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Autocall analysis
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13th October 2011
F actshee t - F or Pr ofe ssi onal Inte r medi ar i es Onl y
Background
During a client meeting recently we were discussing a HSBC FTSE Defensive Autocall with very low autocall barriers (number 360 on our website: link). A
client asked how this would compare to a similar structure with slightly different barriers. Rather than give an approximation at the time we decided to carry
out some more detailed work into the structures discussed. The results were quite interesting and have led to us producing this analysis.
The content of this document aims to educate the reader about autocall pricing through both breaking down the generic components of an autocall, and
then comparing the values of these different components for different autocall structures. It is aimed at finance professionals with some experience of
autocall investments.
Generic Components
We think the best way to decompose an autocall is to split it into three components, two of which the investor is long, and one of which he is short. Let us
assume the underlying asset is the FTSE 100 index:

Component 1: Long a strip of escalating coupons, payment of which are contingent on the FTSE 100 index being above pre-defined levels.

Component 2: Long a zero coupon bond, the duration of which is dependent on when or if the structure autocalls.

Component 3: Short a knock-in put which gives the investor some downside risk. This downside risk disappears in the event of an autocall.
The values of each of these components are dependent on prevailing implied volatility, interest rates and dividend expectations, as all financial derivatives
are, but probability assumptions are at the heart of pricing.
Component 1 – Strip of contingent, escalating coupons
The models used in derivative pricing assign equal probabilities to an underlying asset moving up or down at any point in time. Applying this assumption to
the first escalating coupon of an autocall whose first autocall barrier is set at 100% of the initial underlying asset level, the model will assume that there is
approximately a 50:50 chance of this first coupon being paid out (It is not exactly 50:50 because the forward level of the FTSE is important, but in most
cases it will not be far from 50:50). It is therefore quite simple to value this first coupon. It will be equal to:

Size of coupon x (approx) 50% x Present Value of coupon
For example, if a structure being valued had a 10% per annum escalating coupon, with interest rates as low as they currently are, the price of this first
contingent coupon would be close to 5%.
How about the subsequent contingent coupons? It is easy to make the mistake of assuming that there is a 50:50 chance of receiving them. This is not the
case, and here we enter the world of contingent probabilities.
For example, let us take an autocall whose first two autocall barriers are set at 100% of the initial level. What is the probability of receiving the year 2
coupon? To receive the coupon in year 2, the structure MUST NOT have paid a coupon in year 1. Or, in underlying asset terms, the underlying asset must
be BELOW the initial level at the end of year 1 AND then ABOVE the initial level at the end of year 2. This represents a CONDITIONAL PROBABILITY.
Without going into the maths, the models used in pricing autocalls assign a probability of approximately 10% to 12% for an underlying asset being above its
initial level after two years having been below its initial level after one year. This will almost certainly come as a surprise to you, unless you are a maths
graduate!
For an autocall with barriers set at the underlying asset’s initial level at the end of each year, according to the models, the probabilities of the structure
calling fall in each subsequent year. The graph below illustrates these probabilities assuming a six year autocall on the FTSE using current market
parameters:
Probability of FTSE being above initial level in year X assuming FTSE below initial level in previous years
Year 1 – 52.40%.
Year 2 – 10.69%.
Year 3 – 4.67%.
Year 4 – 2.80%.
Year 5 – 1.88%.
Year 6 – 1.47%.
0.00%
10.00%
20.00%
30.00%
40.00%
50.00%
60.00%
Probabilty
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For example, the probability of FTSE being above current level in 3 years time GIVEN FTSE BELOW CURRENT LEVEL AFTER 1 and 2 YEARS is 4.67%.
This is interesting. The models assign a very low probability to a structure autocalling in later years, hence it is cheap to buy these potentially high coupons.
History has shown that markets tend to be cyclical, but the models do not make this assumption, so investors believing in the cyclicality of markets can take
advantage of this through investing in autocalls. (Link to backtest illustrating how well autocalls would have performed over last 20 years).
Component 2 – Zero Coupon bond of unknown duration
Unlike the contingent coupons, which may or may not be paid out depending on how the underlying asset performs, the zero coupon bond component will
DEFINITELY be paid out. However, the timing of that payment is dependent on the performance of the underlying asset.
Let us use the probabilities in the explanation of the contingent coupons above to value the zero coupon bond element of the same autocall.
Year
Probability of Autocall / Payment
Risk free discount factor
Price
1
52.37%
99.09%
51.89%
2
10.34%
98.17%
10.15%
3
4.78%
96.62%
4.62%
4
2.98%
94.63%
2.82%
5
1.96%
92.28%
1.81%
6
27.57% (100% - sum of above)
89.69%
24.73%
Total
96.02%
You can see that the total cost of the zero coupon bond element is 96.02%, but the majority of this number comes from years 1 and 6. This is another
illustration of the model’s assumptions, namely that if the structure does not call in year 1 it is unlikely to autocall at all. Experience has told us that this is not
the case as frequently as the models suggest.
Component 3 – Knock-In Put
This is the component that cannot be valued as simply as the others. However, it is interesting to compare the value of the embedded put option that the
investor is implicitly short with that of a standard put option.
As a rule of thumb, the value of an at-the-money call or put option is approximately equal to:

