# Option strategies

## Introduction

There are no fundamental dissimilarities between operations in the futures and options markets, i.e. dealings in the options market can be divided into the four types:

• Speculative.

• Hedging.

• Arbitrage.

• Investment.

However, we know that a hedger, speculator or investor has the choice between futures and options, and the essential difference between them is that in the case of the options the buyer has limited downside risk. We also know that there are a number of payoff situations for buyers are sellers of options. In addition, a virtually unlimited variety of payoff patterns may be attained by the * combination *of calls and puts with various exercise prices. Here we consider only two of the combinations of options, the straddle and the strangle.

## Straddle

**Table 14: Profit / loss profile of a long straddle**

**Table 15: Value of straddle at expiry**

The straddle is generally put into place when an investor * believes that the price of the underlying is about to "run" but she is uncertain of the direction. *The straddle involves the purchasing of

**a call and a put at the same strike price and expiration date.**The share price of Company ABC is trading at 480 pence currently. The price of a call at a strike of 480 pence is 10 pence and the price of a put at the same strike is 9 pence. The position is held to maturity (six months from purchase). Table 14 and Figure 19 set out the profit and loss profile.

The solid line in the lowest part of the chart shows the payoff condition of the straddle. At X = SPt the payoff is equal to zero. It is only at this point that the payoff is zero; at all other points the straddle has a positive payoff. One may then ask why these combinations are not more popular. The answer is that if prices are not volatile the holder may lose heavily because she is paying a * much higher premium *than is usually the case.

**Figure 19: profit / loss profile of a long straddle**

The dotted line in the chart represents the profit of the straddle. It is below the solid line by the cost of the straddle, i.e. the premium, in this case 19 pence. This is the maximum that can be lost.

## Strangle

A strangle is the * same as the straddle except that the exercise prices differ. *An example is shown in Table 16.

The share price of Company ABC is trading at 480 pence. The price of a call option at strike 460 is 25 pence, and the price of the put at strike 480 is 9 pence. The table shows the payoff profile. It will be clear that there is a range where maximum losses are made and this is between the two strike prices. The loss is capped at 14 pence. Beyond this range the losses are reduced or profits rise and they do so in a symmetrical fashion.

**Table 16: Profit / loss profile of a long strangle**

## Delta hedging

In normal hedging strategies (for example, holding of an asset and buying a put with the asset as the underlying when it is expected that its price will decline), some hidden risks lurk, requiring an appreciation of the "Greeks": delta, theta, gamma, vega and rho. We covered them briefly earlier. Here we discuss the most prominent one, delta, and specifically delta hedging, in a little more detail.

It will be recalled that * delta *is the rate of change of the option price with respect to the price of the underlying asset. If a call option has a delta of+1 it means that when the value of the underlying increases, the value of the option changes by the same amount. If the delta of a call option is +0.5, it means that when the price of the underlying increases by a number, the price of the option changes by 50% of that number. (It will be clear that the delta of a put option is negative.) When the delta of an option is removed from +1 or -1 (i.e. closer to 0), it constitutes risk in a hedge. The delta can also change over time due to changes in the underlying price, volatility or a shortening of the time to expiration (referred to as

**delta-variable).**A * delta-neutral *position is obtained when an options / underlying instrument position is constructed so that it is insensitive to price movements in the underlying instrument. Thus, if an investor has a long position in shares, she is able to hedge the position against losses by buying puts (long put position) or selling calls (short call position) to the extent of the

*If the delta of a put option is 0.75, the*

**inverse of the delta.***is 1 / 0.75 = 1.33. This means that 1.33 put options are required to offset one unit of the long position in shares. With this in place the investor has a*

**hedge ratio**

**delta-neutral hedge.**An example: if an investors holds 30 000 ABC shares, she will need to buy put options (with a delta of 0.75) to the extent of 30 000 / 0.75 = 40 000 (assuming a put option on 1 share could be bought). If the put option contract size is 1 000 shares, then 40 contracts are required [30 000 / (0.75 x 1 000)] to achieve a **delta-neutral hedge.**

As noted above, the delta values of options contracts do change over time; therefore the position needs to be rebalanced every so often to maintain a hedge ratio of h = -1. This is called **dynamic hedging.**