In the previous post we had sold 100 ATM call options on Tesla and hedged the delta exposure by purchasing 56 shares.  Using a simple example, we illustrated that the position was immune from small changes in the underlying price.  But what are the residual exposures?

Here is a neat trick.  Suppose I were to take 56 of the short call options and ‘match’ them to the long delta hedge position of 56 shares.  We can use the principles of put call parity which state:

Buy a call (+C) & sell a put (-P) = Long position in the underlying asset (+F)

So rearranging

+F – C = -P

This means that combining some of the calls with the entire delta hedge results in a ‘synthetic’ short put position of 56 options.  If we take the residual balance of 44 short call options, we will end up with a short straddle position – admittedly a little ‘lop-sided’ as the number of options differs between calls and puts.  This is shown in the attached diagram. 

This trade is referred to as a ‘short volatility’ trade but as we will see in the next post, it depends on what you mean by volatility……