Parity has three moving parts: the stock, the call and the put. Fix any two and the third is determined, which means any one of them can be built out of the other two. Positions built that way are called synthetics, and professional traders think in them constantly, because the cheapest way to get a payoff is rarely the obvious one.
Synthetic stock
The last lesson showed that a long call plus a short put at the same strike and expiration behaves exactly like owning the stock at that strike on expiration day. That package is synthetic long stock. Stock at $150, the $150 call at $6.00, the $150 put at $5.00: buy the call, sell the put, and you pay $1.00 net. At expiration you own stock at $150, so your all-in cost is $151, which is the forward. You did not tie up $150 of cash, and the $1.00 you paid is the carry someone else charged you for that.
Long the $100 call and short the $100 put, 30 days out. Both lines are straight with a slope of one, exactly like 100 shares, and the breakeven sits just above $100, at the 30-day forward. Drag the rate and the breakeven moves with the carry.
Check it with delta. Say the $150 call has a delta of 0.55 and the $150 put has a delta of -0.45. Long call plus short put gives 0.55 - (-0.45) = 1.00. The package moves dollar for dollar with the stock, exactly like 100 shares.
Long the $100 call plus short the $100 put, 30 days out. Delta is a flat 1.00 at every stock price, gamma and vega are zero, and theta is about a penny a day per share, the interest on the strike. Switch between Greeks, then drag volatility: none of the lines move.
Why do the other Greeks vanish? A call and a put at the same strike and expiration share the same gamma and the same vega. Buy one, sell the other, and those cancel exactly, leaving a delta of one with no curvature, which is what a share of stock is. The small theta that remains is not time decay in the usual sense. It is the interest on the strike you have not paid yet, building day by day: the synthetic's version of carry.
The full set
| You want | Build it with |
|---|---|
| Long stock | Long call + short put |
| Short stock | Short call + long put |
| Long call | Long stock + long put |
| Short call | Short stock + short put |
| Long put | Short stock + long call |
| Short put | Long stock + short call |
Every row uses the same strike and expiration on both options. The last row is the one most retail traders meet first without realizing it: a covered call, long stock plus a short call, has exactly the payoff of a short put. Same maximum profit, same downside, same delta.
Long 100 shares at $100 and short the $105 call, 45 days out. At expiry the line is flat above $105 and falls one for one below it, the payoff of a short $105 put. Drag days down to watch the curve settle into that shape.
A covered call writer and a put seller at the same strike hold the same risk. The only difference is the cash: the covered call has paid for the stock, the short put has the strike sitting on deposit. That is the carry again, and parity prices it.
Why market makers think this way
When a market maker sells you a call, they are not going to buy the same call back from someone else; there may be nobody offering it. Instead they buy stock and buy the put at that strike, which is a synthetic long call, and they are flat. Or they hedge with stock alone and carry the put risk for a while. Every option on the chain is three things at once, and the desk sources whichever version is cheapest that minute. That constant conversion between the three is what keeps the call and put at a strike on the same implied volatility, and it is why a spread that looks expensive in calls is usually the same price in puts.
For you the payoff is simpler. When you see a price you like in one form, check it in the other. A put spread and a call spread at the same strikes are the same trade, and one side often has a tighter market.
The maths: rearranging parity
Start from C - P = S e^(-qT) - K e^(-rT). Each synthetic is one rearrangement. C = P + S e^(-qT) - K e^(-rT) is a long put plus stock, part paid for by borrowing the present value of the strike. P = C - S e^(-qT) + K e^(-rT) is a long call plus short stock plus cash on deposit. That cash term is why the table in the text matches payoffs exactly and prices only up to carry. Take the change in each side for a $1 move in S and the same equation gives the deltas: Δcall - Δput = e^(-qT), which is 1.00 with no dividend.
Worked example: S = K = $150, 60 days (T = 0.1644), r = 4%, no dividend. K e^(-rT) = 150 × e^(-0.00658) = $149.02, so the call should be worth $0.98 more than the put. If the $150 call is $7.00, parity puts the $150 put near $6.02, and synthetic long stock costs $0.98 today for a purchase at $150 in 60 days.
Your turn
Open MSFT on the next monthly expiration. Price the at-the-money synthetic long stock from the call and put mids, then compare it with the quote bar.