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- Hedging DIP

# Hedging DIP

Many structured products use DIPS to generate extra funding that is used to enhance yield or participation.

- non-bearish view --> one would not expect the put to KI and will just receive high coupon/participation.

- capital at risk --> investor can lose money invested if put is knocked in and ITM at maturity.

The trader on the sell-side is usually long the DIP (embedded in the structured products sold).

In the following, we therefore assume the trader has a long position in the DIP.

Long DIP --> short Forward

- short IR

- long dividends

- long borrowing costs

A lower forward price increases DIP price because it increases:

- the potential payoff
- the probability of KI

The trader has to buy stocks to be delta neutral.

There are 2 main risks to consider when trading DIPs:

- Near the barrier, the delta can jump (high gamma) and gamma changes sign
- Volatility/skew exposure

*Monitoring the Barrier*

Traders, long the DIP, have to hedge the risks associated with this position accordingly.

The risks of a barrier option near the barrier can be difficult to manage.

Example: ATM Put with KI Barrier @ 60%.

**Near the barrier, the delta can jump (high gamma) and gamma changes sign**

When S breaches the barrier level, the DIP goes from not being an option to being a put option 40% ITM.

A small move in S --> large impact on the DIP price --> HIGH DELTA.

When S approaches the barrier, | delta | becomes extremely large and typically becomes greater than 1.

Since | delta | of a regular option is always < 1 --> trader would inevitably accumulate too many shares that would need to be sold when barrier is breached.

A small move in S will change the value of delta significantly --> HIGH GAMMA.

A long DIP position goes from being long gamma (delta increases when S decreases and gets closer to barrier) to short gamma as the share price approaches the barrier (delta decreases when barrier breached).

The initial price of the DIP assumes that these excess shares can be sold exactly at the barrier level.

However, in practice, this proves to be extremely difficult as:

- the share price is already going down for the barrier to be breached in the first place.

- the fact that the trader needs to sell a large quantity of shares will push the price down even further.

Therefore, the trader almost certainly sells these excess shares below the barrier level and as a result incurs a loss on the sale of the excess shares.

To avoid this loss, the trader should give himself a cushion to sell any excess shares over the barrier.

One method to smooth out the risks and make them manageable is to apply a barrier shift.

The trader, long the DIP, is long the barrier since higher barrier increase DIP price.

Example: If he wants to bid an ATM put with KI @ 60%, he can price an ATM put with KI @ 58% --> apply a 2% barrier shift to make option cheaper.

*Factors influencing the magnitude of the barrier shift *

*Transaction size / Underlying's liquidity*

The larger the size --> the more shares have to be sold over the barrier --> the more likely the share price will move against the trader, especilly if low liquidity.

The larger the size & the lower the liquidity --> the larger the barrier shift.

*Discontinuity = Size of digital*

The larger the difference between the strike and the barrier --> the larger the barrier shift.

*Underlying's volatility*

The larger the vol --> the larger the risk to the trader of the stock approaching the barrier --> larger barrier shift to protect against a larger move.

*Time to maturity*

The closer to maturity --> the larger the | delta | just before the barrier --> the larger the change in delta over the barrier --> the larger the barrier shift.

*Non-constant barrier shift *

If one were to simulate paths and monitor the points in time at which the barrier was breached, the KI events occur more frequently down the line.

--> One can thus apply a barrier shift that is not constant but is in fact an increasing function of time.

*Example:*

An investor wants to sell an american ATM call with KI @ 60%.

3 IBs are competing for this trade and will all take the same CC and apply the same pricing parameters (volatility, skew, etc…).

They all want to apply a shift of 2% but they have differents way of shifting the barrier.

- Trader 1: very conservative -->
**constant**barrier shift of 2%. - Trader 2: less conservative -->
**linear**barrier shift: the shift grows linearly from zero at inception to 2% at maturity. - Trader 3:
**curvy**barrier in time, which is computed from evaluating KI scenarios.

GRAPH.

**Volatility / Skew exposure**

*Volatility*

Trader = long DIP --> long volatility.

Volatility increases:

- the potential payoff of the put

- the probability of KI

This long Vega position can be hedged, at least partially, by selling vanilla put options with strikes between the barrier and the spot.

*Skew*

Trader = long DIP --> long skew.

Higher skew --> higher downside vol vs ATM vol --> higher probability of crossing the (down) barrier.

From the model point of view, and in order to capture the skew effects, we will need to calibrate a model to the implied volatilities of options on the underlying, across strikes, with specific attention to the downside skew.

If the barrier is monitored continuously we will need to apply a model that gives a smooth calibration through all ends of the surface between short maturities and up to the maturity. This means that one must calibrate to both skew and term structure. The reason is that a continuously monitored barrier option can be triggered at any time up to maturity, and therefore has vega sensitivity through the different time-buckets. European options with different maturities must now be calibrated so that the model shows risk against them.

The vega sensitivity will change as the underlying moves: if a barrier event is close to happening, i.e. the underlying is trading close to the barrier, then the short-term vega will increase and sensitivity to the long-term volatility will decrease.

If the barrier is only monitored at maturity, then getting the skew corresponding to that maturity correct is the primary concern and we would use the exact date-fitting model.

**Dispersion effects on WO DIPs**

The KI event can be triggered by any one of the assets.

If knocked in --> payoff at maturity = put option on the worst performing asset in the basket, irrespective of which element triggered the knock-in.

A WO DIP is more expensive than a DIP with the same characteristics since the potential payoff is much higher.

This makes it more effective when used in the context of yield enhancement or for generating income for a higher upside participation, but this obviously involves the investor bearing additional risk.

We must now account for **dispersion**.

Trader = long DIP --> long volatility and skew on each asset and short correlation (long dispersion) between them.

The individual vegas can be hedged by selling OTM puts on the various underlyings,with strikes between the barrier and the spot.

This can lead to additional transaction costs.

Depending on the individual volatilities, the vegas to each of the underlyings can be different.

The DIP price will be more sensitive to the more volatile stocks, owing to the increased probability that they end up as the WO.

Therefore, the vanilla puts used in the volatility hedges will be of different notionals.

The choice of model breaks down to the same case as the single asset DIP. Also, because this is a multi-asset option we will need to do this for each underlying, and run the simulations based on a correlation matrix and taking into account that the seller of this derivative is short correlation. Correlation skew risk may be exhibited by the option, especially if the barrier is far from the spot.