or
With American options, a put this far in-the-money with less than 71 days
until expiry will be all intrinsic value. Interest, in this case, will not factor
into the put’s value, because the put can be exercised. By exercising the put,
both the long stock leg and the long put leg can be closed for even money,
leaving only the theoretically worthless call. The stock-synthetic spread is
sold at 0.46 and essentially bought at zero when the put is exercised. If the
put is exercised before expiration, the profit potential is 0.46 minus the
interest calculated between the trade date and the day the put is exercised.
If, however, the conversion is held until expiration, the $0.46 is negated by
the $0.486 of interest incurred from holding long stock over the entire 71-
day period, hence the trader’s desire to see the stock decline before
expiration, and thus the negative bias toward delta.
This is, incidentally, why the synthetic price (0.46 over the stock price)
does not exactly equal the calculated value of the interest (0.486). The
trader can exercise the put early if the stock declines and capitalize on the
disparity between the interest calculated when the conversion was traded
and the actual interest calculation given the shorter time frame. The model
values the synthetic at a little less than the interest value would indicate—in
this case $0.46 instead of $0.486.
The gamma of this trade is fairly negligible. The theta is slightly positive.
Rho is the figure that deserves the most attention. Rho is the change in an
option’s price given a change in the interest rate.
The −0.090 rho of the conversion indicates that if the interest rate rises
one percentage point, the position as a whole loses $0.09. Why? The
financing of the position gets more expensive as the interest rate rises. The
trader would have to pay more in interest to carry the long stock. In this
example, if interest rises by one percentage point, the synthetic stock, which
had an effective short price of $0.46 over the price of the long stock before
the interest rate increase, will be $0.55 over the price of the long stock
afterward. If, however, the interest rate declines by one percentage point,
the trader profits $0.09, as the synthetic is repriced by the market to $0.37
over the stock price. The lower the interest rate, the less expensive it is to