0.4 x implied volatility x square root of time to expiry
6 year volatility on the FTSE is currently approximately 26%, so one would expect a standard at-the-money put option on the FTSE to be worth around:

0.4 x 26% x √6 = 25.47%.
At the time of writing it was actually equal to 25.1%, which is not far from our approximation.
There are two differences between this standard put option and the put option the investor is short through owning an autocall. These are:

The normal option will definitely last 6 years whereas the put option embedded in the autocall might terminate early if the structure is autocalled.

The normal option does not have a “soft protection” level, whereas the put option embedded within the autocall is likely to have.
Both of these differences mean that a put option embedded within the autocall is less valuable than a standard put option. The magnitude of this price
difference is the interesting point.
At the time of writing a 6-year put option embedded within an autocall that has autocall barriers set at the initial level in each of the 6 years and a soft
protection level of 50% had a value of 12.5%. Despite multiple chances for the put to terminate early and the 50% protection level, the investor is still being
paid 12.5% for taking this risk. This is significantly (around 12.5%) lower than the value of a standard put option, but you may have thought its value would
have been lower still.
To further illustrate price differences between similar options it is interesting to look at the table.
Option
Price (as at 13th October 2011)
Difference from Standard Option
At-the-money 6 year FTSE put option with no soft protection
25.1%
-
At-the-money 6 year FTSE put option with soft protection at 50%, observed continuously (american)
22.6%
2.5%
At-the-money 6 year FTSE put option with soft protection at 50%, observed at maturity (european)
19.0%
6.1%
Whilst not exactly relevant to autocall pricing this table is quite thought provoking. As an investor, what do you think offers best value? Receive 19% for a 6
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year put option with a 50% european barrier, 22.6% for one with a 50% American barrier, or 25.1% for a standard put option.
By taking the 3 components together we can now see why through investing in an autocall you are implicitly selling volatility. The impact of implied volatility
on the values of the zero coupon bond component and strip of contingent coupons is not large – it is the probability assumptions that are important. The
value of the knock-in put will increase as volatility increases, and as the investor is short this put he would be hurt were volatility to increase.
Comparisons of component values and probabilities for different autocalls
Below are some comparisons for different FTSE autocalls. For each different structure we have highlighted and commented on one specific aspect of the
price. It is interesting to note the lower than expected probabilities of autocalling even with very defensive versions.
Structure:
Coupon:
Protection barrier:
Chance of losing capital:
Comment:
Year
1
2
3
4
5
6
Autocall
Barrier
100%
100%
100%
100%
100%
100%
Discount
Factor
99.00%
97.79%
96.00%
93.87%
91.36%
88.62%
Structure:
Coupon:
Protection Barrier:
Chance of losing capital:
Comment:
Year
1
2
3
4
5
6
Autocall
Barrier
100%
95%
90%
85%
80%
75%
Discount
Factor
99.00%
97.79%
96.00%
93.87%
91.36%
88.62%
Structure:
Coupon:
Protection Barrier:
Chance of losing capital:
Comment:
Year
1
2
3
4
5
6
Autocall
Barrier
100%
100%
100%
100%
100%
60%
Discount
Factor
99.00%
97.79%
96.00%
93.87%
91.36%
88.62%
HSBC 358 FTSE Autocall (13.6%) EIS
13.6%
60%
20.96%
Model gives almost a 21% chance of this structure "knocking-in" and losing capital.
Is there a 1 in 5 chance of the FTSE being below 3000 in October 2017 in your view?
Probability Present Value of
Present Value of
