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Delta Hedging

To show how Delta Hedging can be done with MesoSim, let’s consider a structure consisting of two legs (separate option contracts):

  • 1 Call Option:
    sold at around 160 DTE with the Strike closest to 10 delta. This leg will be referred to as short_call.
  • 1 Put Option:
    sold at the same expiration as the call with the Strike selected to bring the whole structure (Short Call and Short Put together) closest to 0 delta. Practically that delta will also be around 10, but we’ve chosen to do this calculation dynamically. This leg will be referred to as short_put.
    "Structure": {
        "Name": "ShortStrangle",
        "Expirations": [
           {
             "Name": "160dte",
             "DTE": "160",
             "Min": 140,
             "Max": 190
           }
        ],
        "Legs": [
           {
             "Name": "short_call",
             "Qty": "-1",
             "ExpirationName": "160dte",
             "StrikeSelector": {
              "Min": 5,
               "Max": 15,
               "Delta": "10"
             },
             "OptionType": "Call"
           },
           {
             "Name": "short_put",
             "Qty": "-1",
             "ExpirationName": "160dte",
             "StrikeSelector": {
              "Min": 5,
               "Max": 15,
               "Delta": "leg_short_call_delta * -1"
             },
             "OptionType": "Put"
           }
        ]
      }

The delta selector for the short_put leg uses the previously defined short_call leg’s delta.

The resulting structure’s overall delta will be around 0.

The above approach is easy to understand and works, but there is a better, more scalable way of doing it.

To illustrate, let’s consider a three-legged structure, a Broken Wing Butterfly:

"Legs": [
   {
     "Name": "upper_long",
     "Qty": "1",
     "ExpirationName": "160dte",
     "StrikeSelector": {
       "Delta": "40"
     },
     "OptionType": "Put"
   },
   {
     "Name": "short",
     "Qty": "-2",
     "ExpirationName": "160dte",
     "StrikeSelector": {
       "Delta": "30"
     },
     "OptionType": "Put"
   },
   {
     "Name": "lower_long",
     "Qty": "1",
     "ExpirationName": "160dte",
     "StrikeSelector": {
       "Delta": "pos_delta"
     },
     "OptionType": "Put"
   }]

In the above example, the last leg’s (lower_long) delta is specified using a statement that is calculated based on the overall position delta so far.

At the time of the statement evaluation, two legs are already considered, and pos_delta represents their sum:

pos_delta = [ leg_upper_long_delta ] + [ leg_short_delta ]
= [1 x (-40)] + [-2 x (-30)]
= -40 + 60
= 20

If we take this delta value (which should be around: (2*30)-40=20) and choose the last (lower_long) leg using this delta value then we will end up at a delta neutral position at initiation:

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