*This article appeared in Capital page of The Edge Malaysia, Aug 15-21, 2010*

In the last two parts of this series, I explained how Callable Bull and Bear Certificates (CBBCs) evolved from barrier options and its key features with some examples. This final article will discuss important pricing and risk factors that investors must know when trading CBBCs.

**Pricing of the CBBC**

From the previous article, we found that the theoretical price of CBBCs seems to just comprise its intrinsic value and funding costs. Investors ought to note that this theoretical price is only applicable when the product is called or settled at expiry. As the CBBC floats in the market, the trading price quoted by market makers is not necessarily its theoretical price, but more likely a price backed by a model.

As there is no information put forth by Bursa or CIMB (currently the single issuer of CBBCs in Malaysia), my thoughts are based on experiences in other countries, mainly Hong Kong and Europe.

Issuers world-wide mostly use some variant of the Black Scholes model to price CBBCs. We were briefly introduced to the Black Scholes model in my previous article, “Pricing and Risks of Structured Warrants ”,

*Nov 16-22, 2009*. This model has become the market standard to price options since 1970s. The basic model to price standard options can be modified in many ways to accommodate the pricing of exotic options, one of which is the CBBC.Ø

*The replication method*

Here, we construct a portfolio of plain vanilla options (meaning standard options) to represent the CBBC. Very briefly, if we need to value a callable bear (essentially a down-and-out put option) with strike price ‘X’ and call price (barrier) B, we can construct a portfolio with a long position (buy) of an ordinary put option with strike X and a short position (sell) of some ordinary put positions with strike ‘B’ along the tenor of the option. The calls and puts are constructed in such a way so that the portfolio’s payout value is (X-B) at the points where the callable bear knocks-out.

Ø Closed form solution (basically an equation with a definite answer)

In 2005, J. Eriksson derived the closed form solution for “turbo warrants” (the famous name for CBBCs in many countries). The solution is based on the two main possible outcomes for the CBBC’s payoff:

a) The stock price hits the barrier before expiration and is extinguished.

b) The underlying stock price does not hit the barrier. In this case, the callable bear has the same value as an ordinary put option.

The above are displayed in

**Chart 1**.**Chart 1: Random walk for a down and out call. Walk (a) results in a knock out; walk (b) does not. [B=barrier; E=strike]**

**Key model parameters that affects the CBBC’s price**

Like structured warrants, investor must appreciate the key parameters of the model that affects the CBBC’s price:

- Underlying share price movement

As the CBBC’s intrinsic value is the major component of the CBBC’s price, the underlying share price movement is major driver of the CBBC price.

- Funding cost

Finance cost can be considered as interest paid by investors to issuers for borrowing money for investment. Therefore the longer the investment period (i.e. the maturity of the CBBC), the higher the interest and CBBC price.

- But not...underlying asset volatility?

In the last article, we learnt that the price of a CBBC is expected to move in tandem with the underlying share, thus making it less volatile (except when the share is closing close to its barrier). A very important finding by Eriksson was that with the Black Scholes model, the CBBC is less sensitive to the change in volatility when compared to vanilla options. This is how the product became popular and marketable for investors. The CBBC is cheaper than standard warrants, yet less volatile.

**Problems with Black Sholes model in pricing CBBCS**- The constant volatility assumption

In 2006, the Chinese University of Hong Kong was of the view that CBBCs only seemed less sensitive to underlying share volatility due to the Black-Scholes dynamics where volatility is constant. In the real world, volatility or uncertainty in the market is never constant over time.

In 2006, Hoi Ying Wong and Chun Man Chan, in their paper “Turbo Warrants under Stochastic Volatility”, studied these callable bulls and bears using stochastic (i.e. inconstant or random) volatility models which used volatility that changes over time. They found that CBBCs can be very sensitive to volatility in the underlying shares.

Investors must note then, that the statement “CBBC is not sensitive to underlying share volatility” is actually model-dependent.

- The assumption that share prices move with no “jumps”

The Black Scholes model also assumes that the underlying asset only moves in small continuous random movements called the “Brownian motion”. However, in reality, share prices do jump considerably especially in volatile periods. In another paper in 2006, “Analytical Valuation of TurboWarrants under Double Exponential Jump Diffusion” Hoi Ying Wong and Ka Yung Lau found that the “turbo warrants” are less sensitive to the jump parameters than vanilla options, but the sensitivity cannot be ignored. They conclude that jump risk in asset price materially affects the value of a turbo warrant.

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**Message for the investor**Investors need to beware that the apparent “price transparency” hinges on the above key assumptions of the Black Scholes model which is not true at all times. These unrealistic assumptions can lead to a greater risk of knock-out than allowed for in the Black–Scholes price.

In actual fact, it is the behaviour of traders and investors that causes the shares to have stochastic volatility and jumps. This behaviour directly affects the supply and demand of CBBCs, which causes the price of CBBCs to move away from their theoretical pricing and the Black Scholes model.

BNP Paribas

*(http://www.bnpwarrant.com/home/cbbc_tutorial/cbbc_tutorial_e3.html)*recommends a guide to manage this problem. In general, investors can measure market demand and supply by observing the outstanding quantity of the CBBC. Outstanding quantity refers to the amount of CBBC that investors hold overnight. The larger the outstanding quantity, the more the CBBC will be affected by market force. In general, when the outstanding quantity exceeds 50%, the CBBC price will be relatively more prone to be affected by market forces and deviate from theoretical price.**Risk of the CBBC**

Risks in trading CBBCs is explained in Bursa’s and other stock exchanges’ websites. Some of the most crucial risk is discussed below:

**Trading CBBC close to barrier**

Trading the CBBC close to the barrier can be very unsettling for the investor. In general, the larger the buffer between the call price and the spot price of the underlying assets, the lower the probability of the CBBC being called. However, the larger the buffer, the lower the leverage effect (or the conversion ratio).

**Liquidity**Liquidity is said to be one of the major factors influencing CBBC price. Since the delta of CBBCs are close to 1, issuers apparently tend to hedge their exposures by buying / selling the underlying shares with a 1:1 ratio (after considering the conversion ratio), thereby creating a huge demand for the underlying shares. If there is insufficient liquidity in the underlying shares, the hedging cost and finance cost for issuers will increase dramatically, resulting in a wider bid/ask spread of CBBC.

Although CBBCs have liquidity providers, there is no guarantee that investors will be able to buy/sell the CBBCs at their target prices any time they wish. The Bursa warns that although market makers are committed to providing liquidity, there will be circumstances where market makers are exempt from their obligations and these are stated in the issuer’s prospectus.

However, as more issuers come into the Malaysian market, investors can compare Issuers’ ethic, i.e. whether issuers will quote the CBBC price and bid/ask spread and provide sufficient liquidity in a reasonable manner under different circumstances of underlying share price movement and liquidity.

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**Volatilty of the underlying share**While investors of structured warrants prefer high volatility stocks because it increases the probability of the warrants being in-the-money, this is not the case for CBBCs. High volatility of underlying shares increases the probability of the share price touching the barrier and triggering a Mandatory Call Event. Therefore, investors should be watchful when trading CBBCs in a high volatility environment.

**Conclusion**

It is quite obvious now that although the CBBC appears to be cheaper and more transparent than normal warrants, they are in fact, rather complex. Investors may see their investment suddenly lost if the product is terminated upon the call event. The investor will also be tempted to use the CBBC as an alternative to buying the underlying share since the CBBC is claimed to closely track the underlying share. However he should not take this assertion for granted due to the pricing peculiarities around the CBBC. As all free lunches, there is always a price to be paid.

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