of Autocall Contingent Coupons Zero Coupon Bond
52.40%
7.06%
51.88%
10.70%
2.85%
10.46%
4.67%
1.83%
4.48%
2.80%
1.43%
2.63%
1.88%
1.17%
1.72%
1.48%
1.07%
24.41%
15.40%
95.58%
Put Price
Sum of
components
12.51%
98.47%
Generic Defensive Autocall with 5% Barrier drops
11.2%
50%
18.10%
Even though the barriers drop the probability of calling in years 2 to 6 is still low
according to the model.
Probability Present Value of
Present Value of
of Autocall Contingent Coupons Zero Coupon Bond
52.40%
5.81%
51.88%
12.67%
2.78%
12.39%
6.17%
1.99%
5.92%
3.76%
1.58%
3.53%
2.50%
1.28%
2.29%
1.66%
0.99%
19.93%
14.43%
95.94%
Put Price
Sum of
components
11.82%
98.55%
Generic Defensive Autocall with a big drop in the final year
11.10%
50%
19.16%
Despite large barrier drop in year 6 probability of autocall then is still low.
Probability Present Value of
Present Value of
of Autocall Contingent Coupons Zero Coupon Bond
52.40%
5.76%
51.88%
10.70%
2.32%
10.46%
4.67%
1.49%
4.48%
2.80%
1.17%
2.63%
1.88%
0.95%
1.72%
6.17%
3.64%
24.41%
15.34%
95.58%
Put Price
Sum of
components
12.51%
98.41%
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Structure:
Coupon:
Protection barrier:
Chance of losing capital:
Comment:
Year
1
2
3
4
5
6
Autocall
Barrier
100%
80%
70%
60%
50%
40%
Discount
Factor
99.00%
97.79%
96.00%
93.87%
91.36%
88.62%
Structure:
Coupon:
Protection Barrier:
Chance of losing capital:
Comment:
Year
1
2
3
4
5
6
Autocall
Barrier
100%
100%
100%
100%
100%
40%
Discount
Factor
99.00%
97.79%
96.00%
93.87%
91.36%
88.62%
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HSBC 359 FTSE Defensive Autocall (6.85%) Notes
6.85%
40%
13.28%
According to the model there is approximately a 15% chance of this calling between
years 3 and 6. Consequently these latter coupons cost less than 4%. Good value?
Probability Present Value of
Present Value of
of Autocall Contingent Coupons Zero Coupon Bond
52.40%
3.55%
51.88%
21.50%
2.88%
21.02%
7.14%
1.41%
6.85%
3.65%
0.94%
3.43%
2.41%
0.75%
2.20%
1.83%
0.67%
11.44%
10.20%
96.82%
Put Price
Sum of
components
8.56%
98.46%
Generic Defensive Autocall with a very big drop in the final year
8.00%
40%
16.94%
In comparison with the structure above the model thinks that overall there is a
lower probability of autocall. The put option is also worth more. These factors
lead to a higher coupon. However, it is worth noting that an 8% coupon might not
quite be possible due to higher hedge costs for large barrier drops.
Probability Present Value of
Present Value of
of Autocall Contingent Coupons Zero Coupon Bond
52.40%
4.15%
51.88%
10.70%
1.67%
10.46%
4.67%
1.08%
4.48%
2.80%
0.84%
2.63%
1.88%
0.69%
1.72%
11.32%
4.81%
24.41%
13.24%
95.58%
Put Price
Sum of
components
10.33%
98.50%
Summary
A number of conclusions can be drawn:

Probability assumptions are at the heart of autocall, and indeed all financial derivative, pricing.

An autocall can be broken down into three components: long a strip of contingent coupons, long a zero coupon bond of unknown duration and
short a knock-in put.

An investor is short volatility if he buys an autocall, mainly because he will be short a knock-in put whose value increases as volatility increases.

The level of implied volatility is the main driver of autocall pricing because of the impact it has on the value of the knock-in put.

Models assign small probabilities to structures autocalling in later years. Whilst one must always be careful using past data, historically the
probabilities assigned by the models have been too low due to the cyclical nature of markets that the models do not take into account.

Click here to view how a rolling autocall strategy would have worked over the last 20 years. It is a good illustration of how the cyclicality of markets
has generated very good autocall returns.
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E trades@catleylakeman.com
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