to offsetting each other. For all intents and purposes, the trader is out of the
primary risks of the position as measured by greeks when a position is
converted. Let’s look at a more detailed example.
A trader executes the following trade (for the purposes of this example,
we assume the stock pays no dividend and the trade is executed at fair
value):
Sell one 71-day 50 call at 3.50
Buy one 71-day 50 put at 1.50
Buy 100 shares at $51.54
The trader buys the stock at $51.54 and synthetically sells the stock at
$52. The synthetic price is computed as −3.50 + 1.50 − 50. Therefore, the
stock is sold synthetically at $0.46 over the actual stock price.
Exhibit 6.8 shows the analytics for the conversion.
EXHIBIT 6.8 Conversion greeks.
This position has very subtle sensitivity to the greeks. The net delta for
the spread has a very slightly negative bias. The bias is so small it is
negligible to most traders, except professionals trading very large positions.
Why does this negative delta bias exist? Mathematically, the synthetic’s
delta can be higher with American options than with their European
counterparts because of the possibility of early exercise of the put. This
anomaly becomes more tangible when we consider the unique directional
risk associated with this trade.
In this example, the stock is synthetically sold at $0.46 over the price at
which the stock is bought. If the stock declines significantly in value before
expiration, the put will, at some point, trade at parity while the call loses all
its time value. In this scenario, the value of the synthetic stock will be short
at effectively the same price as the actual stock price. For example, if the
stock declines to $35 per share then the numbers are as follows: