effect. Table 10.4 presents the characteristics of each position and how these characteristics influence whether the given position is long or short Theta.
Table 10.4 The net impact of decreases in time to expiration Position How position value is
impacted by the present value effect
How position value is impacted by
optionality value effect
The net impact as time to
expiration decreases
Theta:
long or short Long
forward
Value decreases as time to expiration decreases, because the present value of the forward price to be paid increases.
Value is not impacted as forwards do not have optionality value.
Value decreases Short
Short forward
Value increases as time to expiration decreases, because the present value of the forward price to be received increases.
Value is not impacted as forwards do not have optionality value.
Value increases Long
Long call Value decreases as time to expiration decreases, because the present value of the strike price to be paid increases.
Value decreases as time to expiration decreases, because the value of the optionality that the long call holds decreases.
Value decreases Short
Short call Value increases as time to expiration decreases, because the present value of the strike price to be received increases.
Value increases as time to expiration decreases, because the short call's liability due to providing optionality decreases.
Value increases Long
Long put Value increases as time to expiration decreases, because the present value of the strike price to be received increases.
Value decreases as time to expiration decreases, because the value of optionality that the long put holds decreases.
Value increases when the present value effect is larger than the optionality value effect.
Value decreases when the
optionality value effect is larger than the present value effect.
Long or short
Short put Value decreases as time to expiration decreases, because the present value of the strike price to be paid increases.
Value increases as time to expiration decreases, because the short put's liability due to providing optionality decreases.
Value decreases when the present value effect is larger than the optionality value effect.
Value increases when the
optionality value effect is larger than the present value effect.
Long or short
As Table 10.4 shows, long forwards and calls are always short Theta and short forwards and calls are always long Theta. Interestingly, put positions can be either long or short Theta depending on whether the present value effect or optionality value effect is more impactful.
Generally, we observe that the optionality value effect is most acute when the option has significant optionality value. Near-the-money options have significant optionality value, while deep-ITM options do not, for the following reasons:
Optionality is very valuable when the option is near-the-money, as there are
significant likelihoods that underlying asset price changes will result in the option ending up either ITM or OTM at expiration.
Optionality is not particularly valuable when deep-ITM, as there is not much of a choice to make: If deep-in-the-money, a long option position will almost certainly exercise. The value of a deep-ITM option is therefore primarily driven by its intrinsic value (the difference between underlying asset price and the strike price) and not optionality value.
Further, the present value effect is most acute when interest rates are high, as present
values are more sensitive to decreases in time when interest rates are high.
The implication is as follows: Typically, long puts are short Theta, and short puts are long Theta. However, when interest rates are very high and/or when the put option is deep- ITM, it is possible to observe long puts that are long Theta, and short puts that are short Theta.1
Because long forwards and calls are always short Theta, and long puts are typically short Theta, Theta is referred to as “decay.” This name connotes that options “decay” in value as time to expiration decreases, holding everything else equal.
Let's explore an example to illustrate the net impact of the passage of time on options.
Throughout, we assume:
Strike price = $105
Underlying asset volatility = 20%
European-style, underlying asset pays no income
Figure 10.4 presents the value of a long call and put across time to expiration for the following three scenarios:
Figure 10.4 Examples of long call and put values across time to expiration Base scenario: Underlying asset price = $100; risk-free interest rate = 2%.
Alternative scenario 1: Underlying asset price = $100; risk-free interest rate = 20%.
Alternative scenario 2: Underlying asset price = $50; risk-free interest rate = 2%.
Figure 10.4 illustrates the following:
Base case: Optionality value is very important, as the option is near-the-money, while the present value effect is small, as interest rates are low. The net effect on the long put is that optionality value effect is more impactful than the present value effect. The long put decreases in value as time to expiration decreases and is short Theta.
Alternative scenario 1: Optionality value is important as the option is near-the-money.
However, due to the high risk-free interest rate of 20%, the present value effect is more impactful than the optionality value effect. The long put increases in value as time to expiration decreases and is long Theta.
Alternative scenario 2: Optionality value is not very important, as the option is deep ITM. While the risk-free interest rate is low, the present value effect is more impactful than the optionality value effect. The long put increases in value with less time to
expiration and is long Theta.
For all scenarios, both the optionality value effect and the present value effect lead the long call to decrease in value as time to expiration decreases, and the long call is short Theta.
Knowledge check
Q 10.32: What is the present value effect of a decrease in time to expiration?
Q 10.33: How does the present value effect impact long forwards, long calls, and short puts?
Q 10.34: How does the present value effect impact short forwards, short calls, and long puts?
Q 10.35: What is the optionality value effect of a decrease in time to expiration?
Q 10.36: How does the optionality value effect impact forward positions?
Q 10.37: How does the optionality value effect impact long calls and puts?
Q 10.38: How does the optionality value effect impact short calls and puts?
Q 10.39: Why are long forwards short Theta?
Q 10.40: Why are short forwards long Theta?
Q 10.41: Why are long calls short Theta?
Q 10.42: Why are short calls long Theta?
Q 10.43: Why are long puts either long or short Theta?
Q 10.44: Why are short puts either long or short Theta?
KEY POINTS
Long Vega and long Rho describe positive value sensitivity to changes in the
underlying asset volatility and the risk-free interest rate, respectively. Short Vega and short Rho describe negative sensitivity and Vega neutrality, and Rho neutrality
describes no sensitivity.
Long Theta describes positive value sensitivity to decreases in the time to expiration.
Short Theta describes negative sensitivity, and Theta neutrality describes no sensitivity.
Vega and Rho are measures of risk. Theta communicates a characteristic of a position, described as “decay,” and not risk.
Forward positions are Vega neutral as their payoffs are symmetrical. Long calls and puts are long Vega as their payoffs are asymmetrical: They can benefit from increased volatility and not be harmed. Short calls and puts are short Vega as their payoffs are asymmetrical: They can be harmed by increased volatility and cannot benefit.
Purchasing counterparties are long Rho, as the present value of the forward price/strike price paid decreases as the risk-free interest rate increases. Selling counterparties are short Rho, as the present value of the forward price/strike price received decreases as the risk-free interest rate increases.
The impact on a position of a decrease in the time to expiration is twofold. First, as time to expiration decreases, the present value of the forward price/strike increases.
Second, as time to expiration decreases, optionality value erodes. Whether a given position is long or short Theta depends on the net impact of these two effects. Long forwards and long calls are short Theta; short forwards and short calls are long Theta;
and long and short put options can be either long or short Theta, depending on the relative impact of the present value effect versus the optionality value effect.
__________________
1 The value of a deep-OTM option, while quite low, is exclusively driven by optionality value; and, therefore, erosion of optionality value drives erosion of value.
Part Four
Trading Strategies
Chapter 11
Price and Volatility Trading Strategies INTRODUCTION
In this and the subsequent two chapters we will explore a variety of trading strategies. In this chapter we will explore price and volatility trading strategies. We will learn about price and volatility views, relate them to Delta and Vega, and learn how one can use
positions in forwards and options to monetize combinations of price and volatility views.
We will also learn about volatility trading strategies known as “straddles” and “strangles.”
After you read this chapter, you will be able to Describe price and volatility views.
Relate price and volatility views to sensitivity and Delta and Vega.
Explain how forward and option trading strategies can be used to monetize combinations of price and volatility views.
Describe how to form straddles and strangles.
Explain the Delta and Vega characteristics of straddles and strangles.
Identify the at-the-money Delta-neutral straddle (ATM DNS) strike price.
Contrast the ATM DNS strike price with the at-the-money (ATM) strike price.
Describe the P&L diagrams for straddles and strangles.
Identify the breakeven points for straddles and strangles.