Using GARCH to estimate implied volatility (IV) for structured warrant

In previous article, we discussed about the trading strategy for structured warrants (Read more here).  One of the important criteria is the implied volatility (IV) estimation.  If the structured warrants issuers provide the IV number, we can use it directly in the excel spreadsheet.  That is for short term trading purpose.

If an investor decided to buy the structured warrant and exercise the option at the maturity, then the evaluation approach is different.  For such scenario, one cannot use the IV provided by the issuer because investor has to pay for higher premium if the IV is higher than market rate or statistical rate.

Consider an out of money call warrant that has more than three month’s maturity, where its underlying asset is Hang Seng Index.  The IV provided by one issuer in Malaysia is 27.0% (see Figure 1).  Whereas, the average IV of call warrant with more than 3 months maturity quoted by an issuer in Hong Kong Stock Exchange is 20.96% (see Figure 2) (link). 

Clearly, the call warrant issued by Malaysia issuer carries a premium.  It may look pricier but one has to factor in the exchange rate volatility for a call warrant with foreign underlying asset.

Figure 1

Figure 2

Question: What if there is no similar readily available call or put warrant traded in the market, how can the investor estimate the IV?

Answer: The investor can use the statistical rate to estimate the IV.  One of the popular methods to estimate volatility is the GARCH model.

The generalized autoregressive conditional heteroscedasticity (GARCH) model was developed in 1986 by Tim Bollerslev, a Danish economist (Read more here).  Unlike the conventional volatility estimation, which provided only one value for entire period of analysis; the GARCH model will factor in the most recent market movement impact into the volatility estimation.   There is a very comprehensive lecture note by MIT OpenCourseWare, those who are interested in the background of the mathematics can refer to this link.

I have developed a simple excel spreadsheet model to calculate the IV of Hang Seng Future Index.  User only needs to download the daily closing price for the Index into the spreadsheet and run the solver to get the IV.  Figure 3 is the snapshot of the GARCH excel spreadsheet.  The estimated number is 21.01%, which is very close to the IV quoted by Hong Kong stock exchange issuer, 20.97%.  Table 1 is the comparison between different IV quoted or estimated from different sources.

Figure 3

  Table 1

Method	HSI Implied Volatility	Comment
Market rate (Malaysia issuer)	27.0%	foreign exchange rate influence
Market rate (Hong Kong issuer)	20.96%	-
Statistical rate (Historical)	19.96%	-
Statistical rate (GARCH)	21.01%	-

In order to provide an apple to apple comparison, let’s consider another example that excludes the impact of foreign exchange rate.  Figure 4 is the IV published by a Malaysia issuer.  The IV is 17.5%.  Figure 5 is the KLCI annualized volatility chart estimated by GARCH model, published by the New York University Stern School of Business (link).  Figure 6 is the KLCI GARCH model using my excel spreadsheet.

 

For meticulous readers, I would like to highlight that the 8.56% in Figure 5 is the predicted volatility for the next day (12 August 2016).  Which means, the volatility estimated using GARCH model on 11 August 2016 is 8.56% - 0.40% = 8.16%.  As this is the annualized number, which means that the assumption of total trading days per year is important.  In US market, it is generally assumed that the average trading days per year is 250.  Thus, putting 250 in the excel spreadsheet will obtain the same results as the number published by NYU Stern.  In fact, the total trading days per year for Bursa Malaysia is around 246 days according to the Bursa Malaysia Annual Report (link).  The volatility for KLCI will be slightly lower at 8.09%.  Table 2 is the comparison of various volatility estimations by different methods.

Figure 4

Figure 5

Figure 6

Table 2

	Method	Trading days assumption	KLCI Volatility
Malaysia Issuer	?	?	17.5%
NYU Stern	GARCH	250	8.16%
My Spreadsheet	GARCH	250	8.16%
My Spreadsheet	GARCH	246	8.09%

Again, it is very obvious that the IV published by the Malaysia warrant issuer is very high compare to the volatility estimated by GARCH model, this time is without the influence of foreign exchange.  There is no right or wrong as the name of the IV suggested – “Implied” is the key word.  It is simply the expectation of the issuer to quote any number that the issuer think is appropriate.  However, for retail investors, using GARCH model is a very convenient way to evaluate the price of the structured warrant.

Simple rule – Higher IV means “expensive”!

Disclaimer:  The mathematical calculations in this article do not imply any buy or sell recommendation.   The author disclaims all liabilities arising from any use of the information contained in this article.