The payoff initially presented is the most basic one. 

To increase the value of the coupons, a common practice is to consider a basket of underlying and to condition the recall on the spot of the worst performer at each recalling date. This extends the dimension of the problem and can require the integration of other sources of risk such as the equity correlation skew. 

Moreover, if the stocks are not in the same economy, the number of rate factors also increases and quanto drift terms lead to more complex equations. 


Adding the Put Feature 


If the investor believes that the underlying index will not be lower than a specific level at maturity, she can add a put feature to the autocallable structure to increase the potential coupon received. This means that the capital is no longer protected as the holder is short a put option at maturity T.


The put option can be a vanilla ATM European put option whose maturity is the maturity of the autocall. But most of the time, the buyer is short a DIP ATM put option that can be either European or American style.


When a trader sells an autocall with a put feature at maturity, he is short the autocallable digitals and long a path-dependent put option. In order to price this structured product, one should price the autocallable digitals as described above and deduct the price of the path-dependent put option.


Summary Risk Analysis of the DIP: 

- higher forward --> lower DIP price 

- higher volatility --> higher DIP price

- higher skew --> higher DIP price


The trader selling the autocall will be short the forward but his overall position in volatility and skew are not immediately clear owing to potentially offsetting effects from the 2 components. 


The trader selling an autocall is always long volatility with respect to his long put position but can be long/short volatility with respect to the autocallable digitals. 

The trader selling an autocall is always long skew with respect to his long put position but has a short position with respect to his short position in digitals. 


If the forward price is higher than the coupon level, then volatility decreases the price of the autocallable digitals. A trader selling an autocallable is then usually long volatility with respect to the digitals, and always long volatility with respect to the put.


Worst-of Autocallables

The payoff is exactly the same except that we observed the performance on the worst performing share of the basket.


Risk Analysis: 

The holder of a WO Autocall is long correlation as it increases the probability of receiving the coupons and being autocalled and decreases the probability of being into the DIP. 






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